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In physics, many PDEs' equation can be reduced to a number of ODEs' equations by "Separation of Variables".

According to my knowledge, "Separation of Variables", it just subsitutes the function, for example F(x,y,z), by a product of three function, X(x)Y(y)Z(z).

Why does it work? I mean it is legitimate? How do we know the function F(x,y,z) can be factorized?

Thx.

Will.

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# Separation of Variables

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