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- W2022973437 abstract "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." @default.
- W2022973437 created "2016-06-24" @default.
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- W2022973437 date "2012-04-30" @default.
- W2022973437 modified "2023-09-23" @default.
- W2022973437 title "New integrability case for the Riccati equation" @default.
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- W2022973437 doi "https://doi.org/10.48550/arxiv.1204.6546" @default.
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