UA-UMO 2021 Problem 114

Find all the following functions $f:R\to R$ , which for arbitrary valid $x,y$ holds equality: $f(xf(x+y))+f((x+y)f(y))=(x+y)^2$ (Vadym Koval)

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.