Question while calculating the solution to Laplace using separation of vars

[Zhonghan CHEN]

Hi Prof:

I have a question for solving the Laplacian operation using the separation of variables.
Slide: Week 9 Lecture 1 Page 4.

The queston happens in solving ${\theta}'' + \lambda \theta = 0$.

Q: I do not understand how do you derive the $\lambda_{n} = n^2$.

Also, I do not understand why we can get a expression for $\lambda$ ? To my understading, $\lambda$ is just a constant in the ODE.

Thanks

[Victor Ivrii]

Section 4.1ODE is not enough. You need to take into account also boundary conditions. See Section 4.1