Consider the second-order boundary value problem
y′′ +(2x^2 +3)y′ −y =6x, 0≤x ≤1, (4)
y(0) = 1, y(1) = 0.
(a) Rewrite the second-order equation (4) as a system of twofirst-order equations
involving variables y and z. [2]
(b) Suppose that yn and zn are approximations to y(xn) andz(xn), respectively, where xn = nh, n = 0,...,N and h = 1/N forsome positive integer N. Find the iterative formula when using themodified Euler method to approximate (4) with the modified boundaryconditions:
y(0) = 1, y′(0) = z0.
(c) Hence, employ the shooting method, with underlying modifiedEuler method, to
find approximations yn, n = 1, . . . , N to problem (4)-(5),when N = 5. [Hint: Notice that differential equation (4) islinear.]
