format compact;
clear all;

% INITIAL CONDITIONS

h=.4;

y(1)=1;
z(1)=1;
t(1)=0;

% EULER'S METHOD

for i=1:5
    y(i+1)=y(i)+h*(y(i));
    t(i+1)=i*h;
end

% RUNGE_KUTTA METHOD

for i=1:5
    k1 = z(i);
    k2 = z(i) + h*k1;
    z(i+1)=z(i)+h*(k1+k2)/2;
end

hold on;
plot(t,z,'LineWidth',2,'Color',[1 0 0]);
plot(t,y,'LineWidth',2);
fplot('exp(x)',[0,2],'k');
legend('RUNGE-KUTTA APPROXIMATION','EULER APPROXIMATION','ACTUAL SOLUTION',3)