Tiny question on differential (?) equations.

[Lisa...]

For the potential in an electric field is given:

http://img402.imageshack.us/img402/4162/naamloos8zn.gif

At x=0 V(x) is at a minimum so:

dV/dx =0 and d²V/dx²= kQ/(2 sqrt{2} L³)

Why does it follow that:

V(x) must be in the form V(x)= V(0) + @ x² where V(0)= (sqrt{2} kQ)/L and the constant @ = kQ/ (sqrt{2} L ³) ?

Note that I haven't learned much yet on solving differential equations.

 

[Lisa...]

Doesn't @ need to be kQ/ (4 sqrt {2} L ³)

 

[Astronuc]

Think about V(-x), i.e. is V(x) and odd or even function?