Exact solutions of generalized Lane-Emden equations of the second kind

Kısmet Kasapoğlu

Applications of Mathematics (2024)

  • Volume: 69, Issue: 6, page 747-755
  • ISSN: 0862-7940

Abstract

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Contact and Lie point symmetries of a certain class of second order differential equations using the Lie symmetry theory are obtained. Generators of these symmetries are used to obtain first integrals and exact solutions of the equations. This class of equations is transformed into the so-called generalized Lane-Emden equations of the second kind y ' ' ( x ) + k x y ' ( x ) + g ( x ) e n y = 0 . Then we consider two types of functions g ( x ) and present first integrals and exact solutions of the Lane-Emden equation for them. One of the considered cases is new.

How to cite

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Kasapoğlu, Kısmet. "Exact solutions of generalized Lane-Emden equations of the second kind." Applications of Mathematics 69.6 (2024): 747-755. <http://eudml.org/doc/299619>.

@article{Kasapoğlu2024,
abstract = {Contact and Lie point symmetries of a certain class of second order differential equations using the Lie symmetry theory are obtained. Generators of these symmetries are used to obtain first integrals and exact solutions of the equations. This class of equations is transformed into the so-called generalized Lane-Emden equations of the second kind \[ y^\{\prime \prime \}(x)+\frac\{k\}\{x\}y^\{\prime \}(x)+ g(x)\{\rm e\}^\{ny\}=0. \] Then we consider two types of functions $g(x)$ and present first integrals and exact solutions of the Lane-Emden equation for them. One of the considered cases is new.},
author = {Kasapoğlu, Kısmet},
journal = {Applications of Mathematics},
keywords = {Lie point symmetry; contact symmetry; first integral; Lane-Emden differential equation},
language = {eng},
number = {6},
pages = {747-755},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Exact solutions of generalized Lane-Emden equations of the second kind},
url = {http://eudml.org/doc/299619},
volume = {69},
year = {2024},
}

TY - JOUR
AU - Kasapoğlu, Kısmet
TI - Exact solutions of generalized Lane-Emden equations of the second kind
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 6
SP - 747
EP - 755
AB - Contact and Lie point symmetries of a certain class of second order differential equations using the Lie symmetry theory are obtained. Generators of these symmetries are used to obtain first integrals and exact solutions of the equations. This class of equations is transformed into the so-called generalized Lane-Emden equations of the second kind \[ y^{\prime \prime }(x)+\frac{k}{x}y^{\prime }(x)+ g(x){\rm e}^{ny}=0. \] Then we consider two types of functions $g(x)$ and present first integrals and exact solutions of the Lane-Emden equation for them. One of the considered cases is new.
LA - eng
KW - Lie point symmetry; contact symmetry; first integral; Lane-Emden differential equation
UR - http://eudml.org/doc/299619
ER -

References

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