$(6)$ Determine $($a$)$ the equation of the elastic curve, $($b$)$ the slope at $A,$ and $($c$)$ the maximum deflection and its location. Make sure to show all your work.

$(6)$ Solve parts $($b$)$ and $($c$)$ of Problem $41$ if the beam is a W$1657$ wide$-$flange beam and $w=5$kip$\frac{s}{f}t,L=20ft,$ and $E=30*{10}^6.$ Make sure to show all your work.