So when can and can't I use separable solutions for PDE's?
Rather than look for a general rule on when you can or cannot "separate" functions, it is better to try. Write the function y(x,t) as X(t)T(t). IF you are able to separate the the two functions and varibles, good.
The problem is that whether or not a problem is separable depends not only on equation but also the "geometry" (whether you are working inside a sphere or circle or rectangle) which determines the coordinate system.
I just poured through my profs lecture notes and found: "Separation of variables only works for homogeneous boundary conditions."
Just in case anyone else is interested.
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