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Math Help - 2nd Order differential equation

  1. #1
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    2nd Order differential equation

    d2y/dx2 - 2dy/dx = 5(cos3x - sin 3x) - 7

    I managed to find a Complementary function, but I'm not sure what particular integral i should use, i tried acos 3x + bsin 3x, but since i have another function (-7) i don't know what changes i should make. Anyone can help me with the particular integral please?
    Last edited by jessm001; May 7th 2012 at 01:20 PM.
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  2. #2
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    Re: 2nd Order differential equation

    anyone please ? I would be very grateful
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  3. #3
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    Re: 2nd Order differential equation

    a\cos3x + b\sin3x + cx.
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  4. #4
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    Re: 2nd Order differential equation

    thanks, why is it +cx not c ?
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  5. #5
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    Re: 2nd Order differential equation

    Because a constant is part of the C. F.
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  6. #6
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    Re: 2nd Order differential equation

    Sorry, still didn't really understand, what do you mean the constant is part of the C.F ?
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  7. #7
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    Re: 2nd Order differential equation

    You should have found that the Complementary Function is A + Be^{2x}, where A is a constant.
    Including a constant as part of the Particular Integral is pointless, it will simply differentiate out.
    When your normal choice of P.I. (or part thereof) is contained within the C.F., you have to multiply your normal choice by x.
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