Prove that is the general solution of differential equation

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

3. Prove that `

x^{2}-y^{2}=c\left(x^{2}+y^{2}\right)^{2}

` is the general solution of differential equation `

\left(x^{3}-3 x y^{2}\right) d x=\left(y^{3}-3 x^{2} y\right) d y

`, where `c` is a parameter.