Question

(D-1)x+(D^2+1)y=1
(D^2-1)x+(D+1)y=2
Solve the differential equation by systematic elimination

Answer 1

1: http://prntscr.com/4zj06y
2: http://prntscr.com/4zj09b
3: http://prntscr.com/4zj0cx

Just relabel... C2+C --> C2 it's just a redundant part of the particular solution
because of the double root in the homogenous solution (degeneracy), we get the Ct term, and that happens to correspond to an eigenvalue of 0, so this is a very craftily made problem to trip you up at many turns
so that's y(t)
y(t) = c1 + c2 t - t^2 + c3 exp(-t)
now for x(t) ...

Answer 2

I just noticed a slight booboo...let me fix it with red ink:
1: http://prntscr.com/4zj1h7
2: http://prntscr.com/4zj1kg
3: http://prntscr.com/4zj1o0

Okay, so now for x(t) ...

Answer 3

so to find x(t), we do the same procedure but eliminate y instead

Answer 4

http://prntscr.com/4zj2nu

now we find the homogenous solution and the particular solution again
need the characteristic equation again

Answer 5

So in case it's not clear, these methods are all guess and check more or less. Basically, we know when we have DEs of this form for the homogenous part solutions of the form A exp(kt) work. K can be complex. And when you have a polynomial on the right hand side, polynomials work for the particular solution

Answer 6

no I have a small bamboo table

Answer 7

wacom pen tablet... wacom is the company, they make these kind of tablets and things. digital art is sort of their niche. It's not made of wood, bamboo is just the product line lol... Yes, I put in some capacitive ICs into a bamboo frame It's a tablet for digital art, but I use it just like a normal stylus, which it can be used for

Answer 8

thats cool tho how much was it?

Answer 9

Well this one when I bought it was around $60. Very nice ones are $200-1000 +. There are quite some good ones that are quite expensive. Just stick with wacom. Normally I am not so specific with brand, but it makes a difference because not a lot of companies make these tablets and the other ones tend to be quite cheaply made

Answer 10

These days though, I prefer to get a tablet PC that you can write on with a stylus.
Anyways, back to the solution.

Answer 11

have you studied logic at all? The thing that I like about writing with the pen, is that it's easy to undo mistakes, rather than on paper where you have to cross out. Here I just hit undo

Answer 12

@Dan815, why do you feel the need to delete your comments? Now I feel like talking to myself, how great!

Anyways, back to the solution:
http://prntscr.com/4zj85n

Answer 13

OH I am trying to leave the post neat for the guy when he gets back

Answer 14

@Miracrown

Answer 15

Fair enough.

Answer 16

Thank you so much!

Answer 17

You're welcome! :)

Answer 18

you're welcome!