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Solved: In 23–30, find the solution to the initial value
Chapter 4, Problem 27E(choose chapter or problem)
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