Solved: In 1 through 12 first solve the equation f .x/ D 0
Chapter , Problem 12(choose chapter or problem)
In 1 through 12 first solve the equation f .x/ D 0 to find the critical points of the given autonomous differential equation dx=dt D f .x/. Then analyze the sign of f .x/ to determine whether each critical point is stable or unstable, and construct the corresponding 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 equa dx dt D .2 x/3
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