A note on integration of the Emden-Fowler equation

Philip Rosenau

doi:10.1016/0020-7462(84)90058-1

A note on integration of the Emden-Fowler equation

Philip Rosenau^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Using a simple change of variables, the Emden-Fowler equation, (x^{v + α}y′)′ + ax^vyⁿ = 0 is shown to be integrable provided that either of the constraints (v + α - 1)n = 3 - α + v or (v + α - 1)n = 3 - 2α - v is satisfied. Every integrable case generates a one parameter family of integrable Emden-Fowler equations.

Original language	English
Pages (from-to)	303-308
Number of pages	6
Journal	International Journal of Non-Linear Mechanics
Volume	19
Issue number	4
DOIs	https://doi.org/10.1016/0020-7462(84)90058-1
State	Published - 1984
Externally published	Yes

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10.1016/0020-7462(84)90058-1

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title = "A note on integration of the Emden-Fowler equation",

abstract = "Using a simple change of variables, the Emden-Fowler equation, (xv + αy′)′ + axvyn = 0 is shown to be integrable provided that either of the constraints (v + α - 1)n = 3 - α + v or (v + α - 1)n = 3 - 2α - v is satisfied. Every integrable case generates a one parameter family of integrable Emden-Fowler equations.",

author = "Philip Rosenau",

note = "Funding Information: Acknowledgements--This work was partially supported by U.S. Air Force Contract AFOSR-81-0020 and partially by the Technion V.P.R. Fund-Miami Energy Fund.",

year = "1984",

doi = "10.1016/0020-7462(84)90058-1",

language = "אנגלית",

volume = "19",

pages = "303--308",

journal = "International Journal of Non-Linear Mechanics",

issn = "0020-7462",

publisher = "Elsevier Ltd.",

number = "4",

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T1 - A note on integration of the Emden-Fowler equation

AU - Rosenau, Philip

N1 - Funding Information: Acknowledgements--This work was partially supported by U.S. Air Force Contract AFOSR-81-0020 and partially by the Technion V.P.R. Fund-Miami Energy Fund.

PY - 1984

Y1 - 1984

N2 - Using a simple change of variables, the Emden-Fowler equation, (xv + αy′)′ + axvyn = 0 is shown to be integrable provided that either of the constraints (v + α - 1)n = 3 - α + v or (v + α - 1)n = 3 - 2α - v is satisfied. Every integrable case generates a one parameter family of integrable Emden-Fowler equations.

AB - Using a simple change of variables, the Emden-Fowler equation, (xv + αy′)′ + axvyn = 0 is shown to be integrable provided that either of the constraints (v + α - 1)n = 3 - α + v or (v + α - 1)n = 3 - 2α - v is satisfied. Every integrable case generates a one parameter family of integrable Emden-Fowler equations.

UR - http://www.scopus.com/inward/record.url?scp=0021294567&partnerID=8YFLogxK

U2 - 10.1016/0020-7462(84)90058-1

DO - 10.1016/0020-7462(84)90058-1

M3 - מאמר

AN - SCOPUS:0021294567

VL - 19

SP - 303

EP - 308

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

IS - 4

ER -

A note on integration of the Emden-Fowler equation

Abstract

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