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A New Analytic Solution Method for a Class of Generalized Riccati Differential Equations
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...
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Published in: | Universal journal of mathematics and applications 2023-03, Vol.6 (1), p.1-6 |
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Main Author: | |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites |
Online Access: | Get full text |
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Summary: | 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. |
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ISSN: | 2619-9653 2619-9653 |
DOI: | 10.32323/ujma.1143751 |