Second Order, Bessel-type Differential equation

To solve the differential equations of the standard form,

`xy''+ay'+by=0`

has the solutions, for `bx>0`,

`y=x^((1-a)/2)[c_1J_v(2sqrt(bx)+c_2Y_v(2sqrt(bx)]`

and for `bx<0`,

`y=x^((1-a)/2)[c_1I_v(2sqrt(|bx|)+c_2K_v(2sqrt(|bx|)]`

where J_v is the Bessel Function of the First Kind; Y_v, is the Bessel Function of the Second Kind; I_v, is the Modified Bessel Function First Kind, and K_v, is the Modified Bessel Function of the Second Kind. For their definitions, see here.