Please derive the equation for the elastice curve shown below.

Equations of Elastic Curves

$y(x)=$ Deflection

$\frac{dy}{dx}=(x)$ : Slope

$EI\frac{d^{2}y}{d{x}^2}=M(x)$: Bending Moment

$EI\frac{d^{3}y}{d{x}^3}=V(x)$: Shar Force

$EI\frac{d^{4}y}{d{x}^4}=-w(x)$: Rate $of$ Loading