# Find particular solution

1. Oct 21, 2009

### mansfin

I have to find the particular solution to the differential equation:

(-21/4)y''+2y'+y=4xe^(3x)

First, I chose my trial function to be yp=(Ax+B)*e^(3x). Is this correct???
so yp'=3(Ax+B)*e^(3x)
yp''=9(Ax+B)*e^(3x)

So I plug these into the differential equation and I get:
(-189/4)Axe^(3x)-(189/4)Be^(3x)+6Axe^(3x)+6Be^(3x)+Axe^(3x)+Be^(3x)=4xe^(3x)

I group like terms and I get A=-16/161 and B=0
So yp=(-16/161)Axe^(3x)

This is not correct.
Can someone please tell me where I'm going wrong? Thanks!

2. Oct 21, 2009

### Staff: Mentor

The particular solution you choose is affected by the solutions to the homogeneous equation. For your problem, I'm going to guess that e3x is not a solution to the homogeneous problem, but I don't know that for a fact.

In any case, and assuming that y = e3x is not a solution to the homogeneous problem, your choice for a particular solution is good, but you made a mistake in both of your derivatives. differentiation. =(Ax+B)*e3x is a product, a fact that you seem to have completely overlooked.

3. Oct 21, 2009

### mansfin

Wow. Implied multiplication on my calculator. Next time I will just work that out by hand. Thanks for your help!