There is  a program odesolve in matlab which will graph 2x2 systems. You have
to go directly to a solver like ode45 to do a larger system.

Here is a model program for ode45.



Step one:  Create an m-file for the system by going to the file
menu.  Call it anything you like (spring in my example). You can
go ahead and copy the contents of the sample files to get started.

The contents of the file are, for a system of n equations:

 

function dy=name(t,y)
dy = zeros(n,1)
dy(1) = f(1,t,y(1),  etc)   
dy(2) = f(2,t,y(1)  etc)
.
.
dy(n) = f(n,t,y(1)  etc);

For example, for the 2X2 system
      x' = y; y' = -sin(x)
the contents of the m-file should   be as below.  The system knows to
call the file spring.m .  Here are  the contents of spring.m:


function dy=spring(t,y)
dy = zeros(2,1);
dy(1)= y(2);
dy(2)= -sin(y(1));


Don't forget to save the file.

Step 2:
Now you need to compute it.Make a new file (Don't ask me why).
Here are  the lines of code which compute   the solutions in an interval
[0,40], with initial data y(1) = 0, y(2) = 1.8 at 0 and ask for a plot.

tspan = [0,40];
f0 = [0, 1.8]
[T,Y] = ode45(@spring,tspan, f0);
plot(T,Y(:,1),'-',T,Y(:,2), '-.')


You can use any time interval [0,T] and, of course, you need to give the
entire initial n initial vector  if it is an nXn system rather than a 2X2
one. Also, you will need to ask for each function of the plot (or omit it
if you like)


Now save the second file under a new name.

Type the name of the second file in the command window and if all goes well,
you will either get   your plot or some red stuff telling you what you
did wrong. Be sure to adjust the time intervals appropriately.You will be
graded on this.