# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# DEigensystem

DEigensystem[[u[x,y,]],u,{x,y,}Ω,n]
gives the n smallest magnitude eigenvalues and eigenfunctions for the linear differential operator over the region Ω.

DEigensystem[eqns,u,t,{x,y,}Ω,n]
gives the eigenvalues and eigenfunctions for solutions u of the time-dependent differential equations eqns.

## Details and OptionsDetails and Options

• DEigensystem can compute eigenvalues and eigenfunctions for ordinary and partial differential operators with given boundary conditions.
• DEigensystem gives lists of eigenvalues and eigenfunctions .
• An eigenvalue and eigenfunction pair for the differential operator satisfy .
• Homogeneous DirichletCondition or NeumannValue boundary conditions may be included. Inhomogeneous boundary conditions will be replaced with corresponding homogeneous boundary conditions.
• When no boundary condition is specified on the boundary Ω, then this is equivalent to specifying a Neumann 0 condition.
• The equations eqns are specified as in DSolve.
• N[DEigensystem[]] calls NDEigensystem for eigensystems that cannot be computed symbolically.
• The following options can be given:
•  Assumptions \$Assumptions assumptions on parameters Method Automatic what method to use
• Eigenfunctions are not automatically normalized. The setting Method->"Normalize" can be used to give normalized eigenfunctions.

## ExamplesExamplesopen allclose all

### Basic Examples  (2)Basic Examples  (2)

Find the 4 smallest eigenvalues and eigenfunctions of the Laplacian operator on :

 Out[1]=

Visualize the eigenfunctions:

 Out[2]=

Compute the first 6 eigenfunctions for a circular membrane with the edges clamped:

 Out[2]=

Visualize the eigenfunctions:

 Out[3]=