$\frac{d^{2}y}{d{x}^2}-\frac{Ty}{EI}=\frac{qx(L-x)}{2EI}$

where

$x=$ location along the beam $($in$)$

$T=$ tension applied $\{$lbs$)$

$E=$ Young's modulus of elasticity of the beam $($psi$)$

$l=$ second moment of area $($in$\text{'})$

$q=$ uniform loading intensity $($Ib$/$in$)$

$L=$ length of beam $($:$in$:$)$

Given $T=7200lbs,g=5400lb\frac{s}{i}n,L=75in,E=30$Msi, and $f=120i{n}^4,$

Find the deflection of the beam at $x=45$ in$.$ Use a step slze of $x=15$ and approximate the derivatives by central differences.