Abstract
This paper is concerned with a second-order functional differential equation of the form x″(z) = x(az + bx(z)). By constructing a convergent power series solution of an auxiliary equation of the form α2y″ (αz) y′ (z) = αy′(z)y″(z)+(y′(z))3[y(α2z)−ay(αz)], analytic solutions of the form (y(αyt - 1(z)) − az)/b for the original differential equation are obtained.
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Si, JG., Wang, XP. Analytic Solutions of a Second-order Functional Differential Equation with a State Dependent Delay. Results. Math. 39, 345–352 (2001). https://doi.org/10.1007/BF03322694
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DOI: https://doi.org/10.1007/BF03322694