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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)=C_{1}(0.5)^{n}+C_{2}n(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)^{n}u(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},Cn^{2}(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.

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# Difference equation

Can you offer guidance or do you also need help?

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