Chapter 7.2, Problem 5CP

(a) Find the solution of the BVP ${y^{\prime }}^{\prime }=y$, $y\left(0\right)=0$, $y\left(1\right)=1$ analytically. (b) Implement the finite difference version of the equation, and plot the approximate solution for $n=15$ . (c) Compare the approximation with the exact solution by making a log-log plot of the error at $t=1/2$ versus $n$ for $n=2^p-1$, $p=2,\mathrm{...},7$.