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Math Help - Homogeneous equations with constant coefficients

  1. #1
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    Homogeneous equations with constant coefficients

    y^(4) + 18y'' + 81y = 0

    Find the general solution of the differential equation
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  2. #2
    MHF Contributor Calculus26's Avatar
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    your cahracteristic eqn is L^4 + 18L^2 + 81 = 0

    (L^2 +9)^2 = 0 L = 3i (recall you only need one root)

    so you solutions are cos(3x),sin(3x),xcos(3x), and xsin(3x)
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