1. The given equation is $$x^2 y'' + x y' + (x^2 - \nu^2) y = 0$$. 2. This is a standard form of Bessel's equation of the first kind. 3. The parameter \(\nu\) (nu) in this equation represents the order or index of the Bessel function. 4. Therefore, the equation is called "Bessel's equation of index \(\nu\)". 5. Comparing with the options, the correct choice is option (a).