Region of Stability for the general problem

Let's consider the following example
dy/dt = 4*t*cos(y)
y(0) = 0
0 <= t <= 5
An analysis of this problem for Euler's Method (in class) suggests that the time step should be less than 0.1. Let's look at a few timesteps:


h=0.01
gen_prob_0.01.gif
h=0.1
gen_prob_0.1.gif
h=0.3
gen_prob_0.3.gif

The solution for h=0.01 and h=0.1 are very simlilar; for h=0.3, the solution starts to oscillate, and blows up!