De luz-wiki

Reduction to a second order linear equation

de http://en.wikipedia.org/wiki/Riccati_equation :

As explained on pages 23-25 of Ince's book, the non-linear Riccati equation can always be reduced to a second order linear ordinary differential equation (ODE). Indeed if

then, wherever is non-zero, satisfies a Riccati equation of the form

where and . In fact

Substituting , it follows that satisfies the linear 2nd order ODE


so that

and hence

A solution of this equation will lead to a solution of the original Riccati equation.

But then, the TDHO ODE is equivalent to the Riccati equation.

Este punto también lo menciona Jacobsson [1] en relación a medios estratificados en sentido inverso, es decir que la ecuación lineal de segundo grado puede reescribirse como una ecuación no lineal de primer grado tipo Riccati.

--Mfg 10:50 28 nov 2007 (CST)


  1. R. Jacobsson in Progress in Optics V, Light reflection from films of continuously varying refractive index (1966)