Finding all real valued functions that satisfy $f(f(y) + xf(x)) = y + (f(x))^2$
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
110704
Find all functions $f$ such that $f(x)+f(\frac{1}{1-x})=x$
44670
Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(x+y)=f(x)+f(y)$
153942
Solution of functional equation $f(x+y)=f(x)+f(y)+y\sqrt{f(x)}$
129052
Find all functions satisfying $\frac{1}{f(a)}+ \frac{1}{f(b)} = \frac{1}{f(c)} $ whenever $\frac{1}{a}+ \frac{1}{b} = \frac{1}{c} $
27809
Find the function equation $f(x+f(y)+yf(x))=y+f(x)+xf(y)$
88683
Functional equation $f\left(\frac{x+y}{2}\right)+f\left(\frac{2xy}{x+y}\right)=f(x)+f(y)$ implies $2f(\sqrt{xy})=f(x)+f(y)$
119700
Integrating real valued functions
151947
Finding a pair of functions with properties
1071
Determine all functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $xf(y)+yf(x)=(x+y)f(x^2+y^2)$ for all $x,y\in\mathbb{N}$ (contest question)
24862
Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$
117848
Find all entire functions
104278
Finding function $f(x)$ which satisfy given functional equation
75448
Find all function satisfying $f(f(n))+f(n)=2n+3k$
131586
Hard functional equation: $ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $
11453
Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
129599
Functional Equation: Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $(x+y)(f(x)-f(y))=(x-y)f(x+y)$