Question 43
Denote by $\mathbb{Q}^{+}$ the set of all positive rational numbers. Determine all functions $f: \mathbb{Q}^{+} \rightarrow \mathbb{Q}^{+}$ which satisfy the following equation for all $x, y \in \mathbb{Q}^{+}$:
$$
f\left(f(x)^{2} y\right)=x^{3} f(x y)
$$
$$
f\left(f(x)^{2} y\right)=x^{3} f(x y)
$$