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

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider ISBN: 9780321747730 43

Solution for problem 11E Chapter 4.6

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Fundamentals of Differential Equations | 8th Edition

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Problem 11E

PROBLEM 11E

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

Step-by-Step Solution:

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

        =

Step 5 of 7

Chapter 4.6, Problem 11E is Solved
Step 6 of 7

Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

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