Question

Bessel and legendre differential equation

Answer 1

x
2
y
00 + xy0 + (x
2 − ν
2
)y = 0 , ν ∈ [0,∞) , x ∈ [0, ∞) (1)
(1 − x
2
)y
00 − 2xy0 + n(n + 1)y = 0 , n = 1, 2, . . . , x ∈ (−1, 1) (2)