Properties of differential operators

[mathnoobie]

Homework Statement

Hi, I am solving a system of differential equations and in one of my equations I have this,
(D+2)X+(D+2)Y=0 where X and Y are variables, D is my differential operator.
My question is, would it be mathematically correct to divide out (D+2)
and thus getting X+Y=0, X=-Y ?

 

[LCKurtz]

Homework Statement

Hi, I am solving a system of differential equations and in one of my equations I have this,
(D+2)X+(D+2)Y=0 where X and Y are variables, D is my differential operator.
My question is, would it be mathematically correct to divide out (D+2)
and thus getting X+Y=0, X=-Y ?

No, it wouldn't.

 

[Dick]

Homework Statement

Hi, I am solving a system of differential equations and in one of my equations I have this,
(D+2)X+(D+2)Y=0 where X and Y are variables, D is my differential operator.
My question is, would it be mathematically correct to divide out (D+2)
and thus getting X+Y=0, X=-Y ?

No, (D+2) isn't an invertible operator. There are functions that satisfy (D+2)Z=0 where Z isn't 0. Try to take that into account and try again.

 

[mathnoobie]

Ah alright, thank you. That explains why my answer seemed to make no sense.