Solve $f(x)=c \times f(\frac{x}{2})$ for $c$ Given:


*

*Function $f(x)$ is infinitely differentiable 

*equation (1)
$f(x)=c \times f(\frac{x}{2})$
We have to find all $c$, for which the (1) has non-zero solutions 
Any hints on theorems to apply here, I reckon it's somehow related to ODEs

$f(x) = c^{\ln(x)/\ln(2) - 1}$
By graphing $f(x)$ for different values of $c$, you can observe that $f(x)$ is non-zero for all $c > 0$.
