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Math Help - Undetermiend Coeffecient Problem

  1. #1
    Junior Member
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    Jan 2009
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    Undetermiend Coeffecient Problem

    So the problem is
    y''+y=cosx y(0)=1 y(0)=-1

    The roots are r^2=-1 (+i,-i)

    so that would give a homogeneious equation of

    y=c1cosx +c2sinx

    but how do i figure out the other equation that i need? is it just as simple as y=Acosx?

    if i go that route, then
    y'=-Asinx
    y''=-Acosx.

    plugging that into the original equation, i would get -Acosx+Acosx=cosx. cosx=0
    that doesn't seem right at all. i'm confused on how to figure out how to pick the second equation.
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  2. #2
    Junior Member
    Joined
    Nov 2009
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    Re: Undetermiend Coeffecient Problem

    The forcing function is cos(x), so your particular solution would ordinarily be y = A sin(x) + B cos(x). However, since cos(x) is already a part of the homogeneous solution, you add x's to the particular solution like: y = A x sin(x) + B x cos(x). See if that works.
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