Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

An exact solution of the nonlinear differential equation $ \ddot y+p(t)y=q\sb{m}\,(t)/y\sp{2m-1}$


Author: James L. Reid
Journal: Proc. Amer. Math. Soc. 27 (1971), 61-62
MSC: Primary 34.02
MathSciNet review: 0269907
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An exact solution of the nonlinear differential equation $ \ddot y + p(t)y = {q_m}(t)/{y^{2m - 1}}$ is found to be $ y = {[{u^m} + c{(m - 1)^{ - 1}}{W^{ - 2}}v]^{1/m}}$ if $ {q_m}(t) = c{(uv)^{m - 2}}$. $ u$ and $ v$ are independent solutions of $ \ddot y + p(t)y = 0$ and $ W$ is their Wronskian.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34.02

Retrieve articles in all journals with MSC: 34.02


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0269907-4
Keywords: Exact solution, nonlinear differential equations, homogeneous nonlinear equation, initial conditions
Article copyright: © Copyright 1971 American Mathematical Society