Q$.$

A version of the one$-$dimensional elliptic equation that occurs in Mechanics is the following model for the vertical deflection of a bar with a distributed load $P(x)$ :

$A_{c}E\frac{d^{2}u}{d{x}^2}=P(x)$

Where $A_c=$ cross$-$sectional area, $E=$ Young's Modulus, $u=$ deflection, and $x=$ distance measured along the bar's length. If the bar is simply supported at both ends, use the Finite Element Method $($FEM$)$ to model its deflections for $A_c=0\mathrm{.}21m^2,E=150{10}^9\frac{N}{m^2},L=15m,P(x{)}_2=950\frac{N}{m}.P(x{)}_1$ is linearly increasing from $0\frac{N}{m}$ at the left end of the beam