设函数 $u(x, y) = \varphi(x + y) + \varphi(x - y) + \int_{x - y}^{x + y} \psi(t) \, \mathrm{d}t$ , 其中函数 $\varphi$ 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) $\frac{\partial^2 u}{\partial x \partial y} = \frac{\partial^2 u}{\partial x^2}$ .