If n is an integer, use the substitution R(x) = (x) -1/2 Z(x) to show that the general solution of the differential equation x 2

If n is an integer, use the substitution R(x) = (αx)^-1/2Z(x) to show that the general solution of the differential equation

x²R'' + 2xR'' + [α²x² - n(n + 1)]R = 0

on the interval (0, ∞) is R(x) = c₁j_n(αx) + c₂y_n(αx), where j_n(αx) and y_n(αx) are the spherical Bessel functions of the first and second kind defined in (27).