Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Some solutions of a nonlinear differential equation of high order

Author: P. E. W. Grensted
Journal: Quart. Appl. Math. 24 (1966), 225-238
MSC: Primary 34.02; Secondary 34.45
DOI: https://doi.org/10.1090/qam/203158
MathSciNet review: 203158
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Abstract: Some exact monotonic, and approximate oscillatory, solutions of the nonlinear equation $ {d^n}y/d{x^n} = K{\left\vert y \right\vert^r}{\mathop{\rm sgn}} y$, $ 0 \le r$, are derived. The coefficient $ K$ may be positive or negative, $ r$ may be non-integral and $ n$ is any positive integer. For the case $ r = 0$, exact solutions in closed form are obtained. The conditions under which the approximate solutions will be highly accurate are discussed. Every component of the general solution of the linear equation $ {d^n}y/d{x^n} = Ky$ is shown to be analogous to a corresponding solution of the given nonlinear equation.

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DOI: https://doi.org/10.1090/qam/203158
Article copyright: © Copyright 1966 American Mathematical Society

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