Hi, 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.