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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 Set Up Your DAE Problem.

Functions

equationsToMatrix Convert set of linear equations to matrix form
finverse Functional inverse
linsolve Solve linear system of equations given in matrix form
poles Poles of expression or function
solve Equations and systems solver
vpasolve Numeric solver
dsolve Differential equations and systems solver
massMatrixForm Extract mass matrix and right side of semilinear system of differential algebraic equations
odeFunction Convert system of symbolic algebraic expressions to MATLAB function handle suitable for ode45, ode15s, and other ODE solvers
odeToVectorField Convert higher-order differential equations to systems of first-order differential equations
daeFunction Convert system of differential algebraic equations to MATLAB function handle suitable for ode15i
decic Find consistent initial conditions for first-order implicit ODE system with algebraic constraints
findDecoupledBlocks Search for decoupled blocks in systems of equations
incidenceMatrix Find incidence matrix of system of equations
isLowIndexDAE Check if differential index of system of equations is lower than 2
massMatrixForm Extract mass matrix and right side of semilinear system of differential algebraic equations
odeFunction Convert system of symbolic algebraic expressions to MATLAB function handle suitable for ode45, ode15s, and other ODE solvers
reduceDAEIndex Convert system of first-order differential algebraic equations to equivalent system of differential index 1
reduceDAEToODE Convert system of first-order semilinear differential algebraic equations to equivalent system of differential index 0
reduceDifferentialOrder Reduce system of higher-order differential equations to equivalent system of first-order differential equations
reduceRedundancies Simplify system of first-order differential algebraic equations by eliminating redundant equations and variables

Featured Examples

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