>12

それは変形ベッセル方程式(n=0)。　一般解は
　y = c1･I_0(x) + c2･K_0(x),
ここに
I_0(x) = Σ[k=0,∞) (1/k!)^2 (z/2)^(2k),
K_0(x) = ∫[0,∞) cos(x･sinh(t)) dt = ∫[0,∞) cos(xs) /√(1+s^2) ds,

http://mathworld.wolfram.com/ModifiedBesselDifferentialEquation.html
http://mathworld.wolfram.com/ModifiedBesselFunctionoftheFirstKind.html
http://mathworld.wolfram.com/ModifiedBesselFunctionoftheSecondKind.html