Science:Math Exam Resources/Courses/MATH200/December 2012/Question 02/Statement

Assume that the function $F(x,y,z)$ satisfies the equation $\frac{\partial F}{\partial z}=\frac{{\partial }^{2}F}{\partial x^2}+\frac{{\partial }^{2}F}{\partial y^2}$ and the mixed partial derivatives $\frac{{\partial }^{2}F}{\partial x\partial y}$ and $\frac{{\partial }^{2}F}{\partial y\partial x}$ are equal. Let $A$ be some constant and let $G(\gamma ,s,t)=F(\gamma +s,\gamma -s,At)$. Find the value of $A$ such that $\frac{\partial G}{\partial t}=\frac{{\partial }^{2}G}{\partial {\gamma }^2}+\frac{{\partial }^{2}G}{\partial s^2}$