2. (20 points) Consider solving the following first-order initial value problem:
$\frac{dy}{dx}$ = f(x, y) = x + y, y(0) = 1, 0 ? x ? 1,
using a fourth-order accurate Taylor-series method given as follows:
y(x_i + h) = y(x_i) + h T_4(x_i, y_i, h)
where
T_4(x_i, y_i, h) = y'(x_i) + y''(x_i)\frac{h}{2!} + y'''(x_i)\frac{h^2}{3!} + y^{(iv)}(x_i)\frac{h^3}{4!}$