Chapter 25, Problem 24P

Given the initial conditions, $y\left(0\right)=1\text{ and }{y}^{\prime }\left(0\right)=0$, solve the following initial-value problem from $t=0\text{ to }4$:

$\frac{d^{2}y}{d{t}^2}+4y=0$

Obtain your solutions with (a) Euler's method and (b) the fourth- order RK method. In both cases, use a step size of 0.125. Plot both solutions on the same graph along with the exact solution $y=\cos 2t$.