Solved: In 19–21, solve the given initial value problem.

Chapter 5, Problem 20E

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QUESTION:

In Problems 19-21, solve the given initial value problem.

                     \(\frac{d x}{d t}=2 x+y-e^{2 t} ; x(0)=1\),
                    \(\frac{d y}{d t}=x+2 y ; y(0)=1\)

Equation transcription:

Text transcription:

\frac{d x}{d t}=2 x+y-e^{2 t} ; x(0)=1

\frac{d y}{d t}=x+2 y ; y(0)=1

Questions & Answers

QUESTION:

In Problems 19-21, solve the given initial value problem.

                     \(\frac{d x}{d t}=2 x+y-e^{2 t} ; x(0)=1\),
                    \(\frac{d y}{d t}=x+2 y ; y(0)=1\)

Equation transcription:

Text transcription:

\frac{d x}{d t}=2 x+y-e^{2 t} ; x(0)=1

\frac{d y}{d t}=x+2 y ; y(0)=1

ANSWER:

Solution :

Step 1 :

In this problem we have to solve the given initial value problem.

Given initial value problem is

,  and the initial condition  and

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