Differential Equations

Automatically selecting between hundreds of powerful and in many cases original algorithms, the Wolfram Language provides both numerical and symbolic solving of differential equations (ODEs, PDEs, DAEs, DDEs, ...). With equations conveniently specified symbolically, the Wolfram Language uses both its rich set of special functions and its unique symbolic interpolating functions to represent solutions in forms that can immediately be manipulated or visualized.

y'[x] (Derivative) derivative of a function

DSolve symbolic solution to differential equations

DSolveValue find an expression for the symbolic solution of a differential equation

NDSolve numerical solution to differential equations

InterpolatingFunction interpolating function used in solutions

ParametricNDSolveValue numerical solution to differential equations with parameters

NDSolveValue  ▪  ParametricNDSolve  ▪  ParametricFunction

Differential Equations with Events »

WhenEvent actions to be taken whenever an event occurs in a differential equation

Partial Differential Equations »

DirichletCondition specify Dirichlet conditions for partial differential equations

NeumannValue specify Neumann and Robin conditions

PeriodicBoundaryCondition specify periodic boundary conditions

D  ▪  Grad  ▪  Div  ▪  Curl  ▪  Laplacian  ▪  ...

Differential Eigen Problems

NDEigensystem numerical eigenvalues and eigenfunctions from a differential equation

NDEigenvalues numerical eigenvalues from a differential equation

DEigensystem symbolic eigenvalues and eigenfunctions from differential equations

DEigenvalues symbolic eigenvalues from a differential equation


NBodySimulation simulation of idealized n-body systems

SystemModelSimulate simulate a wide range of system models


AccuracyGoal  ▪  PrecisionGoal  ▪  WorkingPrecision

Method select and tune many possible solver algorithms

StepMonitor, EvaluationMonitor monitor the progress of a solution

Method Functions

GreenFunction Green's function for a differential equation

CompleteIntegral complete integral for a first-order partial differential equation

Wronskian test linear independence of functions or ODE solutions

Orthogonalize  ▪  Normalize

Differential Functions »

DifferentialRoot representation of solutions to linear differential equations

Visualization »

Plot  ▪  StreamPlot  ▪  VectorPlot