A $4$m$-$long I beam with loadings is as shown as below, determine

$($a$)$ the equation of elastic curve,

$($b$)$ the reaction at each support,

$($c$)$ the deflection at the midpoint of the beam if $\backslash (\backslash$mathrm$\{$E$\}=200\backslash$mathrm$\{$GPa$\}\backslash ).$

Rmk: The answer of $($a$)$ and $($b$)$ can be in term of EI

please use the $210$ kN to calculate, instead copy a wrong answer