Use the finite difference method to solve the following mixed boundary condition BVP$.$

$-2\frac{d^{2}y}{d{x}^2}+y=e^{-0\mathrm{.}2x},$ for $0x1$

$y(0)=1$ and $\frac{dy}{dx}{|}_x|=1=-y{|}_x|=1$

Divide the solution domain into four subintervals and use the central difference approximation for all derivatives.