## Analytic solutions of a functional differential equation with state dependent argument.(English)Zbl 0892.30023

The authors determine the analytic solutions of the functional differential equation $$x'(z)=x (ax+bx(z))$$ where $$a\neq 1$$ and $$b\neq 0$$ are fixed complex numbers.

### MSC:

 30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable 34K25 Asymptotic theory of functional-differential equations

### Keywords:

analytic solutions; functional differential equation
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