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.

ReferenceReference

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

DSolve symbolic solution to differential equations

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

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

Options

AccuracyGoal  ▪  PrecisionGoal  ▪  WorkingPrecision

Method select and tune many possible solver algorithms

StepMonitor, EvaluationMonitor monitor the progress of a solution

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