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Math Help - Separable Differential Equation

  1. #1
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    Separable Differential Equation

    y'=2y^2lnx/x

    with the intial condition that y(1)=1. I tried to separate them and on the left side I have that 1/2y=(lnx)^2 over 2 plus C ... Am I on the right track?
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  2. #2
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    \int\frac{dy}{y^2}=\int\frac{2ln(x)}{x}

    \frac{-1}{y}=(ln(x))^2+C_{1}

    y=\frac{-1}{(ln(x))^2+C_{1}}
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  3. #3
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    I just went through it in my head, and using u=ln(x) to solve ln(x)/x i got the same as you, but you need to have a negative in there from solving int(y^-2), now you just need to use y(1)=1 to find C.
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