Question

Solve: (x² – ay) dx = (ax – y² ) dy

Answer 1

Writing the equation as 

x² dx + y² dy = a (x dy + y dx) 

x² dx + y² dy = a d(xy) 

∫x² dx + ∫y² dy = a ∫d(xy) + c 

x³/3 + y³/3 = axy + c 

Hence the general solution is x³ + y³ = 3axy + c