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Math Help - ODEs

  1. #1
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    ODEs

    Solve the differential equation
    d2y/dx2 − 2dy/dx+ (B^2 + 1)y = e^x sin^2 x
    for general values of the real parameter B.
    Explain why this solution fails for B = 0
    and B= 2 and find solutions for these values of B

    i can find the complementary function but not the PI. how should i got about it?thanks
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  2. #2
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    Quote Originally Posted by paddyb67 View Post
    Solve the differential equation
    d2y/dx2 − 2dy/dx+ (B^2 + 1)y = e^x sin^2 x
    for general values of the real parameter B.
    Explain why this solution fails for B = 0
    and B= 2 and find solutions for these values of B

    i can find the complementary function but not the PI. how should i got about it?thanks
    The homogenous is,
    y''-2y'+(B^2+1)y=0
    The charachteristic equation is,
    k^2-2k+(B^2+1)k=0
    k=1\pm \sqrt{1 - (B^2+1)} = 1\pm \sqrt{-B^2} = 1\pm i|B|
    So if B=0 then there is only one solution, if B\not = 0 then the quadradic has two solutions.
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  3. #3
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    h

    sure but what about the particular integral? ie the e^x sin^2x bit?
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