Question

Solve the differential equation.

Answer 1

Step 1:

The differential equation is .

All the coefficients are constants and the differential equation is of the form .

The auxiliary equation is .

The formula for the roots of the quadratic equation is

.

The roots of auxiliary equation are

.

The roots of auxiliary equation are and .

Step 2:

If the roots of auxiliary equation are the complex numbers , , then the general solution of is .

The roots of auxiliary equation are complex numbers and .

In this case .

The general solution of is .

Solution:

The general solution is .