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Math Help - differential equation

  1. #1
    Junior Member
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    differential equation

    Using the fact that y1 = x^(−1/2)cosx is a solution of the associated homogeneous problem, obtain the general solution of the ODE
    (x^2)y′′ + (x)y′ + (x^2−1/4)y = x^(3/2)

    do i divide everything by x^2 and do wronskian?
    do i use y = x^m, y'=mx^(m-1), and y''=m(m-1)x^(m-2)?

    or do i find y2?
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  2. #2
    MHF Contributor chisigma's Avatar
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    The procedure to arrive, once you know a solution y_{1} of this type of equation, to a second solution y_{2} independent from it, is illustrated here...

    http://www.mathhelpforum.com/math-he...order-ode.html

    Kind regards

    \chi \sigma
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