How do you get this answer by elimination for differential equations?

Question

I have:

3(D+1)x + 3(D-1)y = 6
3(D+1)x + (D+1)(D+2)y = -(D+1)

When I subtract the first equation from the second one, I get:
(D^2 +5)y = -D-7

But the correct answer is:
(D^2 +5)y = -7

How do you get rid of the -D on the right side of the equation? Or am I messing something up in the subtraction?

Answer 1

Best Answer - Chosen by Asker

- (D + 1) acts on 1 (not written explicitly, but it's really there) which results in - (D + 1)1 = - D1 - 1 after distribution. Now since 1 is a constant, and D is the derivative, - D1 = 0; that's how you get rid of - D. Otherwise you have everything else correct.

I hope this helps.... Did you know you can get 3 points back by picking a best answer?

Asker's Rating:

Asker's Comment:

Thank you sooo mcuh. This just made my life easier!

Answer 2

i get the same as u :s
maybe the answer is wrong

3(D+1)x + (D+1)(D+2)y - [3(D+1)x + 3(D-1)y] = -(D+1) -6

3(D+1)x + (D+1)(D+2)y -3(D+1)x - 3(D-1)y = -D - 7

(D+1)(D+2)y - 3(D-1)y = -D-7

(D^2 + 3D + 2) y (-3D +3)Y = -D-7

(D^2 +5)y = -D-7