# Wolfram Language & System 10.4 (2016)|Legacy Documentation

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

# DEigenvalues

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

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

## Details and OptionsDetails and Options

• DEigenvalues can compute eigenvalues for ordinary and partial differential operators with given boundary conditions.
• DEigenvalues gives a list of the n smallest magnitude eigenvalues .
• 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[DEigenvalues[]] calls NDEigenvalues for eigenvalues that cannot be computed symbolically.
• The Assumptions option can be used to specify assumptions on parameters.

## ExamplesExamplesopen allclose all

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

Find the 4 smallest eigenvalues of the Laplacian operator on :

 In[1]:=
 Out[1]=

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

 In[1]:=