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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Homogeneous solution of a nonlinear differential equation

Author: James L. Reid
Journal: Proc. Amer. Math. Soc. 38 (1973), 532-536
MSC: Primary 34A05
MathSciNet review: 0318542
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Abstract: The nonlinear second order differential equation satisfied by the homogeneous function $ y = {[a{u^m} + mb{u^j}{v^n} + c{v^m}]^{k/m}},m = j + n$, is obtained. Functions $ u$ and $ v$ satisfy independently the linear equation $ \ddot y + r(t)\dot y + q(t)y = 0$. The nonlinear equation derived contains previous results as special cases of $ r(t)$, of the constants $ a,b$, and $ c$, and of the numbers $ k$ and $ m$.

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Keywords: Exact homogeneous solution, nonlinear second order differential equation, homogeneous linear differential equation
Article copyright: © Copyright 1973 American Mathematical Society