Hi, I have this problem, but I am stuck in one thing.

Assuming that solutions to are of the form , and that the separation constant is negative, written as with , I need to show that and must satisfy the differential equations

, and

So well, I kind know what to do once I have substituted into ... However, I keep on getting the wrong results:

I get this:

But this is clearly not what should be on both sides :/

I would really appreciate it if any of you could give me a hand. Once I get both results on each side, I will be able to separate the variables.

Thanks a lot!