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find particular solution of I.V.P.

0 votes
dy/dx+3y=x^2 satisfying initial condition x=0, y=0
asked Nov 17, 2015 in CALCULUS by anonymous

1 Answer

0 votes

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  image.

Consider .

Apply integration by parts: image.

Let .

Apply derivative on each side.

Let .

Apply integral on each side.

Step 2:

Consider .

Apply integration by parts: image.

Let .

Apply derivative on each side.

Let .

Apply integral on each side.

Substitute above result in (2).

image

Substitute above result in (1).

image

image

Step 3:

Apply initial conditions .

image

Substitute image in (3).

image

image

Partical solution of the differential equation is image.

Solution:

Partical solution of the differential equation is image.

answered Nov 17, 2015 by cameron Mentor
edited Nov 17, 2015 by cameron

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