Timeline for Solutions of $\Delta \phi + \phi =0$ on $\mathbb{R}^2$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 7, 2019 at 14:19 | comment | added | Willie Wong | This set is however not the full set of solutions, though. The second example given in Francois' answer is not in this form. This looks like the set of stuff you get from separation of variables (which incidentally, immediately tells you that $e^{\pm x}$ and $e^{\pm y}$ are unbounded solutions to the original PDE). | |
| Oct 6, 2019 at 10:30 | comment | added | user64494 | From the help: "The strategy pdsolve uses is to look for the most general solution to the given PDE or, in the worst case, to look for a complete separation of variables. Thus, when successful, the command returns one of the following: - A general solution, - A quasi-general solution (a solution containing arbitrary functions, but not in sufficient number or not having enough variables to constitute a general solution), or - A set of uncoupled ODEs with all the variables separated, or a complete solution obtained after integrating this set (when the option INTEGRATE is indicated) ". | |
| Oct 6, 2019 at 9:35 | comment | added | April | Great! This answers first part of my first question. Just a small clarification - what really is the Maple command supposed to produce? Is it a class of functions which solves the equation? I am just wondering how/why it chooses one class of examples over some other class (for instance the class of functions $G$ I mentioned in the question)? | |
| Oct 6, 2019 at 7:48 | history | edited | user64494 | CC BY-SA 4.0 |
deleted 9 characters in body
|
| Oct 6, 2019 at 7:41 | history | answered | user64494 | CC BY-SA 4.0 |