An elegant exact solutions for the Emden-Fowler equations of the first kind (Q2800515)
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scientific article; zbMATH DE number 6569633
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An elegant exact solutions for the Emden-Fowler equations of the first kind |
scientific article; zbMATH DE number 6569633 |
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An elegant exact solutions for the Emden-Fowler equations of the first kind (English)
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15 April 2016
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ordinary differential equations
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approximations and expansions
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Lane-Emden equation
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Emden-Fowler equation
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isothermal gas sphere
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Consider the differential equations NEWLINE\[NEWLINE\begin{gathered} y''+{k+1\over x} y'+ x^{2k+km-2} y^{2m+5}= 0,\\ y''+ {k+1\over k} {1\over x} y'+ x^{{2\over k}- 2} y= 0,\\ y''+{k+1\over k} {1\over x} y'+ x^{{2\over k}-2} y^5= 0 \end{gathered}NEWLINE\]NEWLINE which contain the standard Lane-Emden equation as special case. Using series approximations, the author determines exact solutions of these equations.
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