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Chapter 5: Q12E (page 271)

In Problems 11鈥�14, solve the related phase plane differential equation for the given system. Then sketch by hand several representative trajectories (with their flow arrows).

dxdt=-8y,dydt=18x

Short Answer

Expert verified

The solution is9x2+4y2=c.

Step by step solution

01

Find phase plane equation

Here the system is;

dxdt=-8ydydt=18x

And the phase plane equation is;

dydx=-9x4y

02

Solve the equation

Here the equation is.

dydx=-9x4y

Solving by variable separating. Then,

9x2+4y2=c

Since, dxdt=-8yand x increases when y<0 and x decreases when y>0.

03

Sketch some trajectories

This is the required result.

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