Using ODE 45 on a system of equations

Hi, having trouble representing dx^2/d^2t = -sinx as a system of two first order ODE's in MATLAB. I have broken down the second order ODE into

 y_1 = x
 y_1prime = y_2
 y_2prime = -siny_1

Here is my matlab code so far

function yprime = siny(t,y)
    yprime = -sin(y) ;

in one M file and then the run this function

tspan=[0,5];
yzero=0.5;
[t,y]=ode45(@siny,tspan,yzero);
plot(t,y)

now im just not sure how to represent convert this single plot into a system of equations.

[Azzi Abdelmalek]

What does mean: convert this single plot into a system of equations.

[Jme]

sorry i haven't wrote that down correctly. Basically i have to change a second order ODE to into a system of two first order ODEs and plot them.

Answer 1

[Jan]

Your siny function does not correlate to your system of differential equations of order 1. Better:

function yprime = siny(t,y)
yprime = [y(2), -sin(y(1))];

Now you need a [1 x 2] vector as initial value also.

[Jme]

Thank you, i think i've managed it, but with a slight problem. I kept getting an error 'SINY1 must return a column vector', so i created a column vector but i cannot see how to make it work with a [1 x 2] vector as i have a column vector which is a [2 x 1] vector.

tspan=[0,5];
yzero=[0 1]';
[t,y]=ode45(@siny1,tspan,yzero);
plot(t,y)

siny function is as you posted above.

Thank you for the reply