Riccati equation

It is a nonlinear first order ODE that was developed in the context of hydrodynamics. It is of the form

Solution in a particular case:

There is a relation with Schrodinger equation, I think that Riccati equations are what satisfies the exponent of a solution of a Schrodinger equation...

A Riccati-type equation can be transformed into a second order linear homogeneous differential equation (see this). Moreover, it can be "approximately transformed" into a Schrodinger equation (see this).