Problem $9\mathrm{.}3-8$ Derive the equation of the deflection curve for a cantilever beam $AB$ supporting a load $P$ at the free end $($see figure$).$ Also, determine the deflection ${}_B$ and angle of rotation ${}_B$ at the free end. $($Note: Use the second$-$order differential equation of the deflection curve.$)$

Problem $9\mathrm{.}3-9$ Derive the equation of the deflection curve for a simple beam $AB$ loaded by a couple $M_0$ at the left$-$hand support $($see figure$).$ Also, determine the maximum deflection ${}_{\text{m}\text{a}\text{x}}.($Note: Use the second$-$order differential equation of the deflection curve.$)$