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Ordinary Differential Equations

Solve ODEs analytically, test solutions

MuPAD Functions

ode::exponentialSolutionsExponential solutions of a homogeneous linear ordinary differential equation
ode::polynomialSolutionsPolynomial solutions of a homogeneous linear ordinary differential equation
ode::rationalSolutionsRational solutions of a homogeneous linear ordinary differential equation
ode::seriesSeries solutions of an ordinary differential equation
ode::solveSolving ordinary differential equations
odeDomain of ordinary differential equations
ode::companionSystemCompanion matrix of a linear homogeneous ordinary differential equation
ode::cyclicVectorTransforms a linear differential system to an equivalent linear differential system with a companion matrix.
ode::dAlembertD'Alembert reduction of a linear homogeneous ordinary differential equation
ode::evalOdeApplies an expression at a linear ordinary differential equation
ode::exponentsExponents of a linear ordinary differential equation
ode::getOrderOrder of an ordinary differential equation
ode::indicialEquationIndicial equation of a linear ordinary differential equation
ode::isFuchsianTests if a homogeneous linear ordinary differential equation is of Fuchsian type
ode::isLODETest for a linear ordinary differential equation
ode::mkODEBuilds a linear homogeneous ordinary differential equation from a list of coefficient functions
ode::normalizeNormalized form of a linear ordinary differential equation
ode::ratSysRational solutions of a first order homogeneous linear differential system
ode::scalarEquationTransforms a linear differential system to an equivalent scalar linear differential equation
ode::symmetricPowerSymmetric power of a homogeneous linear ordinary differential equation
ode::unimodularUnimodular transformation of a linear ordinary differential equation
ode::vectorizeCoefficients of a homogeneous linear ODE
ode::wronskianWronskian 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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