Solve the following equation using finite difference method where $y(1)=6\mathrm{.}3084$ and $y(2)=55\mathrm{.}4304$ :

$y^{\text{'}\text{'}}-y^{\text{'}}+y=3e^x-sin(x)$

$($a$)$ Solve the equation by manual calculation using a step size of $0\mathrm{.}1.$

$($b$)$ Solve the equation using MATLAB$/$Python code for $100$ nodes $($i$.$e$.,$ the step size will be $0\mathrm{.}01)$

and create a plot of y vs$.x$ in MATLAB$/$Python$.$ Scan your hand calculations properly and

upload them to Blackboard as a PDF$,$ along with the MATLAB$/$Python code saved as a PDF

and the original MATLAB$/$Jupyter Notebook file.