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Can you suggest which method should be used to solve the following DE: $$xdy-2ydx+xy^2(2xdy+ydx) = 0$$
I guess I can rewrite it in the form of Exact Equations, but it is really confusing to find $F(x,y)$.

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Re-write it as $$\frac{(xdy-2ydx)}{xy}+(2xydy+y^2dx)=0 \implies \frac{dy}{y}-2\frac{dx}{x}+d(xy^2)=0$$ Integrating we get $$\int \left (\frac{dy}{y}-2\frac{dx}{x}+d(xy^2) \right)=0$$ $$\implies \ln y-\ln x^2+xy^2=C$$

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