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Math Help - separable first order eqn

  1. #1
    Junior Member
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    separable first order eqn

    This equation was under the heading "separable equations" and I am supposed to solve it explicitly but I do not see how it is separable since the x^{2}y term cannot be manipulated (in any way I can see) so as to only have functions M(x) and N(y) s.t. M(x)+N(y)\frac{dy}{dx}=0

     <br />
\frac{dy}{dx}=\frac{2x}{y+(x^2)y}<br />
    where y(0)=-2

    Any help would be much appreciated. Can N(y)=y+x^{2}y and M(x)=-2x where x is a constant in N(Y)? but that doesn't make sense because x is not a constant in the equation overall...
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  2. #2
    Junior Member bondesan's Avatar
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    \frac{dy}{dx}=\frac{2x}{y+(x^2)y}\Rightarrow\frac{  dy}{dx}=\frac{2x}{y(1+x^2)}\Rightarrow ydy=\frac{2xdx}{1+x^2}. Now integrating both sides will do it.
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