Answer: In 1–14, solve the given initial value problem

Chapter 7, Problem 4E

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QUESTION:

In Problems 1–14, solve the given initial value problem using the method of Laplace transforms.

\(y^{\prime \prime}+6 y^{\prime}+5 y=12 e^{t}\);

\(y(0)=1, y^{\prime}(0)=7\)

Equation transcription:

Text transcription:

y^{prime prime}+6 y^{prime}+5 y=12 e^{t}

y(0)=1, y^{prime}(0)=7

Questions & Answers

QUESTION:

In Problems 1–14, solve the given initial value problem using the method of Laplace transforms.

\(y^{\prime \prime}+6 y^{\prime}+5 y=12 e^{t}\);

\(y(0)=1, y^{\prime}(0)=7\)

Equation transcription:

Text transcription:

y^{prime prime}+6 y^{prime}+5 y=12 e^{t}

y(0)=1, y^{prime}(0)=7

ANSWER:

Solution :

Step 1 of 3 :

In this problem, we need to solve the given initial value problem using the method of Laplace transforms.

y’’ + 6 y’ + 5 y = 12

y(0) = -1  ,  y’(0) = 7

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