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Linear difference equation (order two)



So far i have found a complementary solution

how do i find the particular solution

so that i can get the general solution which = particular + complementary solution


thanks
Reply 1
Avatar for DFranklin
DFranklin
18
Finding the PI is basically guesswork.

For a first guess, a constant multiple of the RHS is usually a good guess. So here you would guess that the PI is a constant.
Reply 2
Avatar for Milan.
Milan.
OP
3
Original post by DFranklin
Finding the PI is basically guesswork.

For a first guess, a constant multiple of the RHS is usually a good guess. So here you would guess that the PI is a constant.


hmm still confused...
i dont think i quite understand what the particular solution is in this case :s-smilie:
Reply 3
Avatar for DFranklin
DFranklin
18
Original post by The Mr Z
This isn't a differential equation, it's a series equation. As the OP says, this is an second order linear difference equation. They are solved using analogous methods to differential equations. And so...

There aren't complementary/particular solutions to be found.
Not true.
Reply 4
Avatar for DFranklin
DFranklin
18
Original post by Milan.
hmm still confused...
i dont think i quite understand what the particular solution is in this case :s-smilie:
If y_x = A (for all n), what is yx+2−yx+1+12yxy_{x+2} - y_{x+1} + \frac{1}{2} y_x? So if this is to equal 40, what must A be?

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