Direct method of solving nonlinear ordinary differential equations through known functions

Chandrasekar V. Lakshmanan M. Dosmagulova K. Zhunussova Z.
2023 DergiPark

Advances in the Theory of Nonlinear Analysis and its Applications
2023 #7 Issue 5 130 - 140 pp.

In this work, we develop a systematic procedure to obtain the general solutions of a class of nonlinear ordinary differential equations (ODEs) directly through the special functions or other known functions. By introducing a suitable transformation in the state variable/dependent variable of the given nonlinear ODE, we can relate it to one of the the special function equations, including Hermite’s equation, Legendre’s equation, and Laguerre’s equation or other equations solvable through known functions, including isochronous and limit cycle solutions. This procedure can be further generalized to higher order nonlinear ODEs. Ob-taining the general solutions of the nonlinear ODEs with the help of special functions is new to the literature to our knowledge.

Hermite equation , Laguerre’s equation , Legendre’s equation , Nonlinear ordinary differential equations , Special functions

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Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA Deemed University, Thanjavur, 613 401, India
Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tamil Nadu, Tiruchirappalli, 620 024, India
Department of Mathematics, Al-Farabi Kazakh National University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling MES RK, Almaty, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium

Centre for Nonlinear Science and Engineering
Centre for Nonlinear Dynamics
Department of Mathematics
Institute of Mathematics and Mathematical Modeling MES RK
Department of Mathematics: Analysis

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