find particular solution of I.V.P.

Question

dy/dx+3y=x^2 satisfying initial condition x=0, y=0

Answer 1

Step 1:

The differential equation is .

The equation is in the form of linear differential equation .

Here and .

Solution of first order linear differential equation  is  .

Consider .

Apply integration by parts: .

Let .

Apply derivative on each side.

Let .

Apply integral on each side.

Step 2:

Consider .

Apply integration by parts: .

Let .

Apply derivative on each side.

Let .

Apply integral on each side.

Substitute above result in (2).

Substitute above result in (1).

Step 3:

Apply initial conditions .

Substitute in (3).

Partical solution of the differential equation is .

Solution:

Partical solution of the differential equation is .