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Homogeneous solution of: y(n) -9/16y(n-2) = x(n-1)

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Homogeneous solution of: y(n) -9/16y(n-2) = x(n-1)

(a) C1(3/4)^n+C2(3/4)^-n

(b) C1-(3/4)^n-1+C2(3/4)^n-1

(c) C1(3/4)^n

(d) C1-(3/4)^n

I got this question in semester exam.

My question is from The inverse z-transform and Response of Linear Discrete Systrems topic in chapter Digital Control Systems of Control Systems

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Right answer is (a) C1(3/4)^n+C2(3/4)^-n

The best explanation: Taking the z-transform of the given difference equation and solving the homogeneous equation and finding the solution using complimentary function.

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