(a) Show that Bessel’s equation of order 1,xy″ + xy′ + (x2 − 1)y = 0, has exponents r1 = 1...

(a) Show that Bessel’s equation of order 1,

xy″ + xy′ + (x2 − 1)y = 0, has exponents r1 = 1 and r2 = −1 at x = 0, and that the Frobenius series corresponding to r1 = 1 is

(b) Show that there is no Frobenius solution corresponding to the smaller exponent r2 = −1; that is, show that it is impossible to determine the coefficients in