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Math Help - Second order non homogeneous differential equation

  1. #1
    lso
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    Angry Second order non homogeneous differential equation

    I have to solve this DE
    ((x+2)^2)y'' -2y=4

    the hint says to get rid of the x+2 but I have no idea where to start from... do I have to replace x+2 with another variable or what?
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  2. #2
    A Plied Mathematician
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    I would replace the x+2 with t=x+2, and you get

    \dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=\dfrac  {dy}{dx}. Hence, the DE becomes

    t^{2}\,\dfrac{d^{2}y}{dt^{2}}-2y=4.

    This equation is a Cauchy-Euler equation.
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