Boundary value problem

Boundary value eigenvalue problem

A boundary value eigenvalue problem involves finding the various eigenfunctions that can satisfy boundary conditions. For example¹

𝑑𝑦𝑑𝑥+𝜆𝑦=0

with boundary conditions

𝑦(0)=0,𝑦(𝜋)=0

has eigenfunctions of the form

𝑦=sin⁡(𝑛𝑥)

with eigenvalues 𝜆 =𝑛2.

Practice problems

• 2017. Elementary differential equations and boundary value problems, p. 468 (§10.1 problems)

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Footnotes

1. 2017. Elementary differential equations and boundary value problems, pp. 466ff. ↩