Maximum Deflection

under a Single Wheel in Terms of $x_1$

$w_0=Y_0=\frac{P}{(64EI{k}^3{)}^{\frac{1}{4}}},[Eq.3]$

$x_1=\frac{}{4}(\frac{4EI}{k}{)}^{\frac{1}{4}},[Eq.2]$

Rearrange Eq$.2$ with $x_1$ as the main variable,

substitute in Eq$.3,$ and simplify, to get:

$w_0=Y_0=0\mathrm{.}391\frac{P}{k{x}_1}$