Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2017 / Paper 1 / 2 / c / Solution

The nonstationary part of $u$ decays exponentially, whereas the integrating factor grows quadratically. For fixed $x>0$,ConsequentlyAt $x=0$, both expressions are identically zero; the ratio formulation is understood for $x>0$. The diffusion modes have died away, leaving the lifted linear profile multiplied by the reaction-induced amplitude factor.