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New integrability case for the Riccati equation by Mak, M. K.; Harko, T. is a scholarly article available to read on EtoBox.

What is New integrability case for the Riccati equation about?

A new integrability condition of the Riccati equation $dy/dx=a(x)+b(x)y+c(x)y^{2}$ is presented. By introducing an auxiliary equation depending on a generating function $f(x)$, the general solution of the Riccati equation can be obtained if the coefficients $a(x)$, $b(x)$, $c(x)$, and the function $f(x)$ satisfy a particular constraint. The validity and reliability of the method are tested by obtaining the general solutions of some Riccati type differential equations. Some applications of the integrability conditions for the case of the damped harmonic oscillator with time dependent frequency, and for solitonic wave, are briefly discussed.

Author

Mak, M. K.; Harko, T.

Published

2012

Language

EN