Functional equation $f(f(x)+y)=f(x^2-y)+4f(x)y$
34343
Determine all $f : \mathbb R \rightarrow \mathbb R$ such that $f(f(x) + y) = f(x^2 - y) + 4yf(x)$.
59063
$f(f(x))=f(x)$ question
10068
$f(x,y)= e^{-\frac{1}{x^2+y^2}}$ when $(x,y)\neq (0,0)$ and $f(0,0)=0$.
64339
Find $f$ where $f'(x) = f(1+x)$
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)
156778
Finding functions satisfying $f(f(x))+f(x)+x=0$
25953
Solving a functional relation $f\left( x \cdot f(y)\right)=x^2 \cdot y^a$
132093
Solve $f(f(x))=f(x)$
100900
Finding maxima and minima of $f(x,y)= x^4 + y^4 - 2x^2 - 2y^2 + 4xy$
117353
Polynomial equation $f(x)f(2x^2)=f(2x^3+x)$
48925
BMO1 2009/10 Q5 functional equation: $f(x)f(y) = f(x + y) + xy$
111789
Solving functional differential equation $f'(x)=2f(2x)-f(x)$
47212
Solving functional equation
69707
If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, then prove that $f(x) = 0$ for all $x ≤ 0$.
103019
Find all functoins $f: \mathbb R \rightarrow \mathbb R$ such that $\forall x,y \in \mathbb R f(xy+f(x))=xf(y)+f(x)$
81720
$f(x) + f(x+f(y)) = y + f(f(x) + f(f(y)))$
76679
Prove there are no other solutions of functional equation $f(x+y) = \frac{f(x)+f(y)}{1-f(x)f(y)}$