On the functional-differential equation of advanced type f′(x)=af(λx)f′(x)=af(λx), λ>1λ>1, with f(0)=0f(0)=0

Solutions to the equation{f′(x)=af(λx),x∈R,f(0)=0, are constructed for constants λ>1λ>1 and a≠0a≠0. The solutions are infinitely differentiable and have some symmetry. By our method, numerical computations can be made effectively.