The beam below is subjected to the distributed load and a concentrated load. Given that EI of the beam is constant $($where E is the Young's Modulus, and I is second moment of Area$)$:

$($a$)$ Determine the expression $($s$)$ for the deflection $v(x)$ and slope $\frac{dv}{dx}$ of the beam. $[17$ points$]$

$($b$)$ Find the values of the deflection $v(x)$ and slope $\frac{dv}{dx}$ of the beam at $x=1\mathrm{.}0m$ and $x=5m[8$ points$]$