function w = Euler

%MATLAB routine for visualizing Euler's method
%Created by Winfried Just, department of Mathematics, Ohio University
%Last modified: February 6, 2003

syms t y 

disp(' ')
input('Enter the right-hand side of the differential equation. \n');

f = ans

disp(' ')
input('Enter the given solution of the boundary value problem. \n');

g = ans

disp(' ')
input('Enter the value of a. \n');

a = ans

disp(' ')
input('Enter the value of y(a). \n');

ya = ans


disp(' ')
input('Enter the argument b for which you want to find y(b). \n');

b = ans

while 0 < 1
    disp(' ')
    input('Enter the value of Delta t or Ctrl^C to quit. \n');

    dt = ans
    y0 = ya;
    t0 = a;
    
    hold off
    ezplot(g, [a - 0.5, b + 0.5])
    hold on
    
    while t0 + 0.0000000000001 < b
        
        t1 = t0 + dt;
        y1 = double(subs(f, [t y], [t0 y0])*dt + y0);
       
        x = t0:dt/50:t1;
        plot(x, (y1 - y0)*(x - t0)/(t1 - t0) + y0)
        t0 = t1;
        y0 = y1;
    end  
    error = subs(g, t, b) - y1
end