Differntial of wave equation solution

[bfed]

Homework Statement

consider the differential d²ψ(x)/dx²=k²ψ(x); for which values of a is the equation e^(a*x) is a solution to the above equation.

Homework Equations

The Attempt at a Solution

I have been working on this problem but I do not know how relate the 2 equations, or if I should use the Schrödinger equation. Any help is greatly appreciated.

 

[dacruick]

You may encounter some more help if you post this under the right name. This is probably more quantum mechanics than it is introductory physics. and Is psi(x) = e^(a*x)?