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Chapter 5: Q6E (page 271)

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

dxdt=y2-3y+2,dydt=(x-1)(y-2)

Short Answer

Expert verified

The only critical points are (1, 1).

Step by step solution

01

Find critical points

Consider the system as;

dxdt=y2-3y+2dydt=(x-1)(y-2)

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

So,

y2-3y+2=0(x-1)(y-2)=0

02

Solve for x and y

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

(y-2)(y-1)=0y=2  or  1(x-1)(y-2)=0x=1,y=2

Thus, the only critical points are (1,1).

This is the required result.

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Most popular questions from this chapter

For the interconnected tanks problem of Section5.1, page241, suppose that instead of pure water being fed into the tankA, a brine solution with concentration0.2kg/L is used; all other data remain the same. Determine the mass of salt in each tank at time tif the initial masses are and y0=0.3kg.

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