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Math Help - Nonhomogeneous equation

  1. #1
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    Nonhomogeneous equation

    Can someone show how to solve:

    y'' + 9y = sin^4(x)
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  2. #2
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    First find the charateristic equation to the homogeneous equation and solve it.

    y'' + 9y = 0

    gives

    r^2 + 9 = 0

    Now solve this guy, you should get complex solutions. What does this mean?
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  3. #3
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    Got that.
    yc(x) = c1cos3x + c2sin3x

    I get duplication tho right? what do I do from here?
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  4. #4
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    Quote Originally Posted by jzellt View Post
    Got that.
    yc(x) = c1cos3x + c2sin3x

    I get duplication tho right? what do I do from here?
    To get a particular solution, note (using the usual double angle formulae) that \displaystyle \sin^4 (x) = -\frac{1}{2} \cos (2x) + \frac{1}{8} \cos (4x) + \frac{3}{8}.
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