Properties of solutions of Riccati equation

The paper studies some properties of solutions of the Riccati equation

$y'(t) + a(t)y^2 (t) + b(t)y(t) + c(t) = 0$

on a semiaxis [t ₀, +∞) for different types of initial value sets. Two types of solutions are singled out: normal, that are in a sense stable, and extremal, that are non-stable in the Lyapunov sense. Relations expressing the extremal solutions by means of a given normal solution in quadratures and elementary functions are obtained and some relations between solutions the extendable to [t ₀, +∞) are derived.