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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
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