Question

Slove the homogeneous differential equation.

Answer 1

Step 1:

The homogeneous differential equation is .

The standard form of homogeneous differential equation is .

If the differential equation is homogeneous, then substitute .

Apply derivative on each side with respect to .

Apply product rule of differentiation .

Substitute and  in .

Step 2:

Apply integral on each side.

Apply integration formula .

.

Cancel ln on each side.

Step 3:

Back substitute in .

Cancel common terms.

.

Solution:

The equation is .