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Math Help - second order differential eq

  1. #1
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    second order differential eq

    x^2 y" - x y' + y = 2 log x+ x^2 log x + x^2 + 1/x
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  2. #2
    MHF Contributor matheagle's Avatar
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    You can solve the homogeneous part via y=x^m.
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  3. #3
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    You can also let u = x y' - y so u' = x y'' so your equation becomes

    xu' - u = 2 \log x+ x^2 \log x + x^2 + 1/x

    a first order linear equation. Once you solve it you then solve xy' - y = u which also a first order linear equation.
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  4. #4
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    thank u!!
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