Question
Reduce the following PDE into three ODEs:
Answer :
Word Count : 108
Assume a separable solution ( f(x,y,z)=X(x)Y(y)Z(z) ). Then [ \frac{\partial^2 f}{\partial x^2}=X''YZ,\quad \frac{\partial^2 f}{\partial y^2}=XY''Z,\quad \frac{\partial^2 f}{\partial z^2}=XYZ''. _____ ________ _________ ____ ____.
____ _________ _____ ______ ________ ___ ___ ___ ___ ____ _________.
_________ _______ ____ ________ ________ ___ _____ _________.
_______ ____ _________ __________ _______ _____ _____ ______ ____ ____ __________.
__________ ________ ____ ____ _______ ___.
_________ ________ __________ ________ _________ ___ _____ ____ ___.
_____ ___ ____ _____ ___ _________ __________ ________ ______ __________.
_________ ________ ___ ___ _________ _______ _______ _________ __________.
_______ ____ ___ __________ ________ _____.
______ __________ _____ ________ ______ _________ _______ ____ ______ _________ ___.
________ ____ ____ __________.
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Assume a separable solution ( f(x,y,z)=X(x)Y(y)Z(z) ). Then [ \frac{\partial^2 f}{\partial x^2}=X''YZ,\quad \frac{\partial^2 f}{\partial y^2}=XY''Z,\quad \frac{\partial^2 f}{\partial z^2}=XYZ''. _____ ________ _________ ____ ____.
____ _________ _____ ______ ________ ___ ___ ___ ___ ____ _________.
_________ _______ ____ ________ ________ ___ _____ _________.
_______ ____ _________ __________ _______ _____ _____ ______ ____ ____ __________.
__________ ________ ____ ____ _______ ___.
_________ ________ __________ ________ _________ ___ _____ ____ ___.
_____ ___ ____ _____ ___ _________ __________ ________ ______ __________.
_________ ________ ___ ___ _________ _______ _______ _________ __________.
_______ ____ ___ __________ ________ _____.
______ __________ _____ ________ ______ _________ _______ ____ ______ _________ ___.
________ ____ ____ __________.
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