Use method of undetermined coefficients to find the general solution to
Y (double prime)+3y (prime)=2t^(4)+e^(t) sin3t

Question

Use method of undetermined coefficients to find the general solution to 
Y (double prime)+3y (prime)=2t^(4)+e^(t) sin3t

kainui · Answer

The method I use to solve undetermined coefficients is to just take the functions on the right side and drop off the coefficients on them, so just use

t^4 and e^tsin(3t)

then take their derivatives over and over again until you get 0 or they start repeating again. Then replace all the coefficients with variables.

For example, if your right hand side was this:

7t^2 + 9sin(t)

I would get:

t^2, t, and 1 for the polynomial part without considering coefficients and
sin(t) and cos(t) for the other part without considering coefficients and I would choose:

y=A+Bt+Ct^2+Dsin(t)+Ecos(t)

and try to solve for my coefficients from there for MY example.

anonymous · Answer

What should Y (t) be in that case? If I can get Y (t) then I can do the rest

kainui · Answer

I just told you how to get it.

kainui · Answer

It's actually pretty insulting that I spent that time to show you how to do it and you didn't even try.

anonymous · Answer

It's not that I'm insulting you by not even trying, actually I'm tired or trying. I got 
Y (t)=At^(5)+Be^(t) cos3t+Ce^(t) sin3t