Prove that x² – y² = c(x² + y²)² is the general solution of the differential equation (x³ – 3xy²)dx = (y³ – 3x²y) dy, where C is a parameter.

Given equation is
(x³ – 3xy²)dx = (y³ – 3x²y) dy

which is a homogeneous equation.
Therefore substituting y = vx
We have,

Integrating the equation both sides, 

thus substituting the values of I₁ and I₂,