The routines eul, rk2, rk4 are supplied by John Polking, of
Rice University. You can refer to the source files eul.m, rk2.m,
and rk4 for the details.

But here is a fast overview. These files are not as GUI-friendly as
the dfield5/pplane packages as far as input or output .

Here is the information on eul.m :

% EUL   Integrates a system of ordinary differential equations using
%       Euler's method.  See also ODE45 and ODEDEMO.
%       [t,y] = eul('yprime', tspan, y0) integrates the system
%       of ordinary differential equations described by the M-file
%       yprime.m over the interval tspan = [t0,tfinal] and using initial
%       conditions y0.
%       [t, y] = eul(F, tspan, y0, ssize) uses step size ssize
%
% INPUT:
% F     - String containing name of user-supplied problem description.
%         Call: yprime = fun(t,y) where F = 'fun'.
%         t      - Time (scalar).
%         y      - Solution vector.
%         yprime - Returned derivative vector; yprime(i) = dy(i)/dt.
% tspan = [t0, tfinal], where t0 is the initial value of t, and tfinal is
%         the final value of t.
% y0    - Initial value vector.
% ssize - The step size to be used. (Default: ssize = (tfinal - t0)/100).
%
% OUTPUT:
% t  - Returned integration time points (column-vector).
% y  - Returned solution, one solution row-vector per tout-value.
%
% The result can be displayed by: plot(t,y).

So to use this, you need to have prepared a .m file, say

myf.m in your MATLABPATH. For example, under UNIX,
MATLABPATH=/home/a/wilker/.mymatlab
With the Windows version of MATLAB, use the Set Path menu under
the File menu.

Here is a sample

wilker@peano> more yprime.m
function w = yprime(t,y)
w = 1-t+4*y;

The name of the function in the function definition must match
the basename of the m-file that defines it.

Then, within MATLAB, do
>>  [t,y] = eul('yprime',[1,2],3,0.1) ;
Note: 'yprime' is a string and not the same as yprime without the single
quotes.

To calculate estimated values for the solution on the interval [1,2]
for the ODE, y' = 1-t + 4*y, y(1)=3.

yields

>> [t,y]

ans =

    1.0000    3.0000
    1.1000    4.2000
    1.2000    5.8700
    1.3000    8.1980
    1.4000   11.4472
    1.5000   15.9861
    1.6000   22.3305
    1.7000   31.2027
    1.8000   43.6138
    1.9000   60.9793
    2.0000   85.2811
You can graph this data by

>> plot([t,y])