What Conditions Make This Differential Operator Self-Adjoint?

[MarkovMarakov]

Homework Statement

When is the following operator self-adjoint? I am looking for constraints on $f_n$'s s.t. The operator below becomes self-adjoint.

$O:= \sum_{n=0}^4 f_n(x){d^n\over dx^n}$ subjected to boundary conditions $y(0)=y'(0)=y(1)=y'(1)=0$ and where $f_n$'s are real functions.

Thanks.

Homework Equations

See above.

The Attempt at a Solution

Totally clueless. Please help.

 

[HallsofIvy]

Well, what is the definition of "self adjoint"? That would be a good place to start.