Riccati Differential Equations (Enhanced Edition‪)‬

An ordinary differential equation of the form
(1.1) t [ w ] ( t ) = w'(t) + f ( t ) w ( t ) + b(t)W2(t) - c ( t ) = 0
is known as a Riccati equation, or a generalized Riccati equation, deriving
its name from Jacopo Francesco, Count Riccati (1676-1754), who, in
1724 (see Riccati [l] of Bibliography), considered the particular equation
(1.2) w'(t) + t-"w2(t) - ntrn+"-l = 0,
where m and n are constants. At an early stage the occurrence of such equations
in the study of Bessel functions led to its appearance in many
related applications, and to the present time the literature on scalar equations
of the form (1.1) has been extensive. Within recent years much
attention has been directed to the study of the qualitative nature of
solutions of this scalar equation and its matrix generalizations, and it
is in this latter spirit that the present volume is written.