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Chapter 5: Q5E (page 271)

In Problems 3鈥�6, find the critical point set for the given system.

dxdt=x2-2xy,dydt=3xy-y2

Short Answer

Expert verified

The only critical point is (0,0).

Step by step solution

01

Find critical points

Consider the system as;

dxdt=x2-2xydydt=3xy-y2

For finding the critical points put the system equal to 0.

So,

x2-2xy=03xy-y2=0

02

Solve for x and y

Put the value of y in another equation and solve, then;

x(x-2y)=0x=0鈥�鈥�or鈥�鈥�2yy(3x-y)=0y=0鈥�鈥�or鈥�鈥�3x

Thus, the only critical points are (0,0).

This is the required result.

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