Consider the recurrence relation defined by

Monday, 22 April 2019

7:12 PM

Consider the recurrence relation defined by
forn > 2.
The non-homogenous solution is an
+ 6an_1 9an_2 =
Expected answer:
_6n2 n

First find the homogeneous solution

Then find particular solution - ensure it is not a term of the homogeneous solution (if so, multiply by another n)

Substitute into all terms

// can cancel out the …^(n-…) to simplify

Solve to find

The characteristic equation of the recurrence relation is
which has solutions
3, —3. Hence the homogenous solution has the form
for constants A, B. The non-homogenous solution then has the form Cn2(—3)n. The value of C can be determined by substuting an
into the original recurrence relation to find that C = —6.