The initial-value problem y' = y1/3, y(0) = 0, has an infinite number of solution two of which are y(t) = 0 and y(t) = (2t/3)3/2, These solutions are drawn in Fig. 1.4.7; the nonzero solution is tangent to the t-axis at the origin.

(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)?

Transcribed Image Text:

y 3 х0 - (213) rin =0 2.