The simple beam $AB$ shown in the figure has moments $2M_0$ and $M_0$ acting at the ends. $($Assume the beam has constant flexural rigidity $EI.)$

Derive the equation of the deflection curve. Use the third$-$order differential equation of the deflection curve $($the shear$-$force equation$).($Enter the magnitude. Use the following as necessary:

$M_0,L,E,$I, and $x.)$

$v=$

Determine the maximum deflection ${}_{\text{m}\text{a}\text{x}}.($Enter the magnitude. Use the following as necessary: $M_0,L,E,$ and I.$)$

${}_{\text{m}\text{a}\text{x}}=$