It's called separation of variables. The authors assumed that $C(x,t)$ was the product of two functions $X$ and $T$, with each function depending on only one of the independent variables i.e $X$ is only dependent on $x$ ($X = X(x)$) and $T$ is only dependent on $t$ ($T = T(t)$).
– Matthew CassellNov 20 '17 at 14:27
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– sunny Nov 20 '17 at 14:37