Eiler1

function j = Eiler1(u)
t0=0;
tm=4;
t1=0.8;
t2=1.6;
t3=2.4;
t4=3.2;
dt=0.01;
x1=1;
x2=0;
j=0;
x1_res=[];
u_res=[];
t_res=[];

while t0<tm

U=u(1)*exp(u(2)*t0).*(cos(u(3)*t0+u(4)));

u_res=[u_res U];
dx1 = x2*dt;
dx2 = (-1)*x1*dt + (-2)*x2*dt +1*U*dt;
dj = (1*x1^2+U^2)*dt;

x1=x1+dx1;
x1_res=[x1_res x1];
x2=x2+dx2;
j=j+dj;
t0=t0+dt;
t_res=[t_res t0];
end
j=j+20*x1^2;
plot(t_res,x1_res,'--',t_res,u_res)
legend('x(t)','u(t)')
grid on