In a physics textbook I'm reading, the PDE ## \frac{\partial p}{\partial t}=-\mu E \frac{\partial p}{\partial x}+D \frac{\partial^2 p}{\partial x^2}-\frac{p-p_o}{\tau} ## is given where ## \mu, \ E, \ D, \ p_o ## and ## \tau ## are constants. It is then stated(yeah, just stated!) that the solution for E=0 is ## p(x,t)=\frac{N}{\sqrt{4 \pi D t}} \exp{\left( -\frac{x^2}{4 D t}-\frac{t}{\tau} \right)}+p_o## and that for nonzero E, the only change to the solution is ## x \rightarrow x-\mu E t ##. But I'm really wondering how did the author get this solution. Its obvious that he didn't use separation of variables. But I know no other method for solving it. What method is used?(adsbygoogle = window.adsbygoogle || []).push({});

Thanks

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# How is this solution derived?

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