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 $

Question

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The Answer of 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 $

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

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