Consider the initial value problem y = 3t 2 /(3y2 4), y(0) = 0. (a) Draw a direction
Chapter 8, Problem 15(choose chapter or problem)
Consider the initial value problem y = 3t 2 /(3y2 4), y(0) = 0. (a) Draw a direction field for this equation. (b) Estimate how far the solution can be extended to the right. Let tM be the right endpoint of the interval of existence of this solution. What happens at tM to prevent the solution from continuing farther? (c) Use the RungeKutta method with various step sizes to determine an approximate value of tM. (d) If you continue the computation beyond tM, you can continue to generate values of y. What significance, if any, do these values have? (e) Suppose that the initial condition is changed to y(0) = 1. Repeat parts (b) and (c) for this problem.
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