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    He, I'm getting all comfused and myself muddled up with the following differential equation:

    d^4y/dx^4 + 8 d^2y/dx^2 -9y = e^x - sinx

    For the roots of equation I got +/- 1 and +/- 3i.

    When trying to get the Particular Intergral do I try x(Pe^x+Qsinx+Rcosx) then differentiate it 4 times?

    Thanks
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    What about Pxe^x + Qsin x + R cos x? (Which is easy to differentiate any number of times)
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    Notice that the only forcing term which appears in the complimentary function is e^x, and that since neither of \pm i are roots of the characteristic equation, \sin x doesn't appear there. So, when trying to find the particular integral you shouldn't multiply them by x. As such, you need to do as SimonM said.
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    Aww ok sorry got comfused! Thanks.

    Ps just to check, for the particular integral do I need to have Psinx and Qcosx in it? or is it just the sinx ?
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    (Original post by Cw.x)
    Aww ok sorry got comfused! Thanks.

    Ps just to check, for the particular integral do I need to have Psinx and Qcosx in it? or is it just the sinx ?
    In this case you could just use P\sin x, since you have no odd-order derivatives in there (when you differentiate \sin mx an even number of times you still end up with some multiple of \sin mx). Normally, you'd need both, because an odd-order derivative will give you a multiple of \cos mx instead... if unsure, use both.
 
 
 
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