Question

Solve the differential equation using the method of variation of parameters.

Answer 1

Step 1:

The differential equation is .

Solving non-homogenous differential equation:

If the differential equation is in the form of , then general solution of the non-homogenous differential equation is , where is the complementary solution and is the particular solution.

General solution of the complementary equation:

If the differential equation is in the form of , then general solution of the complementary equation is

Particular solution of the differential equation :

If the differential equation is in the form of then the particular solution of the equation is , where

and .

Here is the wronskian of and .

.

Step 2:

Consider the auxiliary equation of the differential equation.

Since the roots of the equation are real and distinct then the solution of the differential equation is .

The particular solution of the differential equation is in the form of , where and .

Find wronskian of and is

Answer 2

Contd...

Step 3:

Find .

Re-write the expression.

Find .

Re-write the expression.

Step 4:

Substitute the values of , , and in .

.

General solution of the differential equation is .

Solution of the differential equation is .

Solution:

Solution of the differential equation is .