- Universal Journal of Mathematics and Applications
- Vol: 6 Issue: 1
- A New Analytic Solution Method for a Class of Generalized Riccati Differential Equations
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 : 14 | Download : 5
Publication Date : 2023-03-28
Article Type : Research
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.Keywords : System of first-order differential equations, Fundamental Matrix., Riccati differential equation, Exact solution, System of first-order differential equations, Fundamental Matrix.