设函数
$$
u(x, y)=\phi(x+y)+\phi(x-y)+\int_{x-y}^{x+y} \psi(t) \mathrm{d} t ，
$$
其中函数 $\phi$ 具有二阶导数， $\psi$ 具有一阶导数，则必有
A. $\frac{\partial^2 u}{\partial x^2}=-\frac{\partial^2 u}{\partial y^2}$
B. $\frac{\partial^2 u}{\partial x^2}=\frac{\partial^2 u}{\partial y^2}$
C. $\frac{\partial^2 u}{\partial x \partial y}=\frac{\partial^2 u}{\partial y^2}$
D. $\frac{\partial^2 u}{\partial x \partial y}=\frac{\partial^2 u}{\partial x^2}$