# Chaplygin's equation

${\displaystyle f_{\theta \theta }+{\frac {v^{2}}{1-{\frac {v^{2}}{c^{2}}}}}f_{vv}+vf_{v}=0.}$
Here, ${\displaystyle c=c(v)}$ is the speed of sound, determined by the equation of state of the fluid and conservation of energy.