let $g(s)$ be real-valued function defined on $[0,T]$ such that $g(T)=0$ and suppose that $g$ is a "nice function" 
Assume that $0<\gamma<1$, $v$ is a positive number, and 
$$\frac{dg}{ds}+(v\gamma) g +(1-\gamma)(e^{\rho s}g)^{\frac{1}{\gamma-1}}g=0$$


Find a closed form for $g$? 



A differential equation 
This seems to be a Bernoulli differential equation. Please cf. <http://en.wikipedia.org/wiki/Bernoulli_differential_equation> for the solution (in your case $n= \frac{\gamma}{\gamma-1}$). 


