Consider the initial value problem y = ty + 0.1y3 , y(0) = , where is a given number
Chapter 2, Problem 18(choose chapter or problem)
Consider the initial value problem y = ty + 0.1y3 , y(0) = , where is a given number. (a) Draw a direction field for the differential equation (or reexamine the one from 8). Observe that there is a critical value of in the interval 2 3 that separates converging solutions from diverging ones. Call this critical value 0. (b) Use Eulers method with h = 0.01 to estimate 0. Do this by restricting 0 to an interval [a, b], where b a = 0.01.
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