A New Analytic Solution Method for a Class of Generalized Riccati Differential Equations

Authors : Adil MISIR

Pages : 1-6

Doi:10.32323/ujma.1143751

View : 16 | Download : 9

Publication Date : 2023-03-28

Article Type : Research Paper

Abstract :We give a useful and practicable solution method for the general Riccati differential equation of the form $w^{\\prime }\\leftinsert ignore into journalissuearticles values( x\\right); =p\\leftinsert ignore into journalissuearticles values( x\\right); +q\\leftinsert ignore into journalissuearticles values( x\\right); w\\leftinsert ignore into journalissuearticles values( x\\right); +r\\leftinsert ignore into journalissuearticles values( x\\right); w^{2}\\leftinsert ignore into journalissuearticles values( 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 $p\\leftinsert ignore into journalissuearticles values( x\\right);,$ $q\\leftinsert ignore into journalissuearticles values( x\\right);,$ and $r\\leftinsert ignore into journalissuearticles values( 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.
Keywords : System of first order differential equations, Fundamental Matrix, Riccati differential equation, Exact solution, System of first order differential equations, Fundamental Matrix