SolvePDE 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[] == , y'[] == , 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. Examples Using InstantCalculators Here are the InstantCalculators for the SolvePDE function. Enter the parameters for your calculation and click Calculate to see the result. In[1]:= Out[1]= In[2]:= Entering Commands Directly You can paste a template for this command via the Text Input button on the SolvePDE Function Controller. In[3]:= Out[3]=

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