Solve the equation EI$($d$^(4)$y$)/($dx$^(4))=$w$($x$)$ subject to the appropriate boundary conditions. The beam is of length L$,$ and w$\_(0)$ is a constant.

$($a$)$ The beam is simply supported at both ends, and y$($x$)=$w$\_(0)=36$EIL$=1$w$($x$)=$w$\_(0)$x$,0.$

y$($x$)=$

$($b$)$ Use a graphing utility to graph the deflection curve when w$\_(0)=36$EI and L$=1.$