(a) Using a computer system (preferably MatLab, Octave, Python, C, C++, etc.) find the approximate solution to

y = x^2 + y^2 y(0) = 0

using a step size of h = 0.1. Write down the approximate values of y(1),y(2) and y(3).

(b) Repeat with a step size of h = 0.01, writing out the approximate values of y(1), y(2) and y(3).

(c) Recall our discussion on the interval over which solutions exist. Do you think the solution of this initial value problem exists for x (0, 3)? If not, over what interval to you suspect it exists on? You may want to plot your approximate solution to help answer this.

Please also attach a copy of your code.