39th Balkan Mathematical Olympiad (BMO 2022 )

Problem 3

Find all functions $f:(0,\infty) \to (0,\infty)$ such that $\displaystyle f\left(y\left(f\left(x\right)\right)^3+x\right)=x^3f(y)+f(x)$
for every x, y> 0 .