% Example: Euler's method for dy/dt = K*(y-s) 
K = 1; 
s = 20; 
y0 = 100; 

npoints = 50; 
dt = 0.1; 

y = zeros(npoints,1); % this initializes the vector y to being all zeros 
t = zeros(npoints,1); 

y(1) = y0; % the initial condition 
t(1) = 0.0; 

for step=1:npoints-1 % loop over the timesteps 
y(step+1) = y(step) + dt*K*(y(step)-s); 
t(step+1) = t(step) + dt; 
end 

plot(t,y,'r'); %plots the numerical solution in red 
hold on; %keep the previously plotted lines 
plot(t,yexact(t,y0,K,s)); %plots the exact solution (default plot is in blue, solid line) 
