clf reset;

F='[-i*cos(t)*exp(i*t)*y(2);-i*cos(t)*exp(-i*t)*y(1)]';

func=inline(F,'t','y');
[t,y]=ode23(func,[0.01,100],[0,1]);

t1=0:0.01:100;
c2=exp(-i.*t1/2).*(-i/(2*sqrt(5/4)).*sin(sqrt(5/4).*t1)+cos(sqrt(5/4).*t1));

hold on;
plot(t,imag(y(:,1)));
plot(t1,imag(c2),'r');