The differential equation $x ^ { 2 } y ^ { \prime \prime } + x y ^ { \prime } + \left( x ^ { 2 } - 1 / 25 \right) y = 0$ is
A) Bessel's equation of order $n$
B) Bessel's equation of order 1/25
C) Bessel's equation of order 1/5
D) Legendre's equation of order 1/25
E) Legendre's equation of order 1/5

Question

Quizplus · Accepted Answer

The given differential equation is a Bessel's equation of the form $x^2y'' + xy' + (x^2 - \alpha^2)y = 0$, where $\alpha^2 = 1/25$, thus $\alpha = 1/5$. This makes it a Bessel's equation of order 1/5.

The Differential Equation x2y′′+xy′+(x2−1/25)y=0x ^ { 2 } y ^ { \prime \prime } + x y ^ { \prime } + \left( x ^ { 2 } - 1 / 25 \right) y = 0x2y′′+xy′+(x2−1/25)y=0

The Differential Equation $x ^ { 2 } y ^ { \prime \prime } + x y ^ { \prime } + \left( x ^ { 2 } - 1 / 25 \right) y = 0$