Question

Find the particular solution of the nonhomogeneous recurrence equation: f_n = 3f_n-1 + 10f_n-2 +2*3^n

Please explain all the steps. Also if there is algebra involved please explain that as well thanks.

The problem is fixed better.

Answer 1

The particular solution must be similar to 2*3^n

Then we guess it's of the form

Substituting this in the recurrence relation we get

2t- , 2n

2n-2

$a3^n-a3^{n}-10a3^{n-2} - 2\cdot 3^n+ b-3b-10b= 0$

$-10a3^{n-2} - 2\cdot 3^n+ b-3b-10b= 0$

2 . 32 . 3n-2-12b 10a3" 0

(-10a-1813n-2-12b = 0

Therefore

10a-18 = 0

Then

18 3 a=-10 =-5

The particular solution is

71 3 5