How to solve matrix exponent equation

Hello,

I will be thankful if someone helps me. Here is my task:

Reduce to a system and solve a matrix exponent equation under zero initial conditions.

y'' + 16y = sin4x

I wrote it in MatLab but im not sure if it is correct and also im not sure about z below. I dont know how we decide the value of z. The current zvalue of z is from another task.

clear all;

A=[0 1;-16 0];

y=[0;0]; h=0.1; n=100; x1=0;

y1(1)=0; y2(1)=0; x(1)=0;

B=[0;1];

A2=expm(A*h)

for i=2:n

y=A2*y+(h/2)*(A2*B*sin(4*x1) + B*cos((4*x1)+h));

y1(i)=y(1); y2(i)=y(2);

x1=x1+h;

x(i)=x1;

end

plot (x, y1, 'r', x,y2,'c'), figure(gcf), pause

z=exp(-x).*(-0.4*cos(2*t)-0.3*sin(2*t)) + 0.4*cos(t)+0.2*sin(t);

plot(x,z,'r',x,y1,'c'), figure(gcf)