Solution Found!
In 21–27, solve the given initial value problem.
Chapter 4, Problem 21E(choose chapter or problem)
QUESTION:
In Problems 21-27, solve the given initial value problem.
\(y^{\prime \prime}+2 y^{\prime}+2 y=0\) ; \(y(0)=2\) , \(y^{\prime}(0)=1\)
Equation Transcription:
Text Transcription:
y’’+2y’+2y=0
y(0)=2
y’(0)=1
Questions & Answers
QUESTION:
In Problems 21-27, solve the given initial value problem.
\(y^{\prime \prime}+2 y^{\prime}+2 y=0\) ; \(y(0)=2\) , \(y^{\prime}(0)=1\)
Equation Transcription:
Text Transcription:
y’’+2y’+2y=0
y(0)=2
y’(0)=1
ANSWER:
Solution:-
Step1
Given that
We have to solve the given initial value problem.
Step2
We have
y”+2y’+2y=0, y(0)=2 y’(0)=1
The auxiliary equation for y”+2y’+2y=0 is
We know that ,
A quadratic equation is in form
The roots of the equation is: