The following is a Matlab program (second version)
to solve differential equations
numerically using
Euler's Method .
This variation will give the graph/solution on two sides of
the innitialtime.
I will explain how to use it at the end:
The Program:
function y=y(n,t0,t1,y0)

h=(t1t0)/n;

t(1)=t0;

y(1)=y0;

for i=1:n

t(i+1)=t(i)+h;

y(i+1)=y(i)+h*ex(t(i),y(i));

end;

t(n+1)=t0;

y(n+1)=y0;

for i=n+1:2*n

t(i+1)=t(i)h;

y(i+1)=y(i)h*ex(t(i),y(i));

end;

for i=1:n

T(i)=t(2*ni+1);

Y(i)=y(2*ni+1);

end;

for i=n+1:2*n

T(i)=t(in);

Y(i)=y(in);

end;

V=[T',Y']

plot(T,Y)

title('satya')

How to Use the Program?
 You have to have the above program in a
filename.mfile. I would call it
eulertwo.m.
 You also have to have a file ex.m
and you type in your equation in the file.
I typed in a problem as follows:
%x is a function of t and y is the first derivative x'(t)

function y=y(t,x)

y=(t^2x^2)*sin (x);

 Now, on matlab prompt, you write
eulertwo(n,t0,t1,y0) and return
, where n is the number of tvalues, t0 and t1 are the left
and right end points and
y(t0)=y0
is the innitial condition.
 Matlab will return your answer. You should also get the graph, if
your computer is set up properly. I do not get the graph in my office
but I get it in the lab.