Solution Found!
In 1–14, solve the given initial value problem
Chapter 7, Problem 13E(choose chapter or problem)
In Problems 1–14, solve the given initial value problem using the method of Laplace transforms.
\(y^{\prime \prime}-y^{\prime}-2 y=8 \operatorname{cost}-2 \sin t\);
\(y(\pi / 2)=1, y^{\prime}(\pi / 2)=0\)
Equation transcription:
Text transcription:
y^{prime prime}-y^{prime}-2 y=8 operatorname{cost}-2 sin t
y(pi / 2)=1, y^{prime}(pi / 2)=0
Questions & Answers
QUESTION:
In Problems 1–14, solve the given initial value problem using the method of Laplace transforms.
\(y^{\prime \prime}-y^{\prime}-2 y=8 \operatorname{cost}-2 \sin t\);
\(y(\pi / 2)=1, y^{\prime}(\pi / 2)=0\)
Equation transcription:
Text transcription:
y^{prime prime}-y^{prime}-2 y=8 operatorname{cost}-2 sin t
y(pi / 2)=1, y^{prime}(pi / 2)=0
ANSWER:Solution
Step 1
In this problem we find solution of equation using method of Laplace transform.
Given differential equation is
………………………………………………….(1)
Initial conditions are y()=1 and
……………………..…………………….(2)