Solved: In each of 1 through 3, verify that (0, 0) is a critical point, show that the

Chapter 9, Problem 3

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QUESTION:

In each of 1 through 3, verify that (0, 0) is a critical point, show that the system is locally linear, and discuss the type and stability of the critical point (0, 0) by examining the corresponding linear system.dx/dt = x + y2, dy/dt = x + y

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QUESTION:

In each of 1 through 3, verify that (0, 0) is a critical point, show that the system is locally linear, and discuss the type and stability of the critical point (0, 0) by examining the corresponding linear system.dx/dt = x + y2, dy/dt = x + y

ANSWER:

Step 1 of 4

First, write the system in the matrix form

Now substitute

into the right side of upper equation to verify that  is critical point

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