Given the initial conditions, y(0) = 1 and y'(0) = 0, solve the following initial-value problem from

Question:

Given the initial conditions, y(0) = 1 and y'(0) = 0, solve the following initial-value problem from t = 0 to 4:
d2y/dt2 + 4y = 0
Obtain your solutions with
(a) Euler's method and
(b) The fourthorder RK method.
In both cases, use a step size of 0.125. Plot both solutions on the same graph along with the exact solution y = cos 2t.