(Airy equation)For the Airy equation,y″− xy −0, (−∞ < x < ∞) (9.1)derive the power s...

(Airy equation)For the Airy equation,

y″− xy −0, (−∞ < x < ∞) (9.1)

derive the power series solution

and verify that it is a general solution. NOTE: These series are not summable in closed form in terms of elementary functions thus, certain linear combinations of r/i andp2are adopted as a usable pair of LI solutions. In particular, it turns out to be convenient (for reasons that are not obvious) to use the Airy functions Ai(x) and Bi (x),which satisfy these initial conditions:Ai(0) = 0.35502,Ai′ (0) = −0.25881 and Bi(0) = 0.61493, Bi ′ (0) = 0.44829.