Difference equation: a_{n+2) = 5a_{n+1} - 6a_n + n^3 + 4n + 2 for a_0 = 0, a_1 = 3

[Mer]

Hey!

I need a little help with this difference equation. I tried solving it but I can't find anything similar online and it would be great if I see other solutions and compare.

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Solve the difference equation:

. . . . .\(\displaystyle \large{ a_{n+2}\, =\, 5\, a_{n+1}\, -\, 6\, a_n\, +\, n^3\, +\, 4n\, +\, 2 }\)

...if:

. . . . .\(\displaystyle \large{ a_0\, =\, 0\, \mbox{ and }\, a_1\, =\, 3 }\)

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with A) the normal (direct method)
B) generating function

 

[Deleted member 4993]

Hey!

I need a little help with this difference equation. I tried solving it but I can't find anything similar online and it would be great if I see other solutions and compare.

---

Solve the difference equation:

. . . . .\(\displaystyle \large{ a_{n+2}\, =\, 5\, a_{n+1}\, -\, 6\, a_n\, +\, n^3\, +\, 4n\, +\, 2 }\)

...if:

. . . . .\(\displaystyle \large{ a_0\, =\, 0\, \mbox{ and }\, a_1\, =\, 3 }\)

---

with A) the normal (direct method)
B) generating function

Please explain to us - what do you understand regarding the terms:

A) the normal (direct method)
B) generating function

 

[stapel]

I need a little help with this difference equation. I...can't find anything similar online...

You didn't find anything on solving difference equations? What search terms did you use? I tried "solving difference equations", and got a nice long list (here)!

...and it would be great if I see other solutions and compare.

There are loads of worked examples at the links (in addition to the worked examples in your textbook and in your class notes), so doing one more example is obviously unlikely to help.

Instead, please re-read the "Read Before Posting" announcement, and then please reply with a clear listing of your thoughts and steps for at least one of your efforts at solution, specifying the method you are using.

Thank you!

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Solve the difference equation:

. . . . .\(\displaystyle \large{ a_{n+2}\, =\, 5\, a_{n+1}\, -\, 6\, a_n\, +\, n^3\, +\, 4n\, +\, 2 }\)

...if:

. . . . .\(\displaystyle \large{ a_0\, =\, 0\, \mbox{ and }\, a_1\, =\, 3 }\)

---

with A) the normal (direct method)
B) generating function