In 21–27, solve the given initial value problem.

Chapter 4, Problem 21E

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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:

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