Mathematical Physics

    

On a Nonlinear Differential Equation of Lienard Type

Authors: M. D. Monsia

We present, in this paper, an exceptional Lienard differential equation. In spite of the presence of strong and high order nonlinearity term, the proposed equation is explicitly integrable. The general solution is expressed in terms of trigonometric functions. Also the general solutions of related quadratic Lienard type equations are periodic and may exhibit harmonic oscillations. The presented equation includes many nonlinear equations like the cubic-quintic, and cubic Duffing equations, Mickens truly nonlinear equations and the Ermakov-Pinney equation as special cases so that the explicit general solution of several nonlinear equations may be easily obtained for the first time.

Comments: 7 pages

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Submission history

[v1] 2020-11-07 18:50:28
[v2] 2020-11-08 11:16:19
[v3] 2020-11-11 19:15:25

Unique-IP document downloads: 367 times

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