A New Analytic Solution Method for a Class of Generalized Riccati Differential Equations

Year 2023, Volume: 6 Issue: 1, 1 - 6, 28.03.2023

Adil Mısır

https://doi.org/10.32323/ujma.1143751

Abstract

We give a useful and practicable solution method for the general Riccati differential equation of the form $w^{\prime }\left( x\right) =p\left( x\right) +q\left( x\right) w\left( x\right) +r\left( x\right) w^{2}\left( x\right) $. In order to get the general solution many authors have been interested this type equation. They show that if there exists some relation about the coefficients $p\left( x\right),$ $q\left( x\right),$ and $r\left( x\right) $ then the general solution of this equation can be given in a closed form. We also determine some relations between these coefficients and find the general solutions to the given equation. Finally, we give some examples to illustrate the importance of the presented method.

Keywords

System of first-order differential equations, Fundamental Matrix., Riccati differential equation, Exact solution, System of first-order differential equations, Fundamental Matrix.

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