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On the question of exponentially polynomial solutions of a nonlinear differential equation. (Russian. English summary) Zbl 0622.34010
Consider the nonlinear differential equation $(1)\quad dy/dx=\sum^{n}_{i=0}\{A_ i(x) \exp B_ i(x)\}y^ i,\quad n\geq 2$ where $$A_ i(x)$$ and $$B_ i(x)$$ are polynomial functions of the complex variable x with power $$\alpha_ i\geq 0$$ and $$\beta_ i\geq 0$$ respectively, and $$A_ n(x)\neq 0$$. The solution of the equation (1) is represented by (2) $$y=P(x) \exp Q(x),$$ where P(x) and Q(x) are polynomials of degree $$p>0$$ and $$q\geq 0$$. The authors investigate properties of the solutions (2).
Reviewer: M.Shahin
##### MSC:
 34A34 Nonlinear ordinary differential equations and systems, general theory
##### Keywords:
first order differential equation