1) In a plane problem of linear elasticity the 2-D strain field is:
$\epsilon_x = Axy$
$\epsilon_y = BAxy$
$\gamma_{xy} = -A\frac{(1+B)}{2}(C^2 - y^2)$
where $A$, $B$, $C$ are constants. Find $u(x, y)$ and $v(x, y)$ if $u(0,0) = v(0, 0) = 0$ and
$\frac{\partial u(0,0)}{\partial y} = \frac{\partial v(0,0)}{\partial x}$