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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Autor*in:	Adil Mısır [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	system of first-order differential equations fundamental matrix. riccati differential equation, exact solution, system of first-order differential equations, fundamental matrix.

Übergeordnetes Werk:	In: Universal Journal of Mathematics and Applications - Emrah Evren KARA, 2023, 6(2023), 1, Seite 6
Übergeordnetes Werk:	volume:6 ; year:2023 ; number:1 ; pages:6

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.32323/ujma.1143751

Katalog-ID:	DOAJ097439592

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spelling	10.32323/ujma.1143751 doi (DE-627)DOAJ097439592 (DE-599)DOAJ0cc23ec501c648b3b13b256642e494de DE-627 ger DE-627 rakwb eng QA1-939 Adil Mısır verfasserin aut A New Analytic Solution Method for a Class of Generalized Riccati Differential Equations 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. system of first-order differential equations fundamental matrix. riccati differential equation, exact solution, system of first-order differential equations, fundamental matrix. Mathematics In Universal Journal of Mathematics and Applications Emrah Evren KARA, 2023 6(2023), 1, Seite 6 (DE-627)1882659317 (DE-600)3181000-7 26199653 nnns volume:6 year:2023 number:1 pages:6 https://doi.org/10.32323/ujma.1143751 kostenfrei https://doaj.org/article/0cc23ec501c648b3b13b256642e494de kostenfrei https://dergipark.org.tr/tr/download/article-file/2538201 kostenfrei https://doaj.org/toc/2619-9653 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6 2023 1 6
allfields_unstemmed	10.32323/ujma.1143751 doi (DE-627)DOAJ097439592 (DE-599)DOAJ0cc23ec501c648b3b13b256642e494de DE-627 ger DE-627 rakwb eng QA1-939 Adil Mısır verfasserin aut A New Analytic Solution Method for a Class of Generalized Riccati Differential Equations 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. system of first-order differential equations fundamental matrix. riccati differential equation, exact solution, system of first-order differential equations, fundamental matrix. Mathematics In Universal Journal of Mathematics and Applications Emrah Evren KARA, 2023 6(2023), 1, Seite 6 (DE-627)1882659317 (DE-600)3181000-7 26199653 nnns volume:6 year:2023 number:1 pages:6 https://doi.org/10.32323/ujma.1143751 kostenfrei https://doaj.org/article/0cc23ec501c648b3b13b256642e494de kostenfrei https://dergipark.org.tr/tr/download/article-file/2538201 kostenfrei https://doaj.org/toc/2619-9653 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6 2023 1 6
allfieldsGer	10.32323/ujma.1143751 doi (DE-627)DOAJ097439592 (DE-599)DOAJ0cc23ec501c648b3b13b256642e494de DE-627 ger DE-627 rakwb eng QA1-939 Adil Mısır verfasserin aut A New Analytic Solution Method for a Class of Generalized Riccati Differential Equations 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. system of first-order differential equations fundamental matrix. riccati differential equation, exact solution, system of first-order differential equations, fundamental matrix. Mathematics In Universal Journal of Mathematics and Applications Emrah Evren KARA, 2023 6(2023), 1, Seite 6 (DE-627)1882659317 (DE-600)3181000-7 26199653 nnns volume:6 year:2023 number:1 pages:6 https://doi.org/10.32323/ujma.1143751 kostenfrei https://doaj.org/article/0cc23ec501c648b3b13b256642e494de kostenfrei https://dergipark.org.tr/tr/download/article-file/2538201 kostenfrei https://doaj.org/toc/2619-9653 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6 2023 1 6
allfieldsSound	10.32323/ujma.1143751 doi (DE-627)DOAJ097439592 (DE-599)DOAJ0cc23ec501c648b3b13b256642e494de DE-627 ger DE-627 rakwb eng QA1-939 Adil Mısır verfasserin aut A New Analytic Solution Method for a Class of Generalized Riccati Differential Equations 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. system of first-order differential equations fundamental matrix. riccati differential equation, exact solution, system of first-order differential equations, fundamental matrix. Mathematics In Universal Journal of Mathematics and Applications Emrah Evren KARA, 2023 6(2023), 1, Seite 6 (DE-627)1882659317 (DE-600)3181000-7 26199653 nnns volume:6 year:2023 number:1 pages:6 https://doi.org/10.32323/ujma.1143751 kostenfrei https://doaj.org/article/0cc23ec501c648b3b13b256642e494de kostenfrei https://dergipark.org.tr/tr/download/article-file/2538201 kostenfrei https://doaj.org/toc/2619-9653 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6 2023 1 6
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callnumber-first	Q - Science
author	Adil Mısır
spellingShingle	Adil Mısır misc QA1-939 misc system of first-order differential equations misc fundamental matrix. misc riccati differential equation, exact solution, system of first-order differential equations, fundamental matrix. misc Mathematics A New Analytic Solution Method for a Class of Generalized Riccati Differential Equations
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topic_title	QA1-939 A New Analytic Solution Method for a Class of Generalized Riccati Differential Equations system of first-order differential equations fundamental matrix riccati differential equation, exact solution, system of first-order differential equations, fundamental matrix
topic	misc QA1-939 misc system of first-order differential equations misc fundamental matrix. misc riccati differential equation, exact solution, system of first-order differential equations, fundamental matrix. misc Mathematics
topic_unstemmed	misc QA1-939 misc system of first-order differential equations misc fundamental matrix. misc riccati differential equation, exact solution, system of first-order differential equations, fundamental matrix. misc Mathematics
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title	A New Analytic Solution Method for a Class of Generalized Riccati Differential Equations
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title_full	A New Analytic Solution Method for a Class of Generalized Riccati Differential Equations
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title_sort	new analytic solution method for a class of generalized riccati differential equations
callnumber	QA1-939
title_auth	A New Analytic Solution Method for a Class of Generalized Riccati Differential Equations
abstract	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.
abstractGer	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.
abstract_unstemmed	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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title_short	A New Analytic Solution Method for a Class of Generalized Riccati Differential Equations
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