# Math Help - Functional equeation

1. ## Functional equeation

Is it possible to find nonzero solution of functional equation

$
(1+4x)f(2x)=2f(x+2x^2)
$

defined and analitic in some neighbourhood of $0$

2. Originally Posted by ns1954
Is it possible to find nonzero solution of functional equation

$
(1+4x)f(2x)=2f(x+2x^2)
$

defined and analitic in some neighbourhood of $0$
never mind!

3. After taking first derivate in FE, by shain rule, we have relation

$4f(2x)+2(1+4x)[f'(2x)-f'(x+2x^2)]=0$ or $4f(2x)+2(1+4x)[g(2x)-g(x+2x^2)]=0$, by your notion.

I can't see how you derived $g(2x)=g(x+2x^2)$ from this.