help w/ differentiable eqns

[RichieZ]

So I have the eqn:
4y'' + 4y' + y = 3xe^x

I'm supposed to solve this via undetermined coefficients.

The trial solution I'm using: Axe^x + Be^x (because if u differntiate the RHS is always some form of xe^x + e^x)

is this right? I don't want ppl to solve this for me, I just want to know if i've got the trial solution correct, and if its wrong why?

 

[Orsorum]

Looks about right. Use the undetermined coefficients, multiply them by the scalars used in the d.e., then set those answers (coefficients only) equal to 3... make sense?

 

[RichieZ]

here's what i'm doing:

yp=Axe^x + Be^x
yp'=Ae^x + Axe^x + Be^x
yp''= Ae^x + Ae^x + Axe^x + Be^x

then when i do 4yp" + 4yp' + yp = 3xe^x

then set those answers (coefficients only) equal to 3... make sense?

I thought you had to equate the terms becuse after you add it all up its 9Axe^x + 12 Ae^x + 5Be^x = 3xe^x
so:
9A = 3
12A + 5B = 0

I think I'm messing up because if I plug my answer back into the original equation it doesn't work out

 

[RichieZ]

Blah I added wrong

should have been:
9Axe^x + 12 Ae^x + 8Be^x = 3xe^x

so yp = 1/3xe^x - 4/9e^x