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

∫cosec²vdv = - logx – logC

-cot v = - logx – logC

cot v = logx + logC

1 = C

e¹ = C

The required solution of the differential equation.