Separation of Variables - Laplace Eq Part 1

We use Separation of Variables to solve the Laplace Equation, including boundary conditions.

[Muradsahar]

Is the choice of lambda (negative or positive) based on, if it can get DE with positive or negative constant coefficient.?

[ricky]

why is Y(y) not a complex function? From my class notes, is k^2 is negative it's sin+cos, but if it's positive then the solution to the de is a function of sinh(ix) + cos(ix)

[jacobmoralesgonzalez]

lambda=0 ends up being a trivial answer that not fulfill the boundary conditions, but lambda>0 has non trivial solutions (and that fulfill the boundary conditions)?

[Muradsahar]

The answer could have been sinusoidal in second ODE, (y(y)), why didn't you write it in Sine and cosine.?

[sakshamchopra]

Sir why you have not taken d^2x/dx^2 = -lamda × Y?

[thelastpigeon]

Should there not be a B sub n at 6:53?

[adgilbert]

Please how do I approach a problem with two non-homogeneous boundary conditions?
Thank you

[theopdiamond]

Your proof for the separation of variables is inconclusive at point where F or G are 0. At those points you cant divide by FG

[apoorvvyas]

why is summation of n started from 1 and not zero?