MATLAB and 4th order Runge Kutta Method

Hi everyone!

I'm trying to solve a second order ode in MATLAB using the RK4 method. I know that I need to separate the second order into a system of first order odes, which i've already done. However, I'm not familiar with matlab and am unsure of how to approach the actual graphing part, although I do know how to do RK4 manually.

also, there are two initial conditions that are given.

From what I've read online, I need to write two m-files, one that defines the system of linear equations and another that actually establishes the RK4 method. Would the below work work?

function y = rk4step(f,t,x,h)

% f - Matlab inline function f(t,y)

% t - initial time

% x - initial condition

% h - stepsize

h2 = h / 2;

k1 = f(t, x);

k2 = f(t + h2, x + h2 * k1);

k3 = f(t + h2, x + h2 * k2);

k4 = f(t + h, x + h * k3);

y = x + (k1 + 2 * k2 + 2 * k3 + k4) * h / 6

and then in a separate m-file:

function z=ydot(x,y)

z(1)=y(2);

z(2)=(1-x.^2)/4*y(1);

my ode is y'' + (1-x^2)/4*y=0, y(0) = 1, y'(0) = 0 which i've split into

y' = Y

Y' = (1-x^2)/4*y

Where and how do I define rk4step?

once I finish everything how do I get it to plot? I need y and y' against x and y against y'. I also need to plot a phase portrait.

help is appreciated! thanks in advance!