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

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)y2. 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 t...

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Main Author: Lazhar Bougoffa
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:The Scientific World Journal
Online Access:http://dx.doi.org/10.1155/2014/401741
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spelling doaj-8b4e026e1dff482cbadc88cce393c22a2020-11-25T02:15:23ZengHindawi LimitedThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/401741401741New Conditions for Obtaining the Exact Solutions of the General Riccati EquationLazhar Bougoffa0Department of Mathematics, Faculty of Science, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11623, Saudi ArabiaWe propose a direct method for solving the general Riccati equation y′=f(x)+g(x)y+h(x)y2. 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.http://dx.doi.org/10.1155/2014/401741
collection DOAJ
language English
format Article
sources DOAJ
author Lazhar Bougoffa
spellingShingle Lazhar Bougoffa
New Conditions for Obtaining the Exact Solutions of the General Riccati Equation
The Scientific World Journal
author_facet Lazhar Bougoffa
author_sort Lazhar Bougoffa
title 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_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_sort new conditions for obtaining the exact solutions of the general riccati equation
publisher Hindawi Limited
series The Scientific World Journal
issn 2356-6140
1537-744X
publishDate 2014-01-01
description We propose a direct method for solving the general Riccati equation y′=f(x)+g(x)y+h(x)y2. 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.
url http://dx.doi.org/10.1155/2014/401741
work_keys_str_mv AT lazharbougoffa newconditionsforobtainingtheexactsolutionsofthegeneralriccatiequation
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