difference equation

sami_boy

Hi guys

I have this difference equation.

y(n)-y(n-1)+0.25y(n-2)=x(n)-0.25x(n-1)

I found the step response of the system from the homogeneous solution and it's

y_h(n)=C₁(0.5)ⁿ+C₂n(0.5)ⁿ >>>homogeneous

h(n)=(0.5n+1)(0.5)ⁿ >>> step response

The 2nd part of the problem is I'm supposed to find the response of the system if x(n)=(0.25)ⁿu(n) is the input and initial conditions =0.

so my question is how do I find the particular solution ( y_p(n))?
I tried for y_p(n)=C(0.25)ⁿ,Cn²(0.25)ⁿ, but i couldn't find the response.
I also tried to solve it with convolution but it didn't work.

So please guys i would really appreciate your help.
thanks.