Please show clear working and steps

2. (a) The Airy function Ai(2) is the unique solution to the ordinary differential equation d2 1 x Ai(x) = 0 subject to lim Ai(x) = 0 and Ai(0) w3 COS dw. dx2 Ai(x) 2-too 3 By applying the Fourier transform to the equation, determine an integral representation for Ai(2) that does not have any imaginary numbers in it. (b) If k = 0 is a constant and f(x) an arbitrary function satisfying l \f(x) dx