PDEs occur naturally in applications; they model the rate of change of a physical quantity with respect to both space variables and time variables. At this stage of development, DSolve typically only works with PDEs having two independent variables.
Here are some well-known examples of PDEs (clicking a link in the table will bring up the relevant examples). DSolve gives symbolic solutions to equations of all these types, with certain restrictions, particularly for second-order PDEs.
name of equation
|transport equation||with constant||linear first-order PDE|
|Burgers' equation||quasilinear first-order PDE|
|eikonal equation||nonlinear first-order PDE|
|Laplace's equation||elliptic linear second-order PDE|
|wave equation||where is the speed of light||hyperbolic linear second-order PDE|
|heat equation||where is the thermal diffusivity||parabolic linear second-order PDE|