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Math Help - Checking differential equation (2)

  1. #1
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    Checking differential equation (2)

    Can someone check my working?

    Solve x^2y''-2xy'+2y=0 by letting y=x^m

    y=x^m \Rightarrow y'=mx^{m-1} \Rightarrow y''=m(m-1)x^{m-2}

    m(m-1)x^2x^{m-2}-2mx^{m-1}x+2x^m=0

    m(m-1)x^m-2mx^m+2x^m=0

    x^m(m(m-1)-2m+2)=0

    x^m(m^2-m-2m+2)=0

    x^m(m^2-3m+2)=0

    x^m(m-1)(m-2)=0

    \Rightarrow m=1, 2

    y=x or y=x^2
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  2. #2
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    Looks good to me.
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