Equation Solving

Solve algebraic and differential equations

You can solve algebraic equations, differential equations, and differential algebraic equations (DAEs).

Solve algebraic equations to get either exact analytic solutions or high-precision numeric solutions. For analytic solutions, use solve, and for numerical solutions, use vpasolve. For solving linear equations, use linsolve. These solver functions have the flexibility to handle complicated problems. See Troubleshoot Equation Solutions from solve Function.

Solve differential equations by using dsolve. Create these differential equations by using symbolic functions. See Create Symbolic Functions.

Solve differential algebraic equations (DAEs) by first reducing their differential index to 1 or 0 using Symbolic Math Toolbox™ functions, and then using MATLAB® solvers, such as ode15i, ode15s, or ode23t. See Solve Differential Algebraic Equations (DAEs).

Live Editor Tasks

Solve Symbolic EquationFind analytic solutions of symbolic equations in Live Editor

Functions

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equationsToMatrixConvert linear equations to matrix form
eliminateEliminate variables from rational equations
finverseFunctional inverse
linsolveSolve linear equations in matrix form
polesPoles of expression or function
solveEquations and systems solver
vpasolveSolve equations numerically
dsolveSolve system of differential equations
massMatrixFormExtract mass matrix and right side of semilinear system of differential algebraic equations
odeFunctionConvert symbolic expressions to function handle for ODE solvers
odeToVectorFieldReduce order of differential equations to first-order
daeFunctionConvert system of differential algebraic equations to MATLAB function handle suitable for ode15i
decicFind consistent initial conditions for first-order implicit ODE system with algebraic constraints
findDecoupledBlocksSearch for decoupled blocks in systems of equations
incidenceMatrixFind incidence matrix of system of equations
isLowIndexDAECheck if differential index of system of equations is lower than 2
massMatrixFormExtract mass matrix and right side of semilinear system of differential algebraic equations
odeFunctionConvert symbolic expressions to function handle for ODE solvers
reduceDAEIndexConvert system of first-order differential algebraic equations to equivalent system of differential index 1
reduceDAEToODEConvert system of first-order semilinear differential algebraic equations to equivalent system of differential index 0
reduceDifferentialOrderReduce system of higher-order differential equations to equivalent system of first-order differential equations
reduceRedundanciesSimplify system of first-order differential algebraic equations by eliminating redundant equations and variables

Topics

Solve Algebraic Equation

Solve equations, return full solutions, and visualize results.

Solve Differential Equation

Solve a differential equation analytically by using the dsolve function, with or without initial conditions.

Solve Differential Algebraic Equations (DAEs)

This example show how to solve differential algebraic equations (DAEs) by using MATLAB® and Symbolic Math Toolbox™.

Featured Examples

The Physics of the Damped Harmonic Oscillator

The Physics of the Damped Harmonic Oscillator

Explores the physics of the damped harmonic oscillator by

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Solving Partial Differential Equations

Solving Partial Differential Equations

Simulates the tsunami wave phenomenon by using the Symbolic Math Toolbox™ to solve differential equations.

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Validate Simulink Model Using Symbolic Math Toolbox

Validate Simulink Model Using Symbolic Math Toolbox

Model a bouncing ball, which is a classical hybrid dynamic system. This model includes both continuous dynamics and discrete transitions. It uses the Symbolic Math Toolbox to help explain some of the theory behind ODE solving in the Simulink® Model of a Bouncing Ball.

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Analyze and Manipulate Differential Algebraic Equations

Analyze and Manipulate Differential Algebraic Equations

Solve differential algebraic equations (DAEs) of high differential index using Symbolic Math Toolbox™.

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Derive and Apply Inverse Kinematics to Two-Link Robot Arm

Derive and Apply Inverse Kinematics to Two-Link Robot Arm

Derives and applies inverse kinematics to a two-link robot arm by using MATLAB® and Symbolic Math Toolbox™.

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Solve a Second-Order Differential Equation Numerically

Solve a Second-Order Differential Equation Numerically

Convert a second-order differential equation into a system of differential equations that can be solved using the numerical solver ode45 of MATLAB®.

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Gauss-Laguerre Quadrature Evaluation Points and Weights

Gauss-Laguerre Quadrature Evaluation Points and Weights

Solve polynomial equations and systems of equations, and work with the results using Symbolic Math Toolbox™.

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Simulate a Stochastic Process by Feynman-Kac Formula

Simulate a Stochastic Process by Feynman-Kac Formula

Obtains the partial differential equation that describes the expected final price of an asset whose price is a stochastic process given by a stochastic differential equation.

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The Black–Scholes Formula for Call Option Price

The Black–Scholes Formula for Call Option Price

Calculate the call option price using the Black–Scholes formula. This example uses vpasolve to numerically solve the problems of finding the spot price and implied volatility from the Black–Scholes formula.

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Symbolic Math Toolbox Documentation

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