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Recurrence Relationshard
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For the non-homogeneous recurrence an=5an−1−6an−2+3⋅3na_n = 5a_{n-1} - 6a_{n-2} + 3 \cdot 3^nan​=5an−1​−6an−2​+3⋅3n the homogeneous part has characteristic roots 2 and 3. Since 3 is a simple root of the characteristic equation, what form should the particular solution an(p)a_n^{(p)}an(p)​ take?