analytic solutions of a second-order functional differential equation with a state derivative dependent delay
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2015
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Abstract
We investigate an analytic solution of the second-order differential equation with a state derivative dependent delay of the form x″(z)=x(p(z)+bx′(z)). Considering a convergent power series g(z) of an auxiliary equation γ2g″(γz)g′(z)=[g(γ2z)-p(g(γz))]γg′(γz)(g′(z))2+p′′(g(z))(g′(z))3+γg′(γz)g″(z) with the relation p(z)+bx′(z)=g(γg-1(z)), we obtain an analytic solution x(z). Furthermore, we characterize a polynomial solution when p(z) is a polynomial.
| Reference Key |
somsuwan2015internationalanalytic
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|---|---|
| Authors | ;Jiraphorn Somsuwan;Keaitsuda Maneeruk Nakprasit |
| Journal | structural engineering and mechanics |
| Year | 2015 |
| DOI |
10.1155/2015/904679
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| URL | |
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