For Which of These Partial Differential Equations Can the Method $3 u_{x x}+6 u_{y y}=0$

Multiple Choice

For which of these partial differential equations can the method of separation of variables be used to reduce it to a pair of ordinary differential equations? Select all that apply.

A) $3 u_{x x}+6 u_{y y}=0$
B) $2 u_{y}-3 u_{x x}+7 u_{x}=0$
C) $(3 y+8 x) u_{x}+u_{y}=0$
D) $f(x) u_{x x}+g(y) u_{y}+7=0$ , where $f(x)$ and $g(y)$ are continuous functions
E) $2 u_{y y}+3 x u_{y}-u=0$
F) $u_{x x}+u_{y y}+4 y\left(u_{x}-u_{y}\right) =0$