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Math Help - Separable O.D.E question

  1. #1
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    Separable O.D.E question

    Hi everyone

    Need help to verify this working,thank you in advance for all your kind help & support.

    x^2\frac{dy}{dx}=y^2+2xy(Hint:Substitute u=\frac{y}{x}
    \frac{dy}{dx}=\frac{y^2+2xy}{x^2}
    u+x\frac{du}{dx}=u^2+2u
    \frac{du}{u(u+1}=\frac{dx}{x}
    \int(\frac{1}{u}-\frac{1}{u+1})du=\int \frac{dx}{x}
    ln|u|-ln|u+1|=ln|x|+c
    ln|\frac{\frac{y}{x}}{\frac {y}{x}+1}=ln|cx|
    \frac {y}{x+y}=cx
    y=cx(x+y)

    Thank you in advance.
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  2. #2
    Member Abu-Khalil's Avatar
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    It's good. Notice that u=0,u=1 are also solutions.
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