Consider the initial value problem y = t 2 + y2 , y(0) = 1. (a) Draw a direction field
Chapter 8, Problem 14(choose chapter or problem)
Consider the initial value problem y = t 2 + y2 , y(0) = 1. (a) Draw a direction field for this equation. (b) Use the RungeKutta method or another method to find approximate values of the solution at t = 0.8, 0.9, and 0.95. Choose a small enough step size so that you believe your results are accurate to at least four digits. (c) Try to extend the calculations in part (b) to obtain an accurate approximation to the solution at t = 1. If you encounter difficulties in doing this, explain why you think this happens. The direction field in part (a) may be helpful.
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