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# In 11–18, find a general solution to the differential ISBN: 9780321747730 43

## Solution for problem 11E Chapter 4.6

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

Step 6 of 7

##### ISBN: 9780321747730

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