# Solving the reaction-diffusion equation for a single species

$$\frac{\partial u}{\partial t} =k\Delta u+ru.$$ Where all of the bounds are $0$.

Please help! Very new to PDE's and don't understand how to solve this. I know that I need to use separation of variables somehow.

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You can change variables to arrive to the standard heat equation. Consider $$v(x,t)=e^{-rt}u(x,t).$$ If you multiply the original equation by $e^{-rt}$, you get $$\partial_t v=\partial_t u e^{-rt}-re^{-rt}u=e^{-rt}\Delta u=\Delta v$$ which is the classical heat equation. Now you can solve by separation of variables easily.