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I have recently come across this queastion regarding Z-transforms in maple and am struggling with how to complete the question. Any steps on how to proceed with the folloqwing questions would be greatly appreciated. I have done the first part but cannot fathom where to go with this one.

1. For the difference equation

x[n+2]-(α+β)x[n+1]+α*β*x[n]=n/3^n,  x[0]=a, x[1]=b,

(a) Find the general solution for x[n] in terms of the parameters α,β,a and b

(b)Find the solutions for ithe two cases α=-β and α=β

(c)Examine both solutions found in (b) when α=1, for various values of a and b, choosing values to demonstrate different behaviours of the solutions.

Thanks for reading, any help with steps would be great.

I am relatively inexperienced with Maple and would like to either be pointed in the right direction or shown a similar example to my problem for reference.

My problem is I need to write a programme using the below equations

d^2x/dt^2=ax+by

d^2y/dt^2=cx+by

I then have to use the below values to show my programme works

a=b=c=d=1

x(0)=1

Dx(0)=0

y(0)=0

Dy(0)=1

After proving it works I have to apply it to a mass spring system using realistic parameters. Using visual and analytical ways to show findings.

md^2x/dt^2=-kx-k(x-y)

md^2y/dt^2=-k(y-x)-ky

when x and y are the displacement from the equilibrium. Initially the masses are displaced from their equilibrium posistions and released so that

x(0)=a, y(0)=b, Dy(0)=Dx(0)=0

then repeat with different smaller calculations

Any help would be much appreciated

Thanks