= Separable solution
A solution to a <partial differential equation> that factors into <functions> of separate variables, for example $u(x,t)=X(x)T(t)$. For the <heat equation> $u_t=Du_{xx}$, substitution yields $T'/(DT)=X''/X$, so both sides are a common constant wherever division is valid. The resulting <ordinary differential equations> must be solved together with the original <boundary conditions>. Individual separated solutions generate more general solutions by <superposition> when the equation and boundary data are <linear>.
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