PROBLEM 11E

In Problems 11–18, find a general solution to the differential equation.

Step 1</p>

In this problem, we have to find a general solution of differential Equation

Step 2</p>

A second order linear Differential Equation of the form of

The given equation will be

Now, rewrite the second order linear differential Equation

Here, there are two independent solution to the homogenous equation will be are cos(t) and sin(t)

Step 3</p>

Now, we have to two equation for solving the value of

……………………. Equation (1)

Rewrite the above equation we get

………………… Equation (2)

Now, Using Equation 1 and Equation 2 we have to Evaluate the value of

………. Eqaution (3)

= =

So, =

Use the Trigonometric Identities

Then,

=

Substitute the value back in Equation (3)

=

=

Step 4</p>

Now, we have to integrate to evaluate the value of

= dt

Use the trigonometric Identities

= =

Use the Integral Properties

and

=