设函数 $u=u(x, y)$ 具有二阶连续偏导数, 函数 $F(s, t)$ 具有一阶连续偏导数, 且 $\left(\frac{\partial F}{\partial s}\right)^2+\left(\frac{\partial F}{\partial t}\right)^2 \neq$ $0, F\left(\frac{\partial u}{\partial x}, \frac{\partial u}{\partial y}\right)=0$, 则有
A
$\frac{\partial^2 u}{\partial x^2} \cdot \frac{\partial^2 u}{\partial y^2}=\left(\frac{\partial^2 u}{\partial x \partial y}\right)^2$.
B
$\frac{\partial^2 u}{\partial x^2} \cdot \frac{\partial^2 u}{\partial y^2}=-\left(\frac{\partial^2 u}{\partial x \partial y}\right)^2$.
C
$\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}=\left(\frac{\partial^2 u}{\partial x \partial y}\right)^2$.
D
$\frac{\partial^2 u}{\partial x^2}-\frac{\partial^2 u}{\partial y^2}=\left(\frac{\partial^2 u}{\partial x \partial y}\right)^2$.
E
F