The equation we wish to solve is f''' + (1/2)*f*f'' with f(0) = 0, f'(0) = 0, f'(inf) = 1. This equation arises in the theory of fluid boundary layers, and must be solved numerically. We recast this problem as a system of first-order ODEs: y = [f; f'; f''] = [y(1); y(2); y(3)] so that dy/dEta = y' = [f'; f''; f'''] = [y(2); y(3); -(1/2)*y(1)*y(3)] with y(1)(0) = 0, y(2)(0) = 0, y(2)(inf) = 1. This new system of equations may then be solved numerically using the shooting method. For a description of this numerical method, please follow the given link: https://en.wikipedia.org/wiki/Shooting_method.