Question

Find all solutions of the recurrence relation
an =5an  -1-6an-2 +7n

Answer 1

this will be the answer u question has little problem. 

Answer 2

The solution is:$a_n=\alpha_1 \cdot3^n+\alpha _2\cdot2^n+{(\frac{49}{20})}\cdot7^n$

Given:-   $a_n =5a_{n-1}-6a_{n-2} +7^n$

To find:-  all solutions of the recurrence relation

The solutions of the associated homogeneous recurrence are

$a^{(h)}_n = \alpha _13^n + \alpha _22^n$

Because F(n) =$7^n$ a reasonable trial solution is $a^{(p)}_n$$n = C\cdot7^n$. Making the substitution and solving for C gives C = $\frac{49}{ 20}$, and hence  $a^{(h)}_n ={(\frac{49}{20})}\cdot7^n$

is a particular solution. Hence, a complete parametrization of solutions is:

$a_n=\alpha_1 \cdot3^n+\alpha _2\cdot2^n+{(\frac{49}{20})}\cdot7^n$

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