well, I've just stuck on the question.
I've done something like that:
clear all
dt= 0.01;
t_max=10;
i_max=ceil(t_max/dt)+1;
y=zeros(1,i_max);
x=zeros(1,i_max);
y(1)= 0;
x(1)= 1;
k=0;
t=[0.0:dt:(i_max-1)*dt];
for i=1:i_max-1
k1=-x(i)^2+20;
l1=y(i);
k2=-x(i)^2+dt*l1/2-k+20;
l2=y(i)+dt*k1/2;
k3=-x(i)^2+dt*l2/2-k+20;
l3=y(i)+dt*k2/2;
k4=-x(i)^2+dt*l3-k+20;
l4=y(i)+dt*k3;
y(i+1)=y(i)+(dt/6)*(k1+2*k2+2*k3+k4);
x(i+1)=x(i)+(dt/6)*(l1+2*l2+2*l3+l4);
end
figure(2)
plot(t,x,'b','LineWidth',1),xlabel('t / s'),ylabel('x / m')
but think that's wrong
btw, the exam is opensource based.
