Laplace in Three Dimensions: [math]\frac{\partial^2 u}{\partial x^2} +\frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} = 0[/math]

[mario99]

[math]\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} = 0[/math]

Does anyone have an idea of how to solve the three dimensional Laplace partial differential equation?​

 

[khansaheb]

[math]\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} = 0[/math]

Does anyone have an idea of how to solve the three dimensional Laplace partial differential equation?​

Start the same way as you did while solving 2-D Laplace equations.

 

[mario99]

Start the same way as you did while solving 2-D Laplace equations.

The book is also suggesting that I proceed to solve it like the 2D as you mentioned, but it didn't provide a single example of 3D. I tried it. The constant that I usually assign it to the separated equations gets lost somewhere in the solution when I work in third equation. I watched a video to someone who solves it differently, but the solution gets very complicated after a few steps. Is there an example of solving a complete 3D Laplace problem with clear steps?

Have you ever solved a problem like this??