## Analytic solutions of an iterative equation with first-order derivative.(English)Zbl 1090.34600

Summary: This paper is concerned with nonlinear iterative equation $x'(z) =\frac{1}{x \bigl(p(z)+bx(z)\bigr)}.$ By construction a convergent power series solution, analytic solutions for the original equation are obtained.

### MSC:

 34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)

### Keywords:

iterative differential equation; complex number field