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Solved: In each of 1 through 3, verify that (0, 0) is a critical point, show that the
Chapter 9, Problem 3(choose chapter or problem)
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
Questions & Answers
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