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,