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Math Help - verifying the solution of a differential equation

  1. #1
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    verifying the solution of a differential equation

    verify that y=cx^2+\frac{2}{x} is a general solution of the differential equation x^2\frac{dy}{dx}-2xy+6=0

    \frac{dy}{dx}=\frac{2xy-6}{x^2}

    How do I continue? y seems to be in the way
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: verifying the solution of a differential equation

    Quote Originally Posted by Punch View Post
    verify that y=cx^2+\frac{2}{x} is a general solution of the differential equation x^2\frac{dy}{dx}-2xy+6=0

    \frac{dy}{dx}=\frac{2xy-6}{x^2}

    How do I continue? y seems to be in the way
    y=cx^2+\frac{2}{x}\Rightarrow\frac{dy}{dx}=2cx-\frac{2}{x^2} , now substitute in the differential equation ...
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