Solved: In 23–30, find the solution to the initial value

Chapter 4, Problem 27E

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QUESTION:

In Problems 23-30, find the solution to the initial value problem.
                     

                        \(y^{\prime \prime}(x)-y^{\prime}(x)-2 y(x)=\cos x-\sin 2 x\) ,

                         \(y(0)=-7 / 20, y^{\prime}(0)=1 / 5\)

Equation Transcription:

Text Transcription:

y''(x)-y'(x)-2y(x)=cos⁡ x-sin⁡ 2x

y(0)=-7/20, y'(0)=1/5

Questions & Answers

QUESTION:

In Problems 23-30, find the solution to the initial value problem.
                     

                        \(y^{\prime \prime}(x)-y^{\prime}(x)-2 y(x)=\cos x-\sin 2 x\) ,

                         \(y(0)=-7 / 20, y^{\prime}(0)=1 / 5\)

Equation Transcription:

Text Transcription:

y''(x)-y'(x)-2y(x)=cos⁡ x-sin⁡ 2x

y(0)=-7/20, y'(0)=1/5

ANSWER:

Solution

In this question we have to find the solution of the initial value problem

 and

Step 1

Here we first take one side of the equation as

So,

Putting the value in equation

 +

So on solving we get

On comparing it will give

Putting the value of A and B in  we get

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