Discrete time system difference equation

I want to know what is the method to solve such a problem in matlab. Considering a discrete time system difference equation as follows:

How do I compute the value of y @ time k=5. when the input sequence is U=[1 -2 3 -4] and the initial conditions are Y(1)=1 , y(2)=1.

y=??? Please ; I want information regarding such a problem . I searched everywhere but didn't help me properly. If you can explain the steps of the solving it will be very helpful.... Thanks in advance :)

Answer 1

[Torsten]

u=[1 -2 3 -4];
y(1)=1;
y(2)=1;
for k=2:4
   y(k+1)=-2*y(k)+3*y(k-1)+1.5*u(k)+4*u(k-1);
end
y(5)

Best wishes

Torsten.