The differential equation $\left( 1 - x ^ { 2 } \right) y ^ { \prime \prime } - 2 x y ^ { \prime } + \lambda y = 0$ is
A) Legendre's equation
B) Bessel's equation
C) the Fourier-Bessel
D) the hypergeometric
E) none of the above

Question

Quizplus · Accepted Answer

This is the standard form of Legendre's differential equation, characterized by the presence of $(1-x^2)y'' - 2xy' + \lambda y = 0$, where $\lambda$ is a constant. This equation is fundamental in solving problems in physics and engineering that exhibit spherical symmetry.

The Differential Equation (1−x2)y′′−2xy′+λy=0\left( 1 - x ^ { 2 } \right) y ^ { \prime \prime } - 2 x y ^ { \prime } + \lambda y = 0(1−x2)y′′−2xy′+λy=0

The Differential Equation $\left( 1 - x ^ { 2 } \right) y ^ { \prime \prime } - 2 x y ^ { \prime } + \lambda y = 0$