Finding energy levels in an potential well (finite)

Crucifix

I'm a little lost on one detail of the titular problem.
Basically I want to use the boundary conditions to get a transcendental equation which I have to use trial and error with to find the energy levels. Now, I seem to remember being told I take the wave eq ASinkx+BCoskx, and just take odd or even (Sin or Cos) and barrel on which is fine. But my question is if I pick say odd, do I have to go back and do it again with the even, or would that just give me the same answers? Thanks in advance.

Son Goku

Usually you would have to take both.

However that's a very generic answer, what are the actual boundary conditions.

Crucifix

The wavefunctions should be equal at the boundarys, aswell as the differentiate of the wavefunctions. So at that point I'd break it down to even or odd, and then set the differentiate divided by the wavefunction for each region equal to each other, and from that I'll get down to a tan or a cotan of something equal to a square root of something (can't remember off hand), and they've both got the energy in them so I have to do the trial and error.
I'll try doing out the other way anyway, thanks.