Step by Step 2D Laplace (sorta) Equation on a Square Domain
In the following video, I describe how you can solve the partial differential equation Laplacian u = 16u on a square domain with a lot of homogenous boundary conditions. The idea is to solve the ODE with the most homogenous boundary conditions related to it. Then using the information from that ODE solve for the other one. Superposing solutions and using the final boundary condition we can solve for the function u(x,y) that satisfies the PDE and its boundary conditions. Like most partial differential equations you apply the separation of variables. Thanks for watching the video if you found my video valuable please like and subscribe.Best, KobeTutors.