$2.$ Consider a linear inhomogeneous boundary$-$value problem

y

$+2$y

$15$y $=30,$ y$(0)=3,$ y$(1)=$e

$52(5)$ Consider a linear inhomogeneous boundary$-$value problem

$y^{\text{'}\text{'}}+2y^{\text{'}}-15y=30,y(0)=-3,y(1)=-e^{-5}-2$b$.[5$ marks$]$ Use finite differences to approximate the BVP $(5)$ and represent it in the Consider a linear inhomogeneous boundary$-$value problem

$y^{\text{'}\text{'}}+2y^{\text{'}}-15y=30,y(0)=-3,y(1)=-e^{-5}-2$

b$.[5$ marks$]$ Use finite differences to approximate the BVP $(5)$ and represent it in the

matrix form $\frac{A}{b}ar(y)\frac{?}{b}=ar(b).$ Show your work.

$[5$ marks$]$ Write the Python code that implements the method $($solving $\frac{A}{b}ar(y)\frac{?}{b}=ar(b)),$ plots

approximate and exact solutions in $0,1$ and produces the table of values of exact solution,

approximate solution and errors.

matrix form Ay$=$b$.$ Show your work.

$[5$ marks$]$ Write the Python code that implements the method $($solving Ay$=$b $),$ plots

approximate and exact solutions in $[0,1]$ and produces the table of values of exact solution,

approximate solution and errors.