Checking an answer

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?

Thanks in advance.

Quote:

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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?

Thanks in advance.

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Try substituting into the DE and see if your solution works.

It's not coming out to the right answer.

Was this the correct set-up?

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.

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?

Thanks in advance.

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Yes that is a PI for your ODE.

See attachment showing the check in Maxima.

CB