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New Conditions for Obtaining the Exact Solutions of the General Riccati Equation

We propose a direct method for solving the general Riccati equation y′ = f(x) + g(x)y + h(x)y (2). We first reduce it into an equivalent equation, and then we formulate the relations between the coefficients functions f(x), g(x), and h(x) of the equation to obtain an equivalent separable equation fr...

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Detalles Bibliográficos
Autor principal: Bougoffa, Lazhar
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4151386/
https://www.ncbi.nlm.nih.gov/pubmed/25202724
http://dx.doi.org/10.1155/2014/401741
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author Bougoffa, Lazhar
author_facet Bougoffa, Lazhar
author_sort Bougoffa, Lazhar
collection PubMed
description We propose a direct method for solving the general Riccati equation y′ = f(x) + g(x)y + h(x)y (2). We first reduce it into an equivalent equation, and then we formulate the relations between the coefficients functions f(x), g(x), and h(x) of the equation to obtain an equivalent separable equation from which the previous equation can be solved in closed form. Several examples are presented to demonstrate the efficiency of this method.
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spelling pubmed-41513862014-09-08 New Conditions for Obtaining the Exact Solutions of the General Riccati Equation Bougoffa, Lazhar ScientificWorldJournal Research Article We propose a direct method for solving the general Riccati equation y′ = f(x) + g(x)y + h(x)y (2). We first reduce it into an equivalent equation, and then we formulate the relations between the coefficients functions f(x), g(x), and h(x) of the equation to obtain an equivalent separable equation from which the previous equation can be solved in closed form. Several examples are presented to demonstrate the efficiency of this method. Hindawi Publishing Corporation 2014 2014-08-18 /pmc/articles/PMC4151386/ /pubmed/25202724 http://dx.doi.org/10.1155/2014/401741 Text en Copyright © 2014 Lazhar Bougoffa. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Bougoffa, Lazhar
New Conditions for Obtaining the Exact Solutions of the General Riccati Equation
title New Conditions for Obtaining the Exact Solutions of the General Riccati Equation
title_full New Conditions for Obtaining the Exact Solutions of the General Riccati Equation
title_fullStr New Conditions for Obtaining the Exact Solutions of the General Riccati Equation
title_full_unstemmed New Conditions for Obtaining the Exact Solutions of the General Riccati Equation
title_short New Conditions for Obtaining the Exact Solutions of the General Riccati Equation
title_sort new conditions for obtaining the exact solutions of the general riccati equation
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4151386/
https://www.ncbi.nlm.nih.gov/pubmed/25202724
http://dx.doi.org/10.1155/2014/401741
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