## Why 3rd ODE could be simplified to a 1st ODE?

Verify that the 3rd ODE
$\mu^2\mu'''=\nu (2\mu \mu''-\mu'^2)$
$X_1=\frac{\partial}{\partial x}, X_2=x\frac{\partial}{\partial x}+\mu\frac{\partial}{\partial \mu}.$