  In this Chapter, using Riccati equation as our main example, we tried to
demonstrate at least some of the ideas and notions introduced in Chapter 1 -
integrability in quadratures, conservation laws, etc. Regarding transformation
group and singularities of solutions for RE, we constructed some equivalent
forms of Riccati equation. We also compared three different approaches to the
solutions of Riccati equation and its equivalent forms. The classical form of
RE allowed us to construct easily asymptotic solutions represented by formal
series. Linear equation of the second order turned out to be more convenient to
describe finite-gap potentials for exact solitonic solutions which would be a
much more complicated task for a RE itself while generalization of soliton-like
potentials to finite-gap potentials demanded modified Schwarzian equation.
