Step 1:

The homogeneous differential equation is .

The standard form of homogeneous differential equation is .

If the differential equation is homogeneous, then substitute .

Apply differentiation on each side with respect to .

.

Apply product rule of differentiation .

.

Substitute and  in .

Apply integral on each side .

.

Apply integration formula .

Cancel ln on each side.

Back substitute in .

Cancel common terms.

.

Solution:

The equation is .