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 two
first-order equations
involving variables y and z. [2]
(b) Suppose that yn and zn are approximations to y(xn) and
z(xn), respectively, where xn = nh, n = 0,...,N and h = 1/N for
some positive integer N. Find the iterative formula when using the
modified Euler method to approximate...