The differential equation is $\left( 1 - x ^ { 2 } \right) y ^ { \prime \prime } - 2 x y ^ { \prime } + 12 y = 0$ is
A) Bessel's equation of order 12
B) Bessel's equation of order 3
C) Legendre's equation of order 12
D) Legendre's equation of order 3
E) Legendre's equation of order 4

Question

Quizplus · Accepted Answer

The given differential equation matches the standard form of Legendre's equation, $(1-x^2)y'' - 2xy' + n(n+1)y = 0$, with $n(n+1) = 12$. Solving for $n$, we find $n = 3$.

The Differential Equation Is (1−x2)y′′−2xy′+12y=0\left( 1 - x ^ { 2 } \right) y ^ { \prime \prime } - 2 x y ^ { \prime } + 12 y = 0(1−x2)y′′−2xy′+12y=0

The Differential Equation Is $\left( 1 - x ^ { 2 } \right) y ^ { \prime \prime } - 2 x y ^ { \prime } + 12 y = 0$