• Jul 19th 2009, 05:09 PM
GB89
The question was:

Solve y'' + 2y' + 5y = 2xe^(-x)cos(2x)

Using undetermined coefficients, I found the particular solution to be:
(1/4)(x^2)(e^(-x))sin(2x) + (1/8)x(e^(-x))cos(2x)

Unfortunately, there was a lot of algebra I could've easily messed up on. Is there anything online I could use to check my answer?

• Jul 19th 2009, 06:34 PM
mr fantastic
Quote:

Originally Posted by GB89
The question was:

Solve y'' + 2y' + 5y = 2xe^(-x)cos(2x)

Using undetermined coefficients, I found the particular solution to be:
(1/4)(x^2)(e^(-x))sin(2x) + (1/8)x(e^(-x))cos(2x)

Unfortunately, there was a lot of algebra I could've easily messed up on. Is there anything online I could use to check my answer?

Try substituting into the DE and see if your solution works.
• Jul 19th 2009, 07:08 PM
GB89
It's not coming out to the right answer.

y = A(x^2)(e^-x)cos(2x) + B(x^2)(e^(-x))sin(2x) + Cx(e^(-x))cos(2x) + Dx(e^(-x)sin(2x)) = 2xe^(-x)

Nevermind - I think it actually works out to the right answer. Thanks.
• Jul 19th 2009, 10:22 PM
CaptainBlack
Quote:

Originally Posted by GB89
The question was:

Solve y'' + 2y' + 5y = 2xe^(-x)cos(2x)

Using undetermined coefficients, I found the particular solution to be:
(1/4)(x^2)(e^(-x))sin(2x) + (1/8)x(e^(-x))cos(2x)

Unfortunately, there was a lot of algebra I could've easily messed up on. Is there anything online I could use to check my answer?