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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/401741 |
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| author | Lazhar Bougoffa |
| author_facet | Lazhar Bougoffa |
| author_sort | Lazhar Bougoffa |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-8b4e026e1dff482cbadc88cce393c22a |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-8b4e026e1dff482cbadc88cce393c22a2025-02-03T01:08:07ZengWileyThe 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 |
| spellingShingle | Lazhar Bougoffa New Conditions for Obtaining the Exact Solutions of the General Riccati Equation The Scientific World Journal |
| 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 |
| url | http://dx.doi.org/10.1155/2014/401741 |
| work_keys_str_mv | AT lazharbougoffa newconditionsforobtainingtheexactsolutionsofthegeneralriccatiequation |