% slopef.m 

function z=slopef(ftx,ng)
% SLOPEF(ftx,ng) plots the slope field for the ODE x'=f(t,x) where the string
% variable ftx contains contains the expression in t and x defining the right
% hand side.  A grid using ng points both vertically and horizontally is used,
% covering the ranges obtained from the axis command.

ax=axis;  
%plot([],[]) 
cla; 
axis(ax); 
hold on;
tg=linspace(ax(1),ax(2),ng);
xg=linspace(ax(3),ax(4),ng); 
dt=tg(2)-tg(1); 
dx=xg(2)-xg(1);

for i=1:ng
 t=tg(i);
 for j=1:ng
  x=xg(j);
  v=eval(ftx);
  d=.3/max(1/dt,abs(v)/dx);
  plot([t-d,t+d],[x-v*d,x+v*d],'g');
  xlabel(['Slopefield:  x'' = ',ftx]) 
 end
end