3- NONLINEAR SHOOTING METHOD Consider the boundary value problems (BVPs) for the second order differential equation of the form y" - f(x,y,y), a sxsb, y(a) a and y(b) - B. When f(x, y, y' )is linear in y and y', the Shooting Method introduced in Section 6.1 solves a system of two initial value problems and the solution y(x)of the boundary value problem (*) is of the form B-yi(b) (x) - 11(x) + 12(b)2(x) where y1(x)and y2(x) are solutions of two initial value problems, respectively. Now we consider the cases where f(x, y, y' Dis not linear in y and y'. Assume a given boundary value problem has a unique solution y(x)We will approximate the solution y(x)by solving a sequence of initial value problems (**) y' - x, y,y), a