Two Integrable Classes of Emden–Fowler Equations with Applications in Astrophysics and Cosmology

@article{Mancas2018TwoIC,
  title={Two Integrable Classes of Emden–Fowler Equations with Applications in Astrophysics and Cosmology},
  author={Stefan C. Mancas and Haret C. Rosu},
  journal={Zeitschrift f{\"u}r Naturforschung A},
  year={2018},
  volume={73},
  pages={805 - 814}
}
  • S. Mancas, H. Rosu
  • Published 16 April 2016
  • Mathematics
  • Zeitschrift für Naturforschung A
Abstract We show that some Emden–Fowler (EF) equations encountered in astrophysics and cosmology belong to two EF integrable classes of the type d2z/dχ2=Aχ−λ−2zn${\mathrm{d}^{2}}z/\mathrm{d}{\chi^{2}}=A{\chi^{-\lambda-2}}{z^{n}}$ for λ=(n−1)/2$\lambda=(n-1)/2$ (class 1), and λ=n+1$\lambda=n+1$ (class 2). We find their corresponding invariants which reduce them to first-order nonlinear ordinary differential equations. Using particular solutions of such EF equations, the two classes are set in… 
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