1. The problem statement, all variables and given/known data In aerodynamics, one encounters the following initial value problem for Airy’s equations: y''(x) + xy = 0, y(0) = 1, y'(0) = 0 Using the Runge-Kutta method with h=0.005 and determine values between x=0 and x=10 sufficient to sketch the relationship. 2. Relevant equations y''(x) + xy = 0, y(0) = 1, y'(0) = 0 I think, k1 = h*f(Xn, Yn) k2 = h*f(Xn+h/2, Yn+k1/2) k3 = h*f(Xn+h/2, Yn+k2/2) k4 = h*f(Xn + h, Yn + k3) 3. The attempt at a solution From what I have read you cant do second order ODE using runge kutta without breaking it into a system of first order ODEs so thats what I tried. I tried: d2y/dx2 + xy = 0 dy/dx = z, y(0) = 1 dz/dx + xy = 0 dz/dx = -xy, z(0) = 0 I dont know if that is right or not and if it is I have no idea where to go from here. Thanks for any help.