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Chapter 5: Q7E (page 271)

In Problems 7鈥�9, solve the related phase plane differential equation (2), page 263, for the given system.

dxdt=y-1,dydt=ex+y

Short Answer

Expert verified

The solution isex+ye-y=c .

Step by step solution

01

Find phase plane equation

Here the system is;

dxdt=y-1dydt=ex+y

And the phase plane equation is;

dydx=ex+yy-1

02

Solve the equation

Here the equation is.

dydx=ex+yy-1

Solve by variable separating,

鈭�(y-1)eydy=鈭�exdx-ye-y+c=exex+ye-y=c

This is the required result.

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