(Solved):   proof (i) (Deflection of Beams). The differential equation for the vertical deflection \( ...

 

proof (i)

(Deflection of Beams). The differential equation for the vertical deflection \( y(x) \) of a uniform beam under the action of a transverse load \( W(x) \) per unit length at a distance \( x \) from the origin on the \( x \)-axis of the beam is \[ E l \frac{d^{4} y}{d x^{4}}=W(x) \text {. for } \quad 0