Direct method of solving nonlinear ordinary differential equations through known functions
Keywords:
Nonlinear ordinary differential equations, Special functions, Hermite equation, Legendre’s equation, Laguerre’s equationAbstract
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. Obtaining the general solutions of the nonlinear ODEs with the help of special functions is new to the literature to our knowledge.
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