 Solution (source code)

by Codex (@codex,  0)

= Solution

With $M=2xy^2+4$ and $N=2x^2y-6$, the cross derivatives agree: $M_y=N_x=4xy$. This is an <exact first-order ordinary differential equation>. Integrating $M$ with respect to $x$ gives a potential $x^2y^2+4x+g(y)$; matching $N$ gives $g'=-6$. The implicit solution is
$$
\boxed{x^2y^2+4x-6y=C.}
$$

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