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Ordinary Differential Equations

Solve ODEs analytically, test solutions

MuPAD Functions

ode::exponentialSolutions Exponential solutions of a homogeneous linear ordinary differential equation
ode::polynomialSolutions Polynomial solutions of a homogeneous linear ordinary differential equation
ode::rationalSolutions Rational solutions of a homogeneous linear ordinary differential equation
ode::series Series solutions of an ordinary differential equation
ode::solve Solving ordinary differential equations
ode Domain of ordinary differential equations
ode::companionSystem Companion matrix of a linear homogeneous ordinary differential equation
ode::cyclicVector Transforms a linear differential system to an equivalent linear differential system with a companion matrix.
ode::dAlembert D'Alembert reduction of a linear homogeneous ordinary differential equation
ode::evalOde Applies an expression at a linear ordinary differential equation
ode::exponents Exponents of a linear ordinary differential equation
ode::getOrder Order of an ordinary differential equation
ode::indicialEquation Indicial equation of a linear ordinary differential equation
ode::isFuchsian Tests if a homogeneous linear ordinary differential equation is of Fuchsian type
ode::isLODE Test for a linear ordinary differential equation
ode::mkODE Builds a linear homogeneous ordinary differential equation from a list of coefficient functions
ode::normalize Normalized form of a linear ordinary differential equation
ode::ratSys Rational solutions of a first order homogeneous linear differential system
ode::scalarEquation Transforms a linear differential system to an equivalent scalar linear differential equation
ode::symmetricPower Symmetric power of a homogeneous linear ordinary differential equation
ode::unimodular Unimodular transformation of a linear ordinary differential equation
ode::vectorize Coefficients of a homogeneous linear ODE
ode::wronskian Wronskian of functions or of a linear homogeneous ordinary differential equation

Examples and How To

Choose a Solver

The general solvers (solve for symbolic solutions and numeric::solve for numeric approximations) handle a wide variety of equations, inequalities, and systems.

Solve Ordinary Differential Equations and Systems

An ordinary differential equation (ODE) contains derivatives of dependent variables with respect to the only independent variable.

Test Results

Suppose you want to verify the solutions of this polynomial equation:

Concepts

If Results Look Too Complicated

By default, the MuPAD® solvers return all possible solutions regardless of their length.

If Results Differ from Expected

Symbolic solutions can be returned in different, but mathematically equivalent forms.

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