Definition of Riccati in English:


Pronunciation /rɪˈkati/


(also Ricatti)
  • Attributive In the genitive, and with of. Designating certain kinds of differential equation; specifically a first-order non-linear differential equation of the form d y /d x = P (x) y 2 + Q (x) y + Z (x), which can be reduced to a second-order linear differential equation.

    Two other kinds of differential equation that go under this name are (a) a first-order linear differential equation of the form dy/dx = axn + by 2, where n is an integer and a and b are constants; (b) a second-order non-linear differential equation of the form x 2 d2 y/dx 2 + (x 2-n(n+1))y = 0, where n is an integer.


Late 18th century; earliest use found in The Monthly Review. From the name of Count Jacopo Francesco Riccati, Italian mathematician, who published the first equation of this type, after French equation de Riccati (d'Alembert 1774).