ÖMO 1985 Problem 6

Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfying: $x^2 f(x)+f(1-x)=2x-x^4$ for all $x \in \mathbb{R}$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.