Consider the equilibrium of a two$-$dimensional differential element in Cartesian coordinates, as shown in the following figure. Explicitly sum the forces and moments and develop the two$-$dimensional equilibrium equations

$\frac{\text{d}\text{e}\text{l}{}_x}{\text{d}\text{e}\text{l}\text{x}}+\frac{u_{yx}}{\text{d}\text{e}\text{l}\text{y}}+F_x=0$

$\frac{u_{xy}}{\text{d}\text{e}\text{l}\text{x}}+\frac{\text{d}\text{e}\text{l}{}_y}{\text{d}\text{e}\text{l}\text{y}}+F_y=0$

${}_{xy}={}_{yx}$