Question 84
Let $f,g$ be functions from the real numbers to the real numbers. Find all ordered pairs $(f,g)$ satisfying
$$g(f(x+y))=f(x)+(2x+y)g(y)\quad\text{for all real }x,y.$$
$$g(f(x+y))=f(x)+(2x+y)g(y)\quad\text{for all real }x,y.$$
Math Olympiad Vault · MathNet 2012