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I have a partial differential equation in $F(x,y)$. It is known that the solution is separable i.e. $F(x,y)=f(x)g(y)$ for some unknown functions $f$ and $g$. Can Mathematica express the differential equation in $F(x,y)$ in terms of $f(x)$ and $g(x)$?

Note: I don't care about the explicit solution here. I only want Mathematica to output the differential equation in terms of $f$ and $g$, given the differential equation in terms of $F(x,y)$.

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  • $\begingroup$ Define your multi-variable function F[x_, y_] := f[x] g[x], and put F back into the PDE to see what happens. $\endgroup$
    – Αλέξανδρος Ζεγγ
    Commented Dec 5, 2017 at 12:49
  • $\begingroup$ Check out link $\endgroup$
    – Bill Watts
    Commented Dec 6, 2017 at 1:01

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