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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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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Hindawi Publishing Corporation
2014
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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. |
format | Online Article Text |
id | pubmed-4151386 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2014 |
publisher | Hindawi Publishing Corporation |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT bougoffalazhar newconditionsforobtainingtheexactsolutionsofthegeneralriccatiequation |