In each of the question, show that the given differential equation is homogeneous and solve each of them.

(x² – y²)dx + 2xy dy = 0

Here, putting x = kx and y = ky

= k⁰.f(x,y)

Therefore, the given differential equation is homogeneous.

To solve it we make the substitution.

y = vx

Differentiating eq. with respect to x, we get

Integrating both sides, we get

Put 1 + v² = t

2vdv = dt

log(t)

∴ log(1 + v²) = -logx + logC (∴ From (i) eq.)

The required solution of the differential equation.