Double Trouble or Worse The initial-value problem y' = y1/3, y(0) = 0, has an infinite...

Double Trouble or Worse The initial-value problem y' = y1/3, y(0) = 0, has an infinite number of solutions, two of which are y(t) = 0 and y(t) = (2t/3)3/2, t ≥ 0. These solutions are drawn in Fig. 7; the nonzero solution is tangent to the t-axis at the origin.

Figure 7 Two solutions of the IVP y' = yl/3, y(0) = 0, for Problem 14.

(a) What happens if Euler’s method is applied to this problem?

(b) What happens if the initial condition is changed to y(0) = 0.01? If a preprogrammed Euler solution is available, solve on [0, 6] with h = 0.1.

(c) Use the computer to look at the direction field. How does it correlate with your solution in part (b)?