Question

\[(x \text D + 2)(x\text D - 1)\]

Answer 1

what's its difference from \[(x\text D - 1)(x\text D + 2)\]
then?

Answer 2

something smells fishy :/

Answer 3

ohhh i see it

Answer 4

there's gonna be xD2 instead of 2xD

Answer 5

no it is wrong..

Answer 6

wait what o.O

Answer 7

Wait..

Answer 8

it shouldnt be the same o.O

Answer 9

there are x's here

Answer 10

No.. they are not same..

Answer 11

this is what i think \[(x\text D + 2)(x\text D - 1) \implies x^2 \text D^2 + x\text D(-1) + 2x \text D - 2\]
i think you made a mistake o.O

Answer 12

\[(xD−1)(xD+2) \implies x^2D^2 + xD(2) -xD - 2 \implies x^2D^2 -xD - 2\]

Answer 13

It is the second one..

Answer 14

so then that gives me \[x^2 \frac{d^2y}{dx^2} - x + 2x \frac{dy}{dx} - 2\]
right?

Answer 15

yeah i was saying i think you made a mistake in the original question

Answer 16

\[\large = x^2D^2 +xD(-1) + 2xD - 2 \implies x^2D^2 + 2xD - 2\]

This is the original one..

Answer 17

what happened to -x?

Answer 18

D(constant) = 0

Answer 19

oh yeah...how can i forget

Answer 20

So the two DEs are different..

I don't know the name of person but he told you that they never commutate..
Remember this for lifetime..