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SolvePDE[eqns, y, {x, xmin, xmax}] finds a numerical solution to the ordinary differential equations eqns for the function y with the independent variable x in the range xmin to xmax.
SolvePDE[eqns, y, {x, xmin, xmax}, {t, tmin, tmax}] finds a numerical solution to the partial differential equations eqns.
SolvePDE[eqns, { ,  , ... }, {x, xmin, xmax}] finds numerical solutions for the functions  .

SolvePDE gives results in terms of InterpolatingFunction objects.
SolvePDE[eqns, y[x], {x, xmin, xmax}] gives solutions for y[x] rather than for the function y itself.
SolvePDE solves a wide range of ordinary differential equations, and some partial differential equations.
• In ordinary differential equations, the functions  must depend only on the single variable x. In partial differential equations, they may depend on more than one variable.
• The differential equations must contain enough initial or boundary conditions to determine the solutions for the  completely.
• Initial and boundary conditions are typically stated in form y[ ] Equal  , y'[ ] Equal  , etc., but may consist of more complicated equations.
• The point  that appears in the initial or boundary conditions need not lie in the range xmin to xmax over which the solution is sought.
• The differential equations in SolvePDE can involve complex numbers.
• See also:
D, Integrate, ND, NIntegrate, SolveEquation.


Using InstantCalculators

Here are the InstantCalculators for the SolvePDE function. Enter the parameters for your calculation and click Calculate to see the result.

Entering Commands Directly

You can paste a template for this command via the Text Input button on the SolvePDE Function Controller.