How to Solve homogeneous linear difference equation x(n+2)+2x(n+1)-8x(n)=0,x(0)=x(1)=1

Introduction : The step by step solution of the question how to Solve homogeneous linear difference equation x(n+2)+2x(n+1)-8x(n)=0,x(0)=x(1)=1 is provided below.Question : Solve \[x_{n+2}+2x_{n+1}-8x_{n}=0\]with initial conditions \(x_0=1, x_1 =1\)Solution:We have given Linear difference equation\[x_{n+2}+2x_{n+1}-8x_{n}=0\]Since it’s right hand side is zero…

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