I want to find the eigenvalues and the eigenfunctions of the operator

$\displaystyle ({d^{2}}/{dx^{2}})+k $

so we have the problem

$\displaystyle ({d^{2}y_{n}}/{dx^{2}})+ky_{n}=L_{n} y_{n} $

Now I put in the functie y=A*exp(n*x), is it correct to do this?, and get the equation

$\displaystyle n^{2}+k-L_{n} =0 $

so Ln=n^2+k

but acording to the solutions it has to be Ln=n^2-k. Where do I make the mistake?

and how do I exactly determine the eigenfunctions

thanks