Discretize the non-linear boundary value problem: $7\frac{d^2y}{dx^2} + \frac{dy}{dx} - y^2 + x = 1$, $y(0) = 7$, $y(2) = 2$ using central difference scheme with step length $\Delta x = 0.5$. Assuming $y_i^{k+1} = y_i^k + \Delta y_i$ as the value of $y$ at $x = x_i$ in the $(k+1)^{th}$ iteration, convert this difference equation into a system of equations of the form $a_i\Delta y_{i-1} + b_i\Delta y_i + c_i\Delta y_{i+1} = d_i$ by using Newton's linearization technique. Then the value of $a_i$ is
(a) 25
(b) 26
(c) 23
(d) 27.
