- #1

quantum_smile

- 21

- 1

## Homework Statement

Find the general solution of

[tex] u_{xx} + u = 6y, [/tex]

in terms of arbitrary functions.

## Homework Equations

The PDE has the homogeneous solution, [tex] u(x,y)=Acos(x)+Bsin(x) [/tex].

[tex] u_{xx} + u = 6y [/tex] has the particular solution, [tex] u(x,y)=6y [/tex]

## The Attempt at a Solution

Taking a superposition of the homogeneous and particular solutions, we can write that

u(x,y)=Acos(x)+Bsin(x)+6y. <--my solution

My question is, how do I know whether or not this is *the* most general solution? How do I know that I haven't missed something?