Homogeneous solution of a nonlinear differential equation
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- by James L. Reid PDF
- Proc. Amer. Math. Soc. 38 (1973), 532-536 Request permission
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 $m$.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 532-536
- MSC: Primary 34A05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0318542-X
- MathSciNet review: 0318542