Solution Found!
Solution: In problem first solve the equation f(x) = 0 to
Chapter 2, Problem 5P(choose chapter or problem)
Problem 5P
In problem first solve the equation f(x) = 0 to find the critical points of the given autonomous differential equation dx/dt = f(x). Then analyze the sign of f(x) to determine whether each critical point is stable or unstable, and construct the comsfx/iuling phase diagram for the differential equation. Next, solve the differential equation explicitly for x(t) in terms of t. Finally, use either the exact solution or a computer-generated slope field to sketch typical solution curves for the given differential equation, and verify visually the stability of each critical point.
Questions & Answers
QUESTION:
Problem 5P
In problem first solve the equation f(x) = 0 to find the critical points of the given autonomous differential equation dx/dt = f(x). Then analyze the sign of f(x) to determine whether each critical point is stable or unstable, and construct the comsfx/iuling phase diagram for the differential equation. Next, solve the differential equation explicitly for x(t) in terms of t. Finally, use either the exact solution or a computer-generated slope field to sketch typical solution curves for the given differential equation, and verify visually the stability of each critical point.
ANSWER:
Solution
Step 1 of 7
In this problem, we have to find the critical point of the differential equation.