$1.$ Solve the nonlinear BVP using the Shooting method with RK$4$ solution of the coupled system of IVPs. a$.$ Derive the system of IVPs $$by$-$hand$.$ Show all of your work! b$.$ Program the $=1(,,),$ and $=2(,,)$ functions in python such that they can be called from Excel using xlwings. Be sure to include both function and argument docstrings and provide comments as needed. c$.$ Set up an Excel worksheet similar to the nonlinear Shooting method example solution provided, using RK$4$ to solve the coupled system of IVPs. You may use solver $($or secant method$)$ to determine the value of z$(0)$ that gives the correct value of y$(1).$ d$.$ Confirm stability and accuracy of your solution.