# A more general Bessel equation?

1. Nov 5, 2009

### ZumaBird

In the solution to a recent problem set, my prof referenced a "general Bessel ODE" which he gave in the form:

$$x^{2}\frac{d^{2}y}{dx^{2}}+x\left(a+2bx^{q}\right)\frac{dy}{dx}+\left[c+dx^{2s}-b\left(1-a-q\right)x^{q}+b^{2}x^{2q}\right]y=0$$

The only format of the Bessel ODE that appears in the coursenotes is:

$$x^{2}\frac{d^{2}y}{dx^{2}}+x\frac{dy}{dx}+\left(x^{2}-b^{2}\right)y=0$$

Does anybody recognize the first form and know the general solution in terms of the modified and unmodified Bessel functions of the first and second kinds?

Last edited: Nov 5, 2009