Question

Solve the differential equation or initial-value problem using the method of undetermined coefficients.

Answer 1

Step 1 :

The differential equation is

 

The auxiliary equation is .

Find the roots of the auxiliary equation.

The roots of the auxiliary equation .

The complementary solution is

Step 2 :

Find the particular solution.

The particular solution is of the form .

Apply derivative on each side with respect to x.

Apply derivative on each side with respect to x.

Substitute and in equation (1).

The particular solution is .

The general solution is .

Solution :

The general solution is .