Solve recurring relation :an+2 -10an+1+25an=5n(n≥0)
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Let us solve the recurrence relation The characteristic equation of homogeneous relation is equivalent to and hence it has the roots Therefore, the solution of the non-homogeneous recurrence relation is where the particular solution of non-homogeneous recurrence relation is
It follows that
which is equivalent to
and hence
We conclude that and thus
Consequently, the solution of the recurrence relation is
or