Question

\[y _{n+2}+y _{n+1}-2y _{n} = n ^{2}\]

nonhomogeneous difference equation

Answer 1

Eek! :-D It kind of looks like a mix between a series and a differential equation. It's not separable is it? (probably not, but it doesn't hurt to ask)

Answer 2

not separable :)

Answer 3

Darn.

Answer 4

There's no supplementary text? Are we solving for certain terms..?

Answer 5

no it said asking general solution

Answer 6

Another possibly newbie-ish question here, can "y" be defined as a function here?

Answer 7

This is a non-homogeneous recurrence relation.
See here: http://en.wikipedia.org/wiki/Recurrence_relation

under the section: Solving non-homogeneous recurrence relations

Answer 8

Fibonacci numbers... where have I heard that before...?

Answer 9

http://upload.wikimedia.org/wikipedia/commons/b/bf/PascalTriangleFibanacci.svg

The golden ratio stuff, I see

Answer 10

@asnaseer it is not about recurrence dude

Answer 11

just to clarify - what does your notation of \(y_n\) mean?

Answer 12

just kidding everyone knows it is about recurrence, but how can i solve this with RHS (x^2)

Answer 13

o_O

Answer 14

seems like you should have included that bit in the problem...

Answer 15

I /believe/ you need to use the method of undetermined coefficients: http://en.wikipedia.org/wiki/Method_of_undetermined_coefficients

If you still need more help, then @Zarkon is an expert in this area

Answer 16

oh my good it is very very irrelevant

Answer 17

the method of undetermined for differential equ

Answer 18

from that site:

In mathematics, the method of undetermined coefficients, also known as the lucky guess method, is an approach to finding a particular solution to certain inhomogeneous ordinary differential equations and recurrence relations.

Answer 19

i am surprised maybe questions like that can be solved by this theorem but i never saw it actually