Supplementary Exercise $1.$ Solve$/$demonstrate the deflection function y$($x$)$ of the fixed$-$pinned beam with uniform distributed load q$\_(0),$ as illustrated below, using the ODE approach $($of course, you can check your answer with app. A$-9,$ but the complete demonstration using the steps of the ODE approach is required$).$ Solve the exercise finding the homogeneous solution, particular solution and general one. Then use boundary co ditions to find the displacement y