Differential Equations - 38 - Variation of Parameters (Non-homogeneous)

Solving a 2nd order linear non homogeneous differential equation using the method of variation of parameters. 2y''-y'-y=2e^t

[@raiu]

I'm doing an online math degree and it's so difficult to learn from a book without a teacher going through the steps. You have saved me with your clear explanations, thank you so much.

[@TheLazyEngineer]

Charlie no prob, best of luck! Thanks for watching.

[@lakshyagupta4191]

This series is so great! It helped me a lot...

[@tymofei8586]

just one question at the end why didnt you assume 2/3 as constant and didnt add to c3 so it would be c1*e^(-1/2)t + c2*e^t+c3*t*e^t ? what is the difference it is a constant anyway and they will be linearly independent

[@ivanflebus6877]

Could you do a follow up on this episode explaining how to use green's function? Would be of great help!

[@TheLazyEngineer]

Ivan Flebus great question! Yes I can do that when I pick this series back up.

[@ivanflebus6877]

@@TheLazyEngineer That would be great! Thanks alot for the work you've put in already, I think I can speak for most of the people here when I say you're basically saving my math exam!

[@rdbury507]

I think you missed a 't' copying the u1 value at about 7:10. Might not affect the solution once constants are absorbed though. In general I think it's good practice to plug the solution into the original equation to make sure it's correct.

[@rdbury507]

My mistake, forgot you're taking the derivative.

[@TheLazyEngineer]

do you mean the u1 value? If so, the equation calls for u2' not u2! so that is why there is no t. And I agree, that is a good practice.

[@rdbury507]

Yes, I meant u2. Maybe it would be a bit easier to solve for u1' and u2' first since it's just solving linear equations, then integrate them both to get u1 and u2. It would also help if I was paying more attention, so sorry for the confusion.

[@kingbeauregard]

Goddamn, you're good at this. You're the first person to go through this technique without leaving me with the sense that I was being led into a trap. Also, I was able to understand, looking at your presentation, why it's not unreasonable to apply the constraint where the "prime" terms are set to equal zero. Remembering that we at this point have no idea what u1 and u2 look like, we could hypothetically rewrite the yp' line so that we combined the u1 and u1' terms, and likewise combined the u2 and u2' terms ... but if we did that, wouldn't it kind of mean that we were effectively working with new functions u3 and u4, where u3 = u1 + u1' and u4 = u2 + u2'? And if we did that, we wouldn't see any trace of the "prime" terms any longer, right? It's kind of like how arbitrary constants absorb specific constants.

[@WaynesStrangeBrain]

What's the significance of the 4/9th if it just gets absorbed into a constant anyway?

[@Lionelmarc84]

Bro is this undetermined coefficient method or variation of parameter ?

[@adamm4942]

blessing to you sir.

[@jhondavid1659]

when solving the two system equations could you use Cramer’s rule to make it easier??

[@carultch]

Yes. And that's precisely what the method using the Wronskian (W), and the Cramer Wronskians (W1, W2, etc) does.

[@General12th]

Hey Hey What's your favorite band?

[@TheLazyEngineer]

+J.J. Shank oh man I'm all over the place when it comes to music taste. But let's see.. Today at the gym I lifted to some Tool and Nine Inch Nails. Great artists

[@SKAAYY]

This helped me a lot!! Thank you so much

[@daswin4493]

How to solve x´´(t)=2x(t)+2tx`(t)

[@unsampletezt]

This actually helped me so much unlike my shitty prof

[@MrRyanroberson1]

i'm going to do that thing that pythagoras once (according to myth/legend) did, but in a slightly different way, about sqrt(2) if f(x)=ax, and f(f(1))=2, what is a? sqrt(2). good. if f(f(y))=dy/dx, what is f(y)? what is the.... half-derivative/demi-derivative of a function? surely it must be at least conceivable, yes?

[@aderinmolaogunlewe9168]

Thank you sir

[@ايمنالدماطي-ي9ز]

wonderfull

[@DesportJonas]

very funny :)

[@MrRyanroberson1]

i'm getting too close to your up-to-date videos... i'll be forced to subscribe or lose track of your channel.