The general solution of (x-y^2),dx+y(5x+y^2),dy=0 is (where c is a constant):

Question

The general solution of $(x-y^2)\,dx+y(5x+y^2)\,dy=0$ is (where $c$ is a constant):

Accepted Answer

Writing $y^2\,dx-xy\,dy = -xd(y)\cdot(\dots)$ transforms it, with $t=y/x$-type substitution, to $2x^3+cx^2+y^2=0$-type relation; matching the exponents gives option A.

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