ty''-(t+1)y'+y=t^2 y1=e^t y2=t+1
differential equations variable coefficient equations

Question

ty''-(t+1)y'+y=t^2   y1=e^t    y2=t+1
differential equations variable coefficient equations

anonymous · Answer

@primeralph if you get a chance and would like to help me again it would be appreciated

anonymous · Answer

do I have to let w=-x?

anonymous · Answer

so change t in the first to -wy''??

primeralph · Answer

@rperez36  I have to go now. @timo86m

anonymous · Answer

ok

anonymous · Answer

@Loser66 could you help please? we went over wronskian method today lol

loser66 · Answer

hey, Wronskian is affected directly to RHS, therefore, your LHS must have the coefficient of y" is 1. I mean you have to divide both side by t, then , recheck the solutions whether they still work or not. then apply Wronskian.

anonymous · Answer

yeah that's what I thought but dividing out the t still left me a lil confused cause then I still have t in the denom...

anonymous · Answer

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loser66 · Answer

divide both side by t, you have $$y"-\frac{t+1}{t}y'+\frac{y}{t}=t$$
check solution: e^t , and t+1, both them work?

loser66 · Answer

e^t works,

anonymous · Answer

so I just plug in the initial conditions to the standard equation? and im just supposed to choose the givens that work? he didn't give us any examples of problems like this in class :/

loser66 · Answer

t+1 works, too. Now, wronskian

loser66 · Answer

yes, you should make sure if you divide both side with that coefficient and solutions still work. Most of the case, they work. but when doing that, you get standard form and your g(s) changes. In your case, it turns to t, right? quite simple. do Wronskian, friend

anonymous · Answer

ok thank you I will try

loser66 · Answer

surely you can do it. just that trick, $\huge 1*y"$

anonymous · Answer

after wronskian I got (t+1)te^2t....that was using the y1 and y2 they gave us ...or was I supposed to do it with something else?

loser66 · Answer

just apply formula , nothing else
hey, I need your solution from my posted to compare to mine. Can you do it for me? the whole thing a, b, c, d. Please, If you can, write it out on a paper, scan and post it. Thanks in advance

loser66 · Answer

It's not in hurry, take time, 2 more days is OK

anonymous · Answer

a problem from today or yesterday? if from today I didn't see you post a problem

loser66 · Answer

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