It's all @Paul B's fault... my journey to an immune reef (hopefully!)

[atoll]

First beautiful tank[emoji1531]
When was the last time you took sand and water from the ocean and put in your tank ? And how often are you doing it ?
Just skim the thread will read it when I get in to see how it’s like Paul’s. But I’m not talking about feeding as I feed basically the same way as you know.
It’s my daughter pic day at dance so I’m trying my best to follow.

Thanks,
Now that's not what you stated above and it was a wrong statement to make so I had to correct you.

Now you ask about sand and water from the ocean. I live hundreds of miles from the Ocean so it is not feasible but I would use water from the ocean if I could. Paul and I run and maintain our tanks to suit the animals we keep, we both also add parasites and various bacteria as well as what I have already informed you of in my post above. With regards nutrients, I know a guy with the most beautiful of SPS tanks here in the UK who has sky high NO3 and PO4 and grows SPS like weeds and he is not alone.

 

[Greenstreet.1]

Thanks,
Now that's not what you stated above and it was a wrong statement to make so I had to correct you.

Now you ask about sand and water from the ocean. I live hundreds of miles from the Ocean so it is not feasible but I would use water from the ocean if I could. Paul and I run and maintain our tanks to suit the animals we keep, we both also add parasites and various bacteria as well as what I have already informed you of in my post above. With regards nutrients, I know a guy with the most beautiful of SPS tanks here in the UK who has sky high NO3 and PO4 and grows SPS like weeds and he is not alone.

Then sorry to say but your tank is not like Paul’s it can not be just because you feed the same or run some of the same Eq if that’s the case then my tank is like Paul’s I got my worms from him and most of my feeding ideas.
Also you need to be putting water sand and other things from the ocean like he do into your tank to say your tank is like his I don’t even see a small beer can in your tank([emoji23][emoji33]I had to put that in there)

What statement did you correct me on ?
Is it because I said you have a beautiful tank with sps ?

Forget one thing you keep telling me about people with high po4 & no3 but you are not one of them ?

 

[Paul B]

You have a more controlled system than Paul just look at your nutrients his is off the charts yours is low that’s why you can keep sticks.

That is certainly true. For the first 40 years my tanks nitrates were around 10. Then I got busy with other things and now are so far off the chart, I can't even find the chart any more. For some reason the gorgonians, sponges, duncans and a few SPS like Montipora and a few others which I don't know their names are growing like crazy. They will probably croak when I lower my nitrates to around zero in a few weeks.
My tank actually looks pretty full now, I like it.

Paul and Atoll - the way to prove your tanks are 'immune' is to document that the living parasites are currently in the tank

I don't know how to do that except the many times I posted, with pictures fish I got for free or almost free that were full of parasites. That copperband I spoke about was in a tank where almost all of them died from parsites so I got it very cheap and cured in in a couple of days and put it in my tank. The 3 shrimpfish I also posted were full of parasites but I can't take pictures of parasites so I am not sure how to document it.

Of course if a tank is almost 50 years old and sea water along with mud, snails, crabs, fish, seaweed are added from the sea all summer and any fish that are bought go right in. I only buy fish if something dies of old age after I document it or a fish jumps out or I give it away. For people who say you need to leave the tank fallow for 72 days they, I am sure know i have a load of parasites in there. If not, where would they go?

Doesn't seem "That" bad for nitrates of 160

 

[atoll]

Then sorry to say but your tank is not like Paul’s it can not be just because you feed the same or run some of the same Eq if that’s the case then my tank is like Paul’s I got my worms from him and most of my feeding ideas.
Also you need to be putting water sand and other things from the ocean like he do into your tank to say your tank is like his I don’t even see a small beer can in your tank([emoji23][emoji33]I had to put that in there)

What statement did you correct me on ?
Is it because I said you have a beautiful tank with sps ?

Forget one thing you keep telling me about people with high po4 & no3 but you are not one of them ?

This Quote "the only thing you and Paul do the same is the fish your tank" Far from true as I pointed out in my reply, I pointed out many things we do the same.
Would you agree no 2 tanks are the same? Most people would. Of course, there are differences I never suggested there wasn't. I also don't keep the same fish as Paul so my tank is not the same as his but what I am saying is we share many of the same philosophies along with other things we do as stated.

 

[MnFish1]

I'm pretty sure most of us here aren't biology majors, so no, I'm not in a minority. The scientific articles are a good starting point, yes. But you hold to them like they're your bible. Take cars for example, they may look good on paper, but that doesn't mean they will perform well on the road (Not talking about mechanical issues). The very nature of a "system" in general is that the whole is greater than the sum of the parts. Isolating a small portion of the entire system in a lab tells fractions of the whole story. I honestly don't get how you can argue with people who have done exactly what you are claiming can't be done. Must be that selective memory of mine.

1, What am I claiming 'can't be done'? Obviously Paul has his tank, Atoll has his tank, others (listed in the master aquarist articles I posted) have their tanks)? The Only think I have said 'can't be done' is when Paul states he can guarantee that in 40+ years that no fish has died of an infections disease. I also don't believe his theory that adding random bacteria in 'live or frozen live foods or mud' is any better than feeding a good quality broad based diet and maintaining proper parameters in a tank. If that is such a horrible statement - I apologize lol

2. Of course, I haven't taken a poll, but ,most of the articles written by the admins and other people on this site and which have formed the basis for much of the 'new methods in reef keeping' are based on scientific articles. Just check out the 'reef chemistry forum'. Most of those discussions are not based on non-scientific methods.
The real problem is that there aren't many studies done on 'tanks' because each tank is 'different'. I guarantee you, though, that people that are attempting to breed marine fish are not using natural methods that you are talking about - nor are zoos and other public aquaria. This by it self seems to imply to my small brain that contrary to some - much of this is voodoo/mythology as compared to necessary to success. That said, I have no problem with someone doing anything they want to their tank.

 

[MnFish1]

I don't know how to do that except the many times I posted, with pictures fish I got for free or almost free that were full of parasites. That copperband I spoke about was in a tank where almost all of them died from parsites so I got it very cheap and cured in in a couple of days and put it in my tank. The 3 shrimpfish I also posted were full of parasites but I can't take pictures of parasites so I am not sure how to document it.

Of course if a tank is almost 50 years old and sea water along with mud, snails, crabs, fish, seaweed are added from the sea all summer and any fish that are bought go right in. I only buy fish if something dies of old age after I document it or a fish jumps out or I give it away. For people who say you need to leave the tank fallow for 72 days they, I am sure know i have a load of parasites in there. If not, where would they go?

Doesn't seem "That" bad for nitrates of 160

Well - here is my heretical theory. Fish with partial immunity to ich.velvet,whatever, are more likely to survive. If they do - they may remain as partial carriers - or if the person is using a sterilization method (hi strength UV/Ozone, etc) gradually, the levels of ich die off over long periods of time, unless there are new fish introduced which further boosts the level of parasites in teh tank and again leads to further infection.

If one reads the studies at least on cryptocaryon, they state that immunity STARTS to be lost at 6 months - not that it is 'gone' at 6 months. My guess that at some level immune memory for these parasites - even if not measurable by current techniques - exists.

Also - again - from reading - many fish survive cryptocaryon especially when adults and especially when the bioload of free-swimming parasites in the water is low. My guess (key word) is that the sterilization methods you are using function the same as having low dose copper in the water.

And I also agree with you - your tank looks great for nitrates of 160. I also agree with you that if you decided to add new items that were not used to that level those items would have problems. The good news is that there is little suggestion that lowering nitrates suddenly has a negative effect on tank inhabitants (I guess unless you lower it to 0).

 

[Greenstreet.1]

This Quote "the only thing you and Paul do the same is the fish your tank" Far from true as I pointed out in my reply, I pointed out many things we do the same.
Would you agree no 2 tanks are the same? Most people would. Of course, there are differences I never suggested there wasn't. I also don't keep the same fish as Paul so my tank is not the same as his but what I am saying is we share many of the same philosophies along with other things we do as stated.

It’s not about what you keep it’s how you keep it. And Paul keeps his tank different from you at least the important parts like water and sand and other things from the ocean you do not so right there you are not doing the same

 

[Paul B]

I have a different theory. The feeding of high quality, high protein, varied diet with proper vitamins, etc (even without bacteria) in a low stress environment would produce the same results - including spawning, etc.

I do not really give my fish much of a varied diet, I give them what they need. Fish in the sea (where I got most of my education, not sitting in an air conditioned classroom listening to some guy with degrees who doesn't keep fish,) they eat almost the same thing every day. Most fish eat fish, as Burger Kings require you to wear shoes so fish don't eat there. I give my fish whole things to eat like clams, mysis or worms. I also don't give my fish vitamins or Selcon. My parameters are most likely the worst on here and I have no algae, isn't that special. But the guy who said nutrients cause algae is (as was said above, or below) an Idiot. If nutrients caused algae I could open up a produce stand from my tank.

But if I had no pathogens living in my tank including ich and velvet I wouldn't have such old fish, and yes there has never been a fish in my tank die from a "communicable" disease in maybe 40 years. It could be 35 but whose counting. I have had fish die from pop eye, tumors, swim bladder problems, broken bones, broken hearts etc, but no ich, velvet or bacteria. No one has to believe that, but my fish do.
Remember, to me, you are all Noobs and none of this, including this conversation is new to me.

Before that time, my tank, like all tanks were ich magnets and I had to keep copper pennies in there continousely. But I already posted that here and in my book. But ich or velvet, Not once that I can remember, unless as I said, I got a fish like that on purpose and it croaked as I figured it would. But those fish i consider good as they help the rest of my fish stay immune.

I have an idea. Lets get a bunch of ich or velvet infected fish and put some in my tank, Atolls tank, Mn's tank and a few other people's tank who quarantine just for fun. What do you think will happen?
Yesm Mn I know you said you don't quarantine, but you do keep pathogens and Lady GaGa away from your fish.

With all due respect, your "expert" is an idiot.

HaHa, I love that as it is something I have said many times. Just because someone has more degrees than a thermometer, doesn't mean he can keep fish. I have a cousin who is a marine Biology Professor and knows the name of every name (probably their social security number also,) but knows nothing about keeping fish. He has never even kept a goldfish and SCUBA dove for 30 minutes. To me, book learning is not good at all by itself, it's like trying to learn how to drive a car by reading a book.

I have no degrees and never went to college, we had that Draft thing. But I read everything and did very well in my life. I am an inventor with two patents, wrote a book (OK not the bible, or War and Peace, but a book none the less) along with dozens of articles many of which were well before the internet. I also have art work in 4 galleries in Manhattan. That was all after I was a Sargent in the Army in Nam and a General Foreman running 200 men in NYC. Not bad for a high school graduate.

I got my fish education, not from a book because there were very few salt water books when Noah was alive, but from Diving. This hobby is full of ridiculous theories and practices and in regard to diseases we are almost exactly where we were when I was putting pennies in my tank for parasites. Me and a few others progressed to where we can keep fish healthy forever instead of messing with their immune system then tweeking their medication then coming up with some stupid excuse as to why that fish died and blaming the store or wholesaler. They didn't kill the fish, you did by not giving it a natural place to live and forbiding it to use it's natural God given immune system to do what it gets paid for.

Paul is going to say here...
Something sarcastic about the hobby not being enjoyable

He never says something like that. But this discussion reminds me of a story. Remember Jesus. No, this is not going to be a religious thing. But if I lived then and I was Jesus friend I would have said to him:
Hey Jeez, I realize you know the future and can do cool things like walk on water, cure those sick Dudes, raise orange spotted filefish and come up with cool things to say. But being you can do anything wouldn't it be a good Idea to invent a cell phone first so you can take some selfies of this stuff so we all don't have to argue about it in the future. Like really!

It's like this thread, I say I keep fish 40 years and they don't croak of ich. Mn will say, i don't believe that so you must be senile, then Dom will say something about a pitchfork and I have no idea what that is about, But Atol, with the beautiful tank will say him and me do the same thing almost but I think we even look alike but he speaks like Ringo.

We can go around in circles as we have been doing in this thread but the main thing to remember is, Atoll and myself don't care who believes us. We have some of the oldest fish and never have to post on a disease forum, that is our scientific accomplishment. If you can find a scientist who knows how to keep fish immune bring him over. He may not even be an idiot.

 

[Paul B]

If one reads the studies at least on cryptocaryon, they state that immunity STARTS to be lost at 6 months - not that it is 'gone' at 6 months.

I think that may be true. But I also think (and I am guessing) the parasites continue to live because although the antibodies in the fishes slime will repel the parasites, some will still get enough nutrition to complete their life cycle and reproduce. A few may also be able to get a hold in the fishes gills and get enough to eat but the majority of parasites will die. The living ones will keep the fishes immune system on alert by their slight infection.
Or another theory which I just made up, maybe some parasites can get what they need by sucking some blood from bristle worms or some other creature in the tank getting enough nutrition to keep living. Like I said, I just made that up as i am not sure anyone ever did any tests on if parasites can live on worms.

 

[Brew12]

Let's face it. Nothing can be scientifically proven in a reef tank. Part of scientific proof is the elimination of variables other than the one you are attempting to modify as a proof. We can't do that in a reef tank. It can't be done on a reef tank in a lab.

That does not mean there isn't a role for science in a reef tank. We can look at scientific studies from a lab and extrapolate them for our tanks. Can we be sure it is accurate and proven by science? No. We can say that it is supported by science.

There is no point in holding a discussion on anything in this hobby if finding scientific proof is the end goal. We can't even prove that 0.35ppm copper will kill cryptocaryon irritans in a QT tank. We know that in a laboratory, copper at that level will kill the strains of cryptocaryon irritans that it has been tested against. That is it. We then take this information and attempt to use it to create a QT process. We can't prove it will work, but we say this is based on science.

We know a fishes immune system is boosted by bacteria found in food. We know that fish in a laboratory setting will quickly loose their immunity when exposed to stress so reducing stress is important. Can we prove that feeding food with natural bacteria in a more natural environment will prevent disease/parasites? No. We can say this is based on science.

 

[MnFish1]

But if I had no pathogens living in my tank including ich and velvet I wouldn't have such old fish, and yes there has never been a fish in my tank die from a "communicable" disease in maybe 40 years. It could be 35 but whose counting. I have had fish die from pop eye, tumors, swim bladder problems, broken bones, broken hearts etc, but no ich, velvet or bacteria. No one has to believe that, but my fish do.
Remember, to me, you are all Noobs and none of this, including this conversation is new to me.

Well Paul - though I dont know how old you are - I have had tanks probably as long as you - perhaps -10 years. So there is that. I started keeping saltwater tanks when I was 16 or so - and am now 50+ years older than that. So - I have been through all of the same heresay - as to 'the next best thing' as you have. to answer your question - if you had no pathogens living in your tank - of course you would have old fish - thats common sense. Even if you had Ich and velvet in your tank - you would also have old fish - because they are likely immune. This is also common sense. It has nothing to do (IMHO) with continuous mud dosing, feeding bacteria, etc.

 

[MnFish1]

We know a fishes immune system is boosted by bacteria found in food. We know that fish in a laboratory setting will quickly loose their immunity when exposed to stress so reducing stress is important. Can we prove that feeding food with natural bacteria in a more natural environment will prevent disease/parasites? No. We can say this is based on science.

I would appreciate you documenting this sentence by sentence. Because though all of these things are'thought to be true', im not sure we 'know' them to be true.

For example, starving animals by definition have a decreased immune system. So of course feeding fish an excellent diet will improve the immune system. (it will also improve cardiac, renal and every other bodily function). Since there is no way to know 'which bacteria' is needed to 'boost' the immune system - and its impossible to know which bacteria is present in the 'food we feed' - there is no way to know whether this has any effect.

There is no evidence that fish loose their immunity when exposed to stress - depending on which immunity you are talking about. There is evidence that stressed fish are more susceptible to disease - with or without their innate immune systems.

For example - there is evidence (clear evidence) that elevated cortisol occurs in stressed/moved/QT'd fish. Then again it also happens in tanks when one fish chases another. (also clearly documented). Cortisol decreases immune function as it increases the ability to avoid stress.

As to your last sentence - can we prove that feeding food with natural bacteria in a more natural environment will precent disease parasites, NO, we can say this is based on science - does not make sense to me.

 

[Gareth elliott]

In regards to parasite long term survival post fish immunity, Velvet is also capable of photosynthesis.

If meaning my statement on algae btw was referring to tanks with sparse corals or macro algae to use the raised nutrients. Was on purpose a very narrow application, not a generalization of all tanks with high nutrient loads.
This outcompeting even occurs with undesirable algae, diatoms or gha, often no dinos. Freshwater, have BBA, limits cyano.

My anecdotal view on nutrients is, dont let them get high on a lightly stocked tank. High nutrients, no inverts to use them, leads to algae.

 

[Brew12]

I would appreciate you documenting this sentence by sentence. Because though all of these things are'thought to be true', im not sure we 'know' them to be true.

Of course you would. Although if you were truly interested you could easily find this on your own.

Since there is no way to know 'which bacteria' is needed to 'boost' the immune system - and its impossible to know which bacteria is present in the 'food we feed' - there is no way to know whether this has any effect.

Except that we do know which bacteria can be helpful.
https://www.researchgate.net/publication/41894408_Probiotics_and_immunity_A_fish_perspective
Here is a quote " The involvement of probiotics in nutrition, disease resistance and other beneficial activities in fish has proven beyond any doubt."

So yes, we do know that bacteria boosts the immune system of a fish. You state that it is impossible to know which bacteria is present in the food we feed, which I agree with. We don't. LRS adds probiotic bacteria to their food based on this scientific research. Can we prove that the bacteria in the food is boosting our fishes immunity? No. However, we can say that LRS adds it to boost a fish's immune system based on science.

There is no evidence that fish loose their immunity when exposed to stress - depending on which immunity you are talking about.

Part of the answer is here.

For example - there is evidence (clear evidence) that elevated cortisol occurs in stressed/moved/QT'd fish. Then again it also happens in tanks when one fish chases another. (also clearly documented). Cortisol decreases immune function as it increases the ability to avoid stress.

Do I need to provide a reference or is your own quote good enough?

As to your last sentence - can we prove that feeding food with natural bacteria in a more natural environment will precent disease parasites, NO, we can say this is based on science - does not make sense to me.

I have no doubt that this does not make sense to you. I'm guessing you also think that treating fish with copper for parasites is also not based on science.

 

[elisa h]

It was heart broken that I lost the fish that I have. I did not intentionally introduce disease into my dt. It was on some snail that I bought and I fail qt them. I wan to go fallow and treat my fish but there is a Catalina goby in the 100g rock scape. So my best approach was to feed quality food since I won’t be able take all fish out for qt and fallow.

I’m so sorry I misunderstood your previous post. It read like you had introduced the parasite on purpose to try and get your fish immune. I’m sorry for your losses and also if I offended you.

 

[Paul B]

Well Paul - though I dont know how old you are - I have had tanks probably as long as you - perhaps -10 years. So there is that.

10 years! I have hermit crabs who have canker sores on their lips longer than that. My first tanks were wood, and not even good wood, wood that had wood worms in it that are now extinct. I used trilobites for a clean up crew.
In other words I have had tank continuously since about 1953 or so but I can't really remember much before 1958

I will be 70 this Christmas, but I look like 40. . I have been keeping saltwater tanks since the day they imported them to the US. I was waiting on the dock for them to come in with a bucket.

As to your last sentence - can we prove that feeding food with natural bacteria in a more natural environment will precent disease parasites, NO, we can say this is based on science - does not make sense to me.

I don't understand this quote, but maybe it's me.

Fish in the sea eat the bacteria and parasites that are on all fish and they eat that every day. That is how they stay immune.

 

[MnFish1]

The reason I asked to you give evidence for each of these points is that I didnt agree with the conclusions, here's why:

Let's face it. Nothing can be scientifically proven in a reef tank. Part of scientific proof is the elimination of variables other than the one you are attempting to modify as a proof. We can't do that in a reef tank. It can't be done on a reef tank in a lab.

Of course it can. But the results may not be generalizable to every reef tank. Its the same with all scientific research. The results only apply to the population that was studied - though results are often extrapolated to others. BRS attempts 'semi scientific' studies on reef tanks all the time.

That does not mean there isn't a role for science in a reef tank. We can look at scientific studies from a lab and extrapolate them for our tanks. Can we be sure it is accurate and proven by science? No. We can say that it is supported by science.

'

True enough.

There is no point in holding a discussion on anything in this hobby if finding scientific proof is the end goal. We can't even prove that 0.35ppm copper will kill cryptocaryon irritans in a QT tank. We know that in a laboratory, copper at that level will kill the strains of cryptocaryon irritans that it has been tested against. That is it. We then take this information and attempt to use it to create a QT process. We can't prove it will work, but we say this is based on science.

I guess I think this is kind of specious logic. There may always be an exception to the rule - but generally if used correctly, CI will be killed with copper at that level. Using your logic, the 'rule' that leaving a tank fallow for 72 days (which is based on only one study that showed that some CI survived that long - as compared to other studies that showed much shorter survival) should also not be followed.

We know a fishes immune system is boosted by bacteria found in food. We know that fish in a laboratory setting will quickly loose their immunity when exposed to stress so reducing stress is important. Can we prove that feeding food with natural bacteria in a more natural environment will prevent disease/parasites? No. We can say this is based on science.

Firstly, yes its proven that when a fish gets chased or stressed or netted, that cortisol levels rise. This happens in fish, people, giraffes, etc. It also temporarily affects susceptibility to infection (to a small degree). It is also rapidly returned to normal once the stress is removed. That said, the antibodies, slime coat, etc present on the fish are not much affected by this temporary situation. So fish don't lose immunity, they become temporarily slightly more likely to develop problems.

Lastly, the reason I said your last sentence didnt make sense is because you say 'Can we prove that feeding food with natural bacteria in a more natural environment will prevent disease/parasites? No'. You then go on to say 'We can say this based on science'. There are 2 ways to read this - and the way I read it was that it is proven by science that we CANNOT prevent disease by feeding bacteria in a natural environment'. Since I thought you were trying to make the opposite case, it didnt make sense to me. So it was your wording that confused me. I apologize.

 

[MnFish1]

Except that we do know which bacteria can be helpful.
https://www.researchgate.net/publication/41894408_Probiotics_and_immunity_A_fish_perspective
Here is a quote " The involvement of probiotics in nutrition, disease resistance and other beneficial activities in fish has proven beyond any doubt."
So yes, we do know that bacteria boosts the immune system of a fish. You state that it is impossible to know which bacteria is present in the food we feed, which I agree with. We don't. LRS adds probiotic bacteria to their food based on this scientific research. Can we prove that the bacteria in the food is boosting our fishes immunity? No. However, we can say that LRS adds it to boost a fish's immune system based on science.

And this is a section from another article mentioned by the one you reference- the key point is bolded.

... Favorable effects of probiotics on the health of host has been confirmed in different studies. Today, many researchers believe that probiotics are also becoming an essentialsection of the aquaculture practices that can result high production ( Nayak, 2010).The important issue for selection of microorganisms as probioticsis that they should be compatible with the host organism. Therefore, ideally the probioticsshould be isolated from the host organism and the region where host organism lives. ...

This is/was the point I was trying to make in suggesting that randomly adding bacteria (especially bacteria from areas the tank inhabitants are not usually exposed to) may not be as beneficial as just feeding a healthy diet. It sounds like a cool idea - but is it really helpful?

 

[Brew12]

I guess I think this is kind of specious logic. There may always be an exception to the rule - but generally if used correctly, CI will be killed with copper at that level. Using your logic, the 'rule' that leaving a tank fallow for 72 days (which is based on only one study that showed that some CI survived that long - as compared to other studies that showed much shorter survival) should also not be followed.

The fact that there are exceptions to the rule means it cannot be proven by science. We cannot prove that the copper used at the recommend levels will kill all strains of CI. We cannot prove that a 72 day fallow period will eliminate all CI strains. We use the available science as the basis for these recommendations. Hence, decisions based on science but not proven by science.

Favorable effects of probiotics on the health of host has been confirmed in different studies. Today, many researchers believe that probiotics are also becoming an essentialsection of the aquaculture practices that can result high production ( Nayak, 2010).The important issue for selection of microorganisms as probioticsis that they should be compatible with the host organism. Therefore, ideally the probioticsshould be isolated from the host organism and the region where host organism lives. ...

This is the key. We cannot prove the bacteria we add to our system or are in their food are the strains the fish need to boost their immune system. There is a scientific basis for trying to add these bacteria in an effort to boost the fish's immune system. So again, based on science, not proven by science.

It doesn't matter if it is @atoll or @Paul B using live food and ocean muck to keep fish parasite resistant or myself or @4FordFamily using copper to treat fish prior to adding them to our systems. Any success or failures we have are completely anecdotal. There is science to support both methods. Neither method can be proven to work via science. There are too many variables each way.

 

[Gareth elliott]

There are too many variables each way.

Thats easy we just need to solve some non linear differential equations. Breakfast [emoji23]