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Math Help - Checking an answer

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by GB89 View Post
    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.
    Try substituting into the DE and see if your solution works.
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  3. #3
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    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.
    Last edited by GB89; July 19th 2009 at 06:40 PM.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by GB89 View Post
    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.
    Yes that is a PI for your ODE.

    See attachment showing the check in Maxima.

    CB
    Attached Thumbnails Attached Thumbnails Checking an answer-gash.png  
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