Prove that a[n]=x*2^n+y*3^n is a solution to the equation
a[n] = 5*a[n-1] - 6*a[n-2] when n>=2 ,x and y are integers and numbers in [] s are subscripts and ^ denotes power .
To prove is a solution, substitute this in and see if it satisfies.
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The standard way to solve these homogenus recurrences is to substitute and see what value of r you get.Then the general solution is a linear combination of the obtained
Thus