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Math Help - Dofferential Equation

  1. #1
    Member kjchauhan's Avatar
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    Dofferential Equation

    Find the solution of the differential equation,

    \frac{d^4y}{dx^4}-4 \cdot \frac{d^3y}{dx^3}+8 \cdot \frac{d^2y}{dx^2}-8 \cdot \frac{dy}{dx}+4y=0

    Pl help to solve it. Thanks in adv..
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  2. #2
    Super Member Random Variable's Avatar
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    The characteristic equation is  r^{4}-4r^{3}+8r^{2}-8r+4 = (r^{2}-2r+2)^{2} = 0

    which has roots  1 \pm i , both of multiplicity 2

    so the general solution is  y(x) =  C_{1}e^{x} \cos(x) + C_{2} e^{x} \sin x + C_{3} e^{x}x \cos x + C_{4} e^{x}x \sin x
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