# Wolfram Mathematica

## Compute Symbolic Eigenvalues

Specify a 1D Laplacian operator.

In[1]:=
`\[ScriptCapitalL] = -Laplacian[u[x], {x}];`

Specify a homogeneous Dirichlet boundary condition.

In[2]:=
`\[ScriptCapitalB] = DirichletCondition[u[x] == 0, True];`

Find expressions for the 5 smallest eigenvalues on the interval .

In[3]:=
```DEigenvalues[{\[ScriptCapitalL], \[ScriptCapitalB]}, u[x], {x, a, b}, 5]```
Out[3]=

Specify an Airy operator.

In[4]:=
`\[ScriptCapitalL] = -Laplacian[u[x], {x}] + x u[x];`

Find the 5 smallest eigenvalues and corresponding eigenfunctions.

In[5]:=
```{vals, funs} = DEigensystem[{\[ScriptCapitalL], \[ScriptCapitalB]}, u[x], {x, 0, 1}, 5];```

The eigenvalues are roots of a transcendental equation.

In[6]:=
`vals[[1]] // TraditionalForm`

Compute a transcendental eigenvalue with high precision.

In[7]:=
`N[vals[[1]], 500] // TraditionalForm`
```Plot[Evaluate[funs + Range[5]], {x, 0, 1}, ImageSize -> Medium, PlotTheme -> {"Business", "Bare"}, AspectRatio -> 1]```