Equation Solving
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 Choose an Approach for Solving Equations Using 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 Equation | Find analytic solutions of symbolic equations in Live Editor |
Functions
Topics
- Solve Algebraic Equations
Solve equations analytically, return full solutions, and visualize results.
- Solve Differential Equation
Solve a differential equation analytically by using the
dsolvefunction, 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™.
Related Information
Featured Examples
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Apply the finite element method (FEM) to solve a Timoshenko beam problem, using both linear and quadratic basis functions for analysis. The Timoshenko beam theory is a 1-D problem that reduces the complex 3-D problem of beam deformation to a set of 1-D differential equations along the length of the beam. In contrast to the Euler–Bernoulli beam theory, which does not consider shear deformation, the Timoshenko beam theory accounts for both shear deformation and rotational bending effects. The Timoshenko beam theory is generally more accurate for short, thick beams where shear deformation cannot be neglected. Using a cantilever beam and a beam fixed at both ends, this example discusses the analytical solutions of the Timoshenko beam problem and compares them with the FEM solutions.
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Analyze the transfer function of a T-coil circuit using Symbolic Math Toolbox™ and Control System Toolbox™. In this example, you define symbolic equations, solve for the transfer function, and analyze the stability, frequency response, and step response of the circuit.
