Question

Solve: xy{(dy/dx)² – 1} = (x² – y²)(dy/dx).

Answer 1

The given differential equation is

Integrating, we get

log |y| + log |x| = log c, x² – y² = a²

xy = c, x² – y² = a² 

Hence, the solution is

(xy – c)(x² – y² – a²) = 0.