Originally Posted by

**jguzman** Wov! Thanks!

I first tried to do it with by separation of variables, but I wasn't able to separate the equation into 2 expressions:

From your *separated* expression:

$\displaystyle \frac{dx}{1-(1+\tau U)x}= \frac{dt}{\tau}$

Let be $\displaystyle y = 1-(1+\tau U)x$,

then $\displaystyle dy= -(1+U\tau)dx$,

both expressions that we substitute in the differential equation:

$\displaystyle \frac{dy}{y (-U\tau - 1)}= \frac{dt}{\tau}$

Reorganize the negative symbol:

$\displaystyle \frac{dy}{y (U\tau + 1)}= -\frac{dt}{\tau}$

and moving the constants to the left side:

$\displaystyle \frac{dy}{y}= -\frac{ (U\tau + 1)}{\tau} dt$

then solving for y:

$\displaystyle \log(y) = -\frac{ (U\tau + 1)}{\tau} t $

and applying exponentiation to both sides...

$\displaystyle y= \exp{(-\frac{ (U\tau + 1) t}{\tau})}$

I'm not very sure this is the right answer....