Definition

$X'' (x) + \lambda X(x) = 0 \quad _{0<x<c},\quad X(0)=0,\quad X(c)=0$

If eigenvalue $λ = λ_{n} = \frac{n ^{2} π ^{2}}{c ^{2}}_{(n = 1, 2, 3, \dots)}$ then eigen function $X_{n} (x) = sin \frac{nπ x}{c}_{(n = 0, 1, 2, \dots)}$ If $λ \neq = λ_{n}_{(n = 1, 2, 3, \dots)}$ then $X (x) = 0$ is the only solution of problem