A beam of length $l$ with a thin rectangular cross$-$section is fixed at the end $x=$

$0$ and loaded at the tip by a vertical force $P($as illustrated below$).$ Assume an Airy stress

function of the form:

$=A{y}^3+B{y}^{3}x+Cyx$

Determine the coefficients $A,B,C$ so this Airy function is solution of the given problem.

Also, present the final expressions for the non$-$zero stress components.