数学试题讲解

设函数

u (x, y) = ϕ (x + y) + ϕ (x - y) + \int_{x - y}^{x + y} ψ (t) d t ，

其中函数

ϕ

具有二阶导数，

ψ

具有一阶导数，则必有

\frac{\partial^{2} u}{\partial x^{2}} = - \frac{\partial^{2} u}{\partial y^{2}}

\frac{\partial^{2} u}{\partial x^{2}} = \frac{\partial^{2} u}{\partial y^{2}}

\frac{\partial^{2} u}{\partial x \partial y} = \frac{\partial^{2} u}{\partial y^{2}}

\frac{\partial^{2} u}{\partial x \partial y} = \frac{\partial^{2} u}{\partial x^{2}}