How find the function $f(f(x)+xy)=f(x)+xf(y),\forall x,y\in R$
103019
Find all functoins $f: \mathbb R \rightarrow \mathbb R$ such that $\forall x,y \in \mathbb R f(xy+f(x))=xf(y)+f(x)$
118727
$g(x+y)+g(x)g(y)=g(xy)+g(x)+g(y)$ for all $x,y$.
50833
Find all $f:\mathbb R\to\mathbb R$ such that $\forall x,y\in\mathbb R$ the given equality holds: $xf(y)+yf(x)=(x+y)f(x)f(y)$.
37966
If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$
49794
Solve $f(x^2+y+f(y))=2y+f(x)^2$ over $\mathbb{R}$
34343
Determine all $f : \mathbb R \rightarrow \mathbb R$ such that $f(f(x) + y) = f(x^2 - y) + 4yf(x)$.
86128
Find all functions $ f : \Bbb R \to \Bbb R$ which satisfy $f(x)f(y) = f(x + y) + xy$ for all $x, y ∈ \Bbb R$.
86367
Computing $f(x)$ if $\int_1^{xy} f(t) dt = y \int_1^x f(t) dt + x\int_1^y f(t) dt$ and $f(1) = 3$
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
23485
Solving $\forall x \in \mathbb{R}_+^*, f'(x) = f\left(\frac1{x}\right)$
44670
Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(x+y)=f(x)+f(y)$
132093
Solve $f(f(x))=f(x)$
126931
Find $f(x)$ such that $f(x)+f\left(\frac{1}{x}\right)=f(x)\cdot f\left(\frac{1}{x}\right)$
153942
Solution of functional equation $f(x+y)=f(x)+f(y)+y\sqrt{f(x)}$
32432
Strategies to find the set of functions $f:\mathbb R\to\mathbb R$ satisfing the functional equation: $f(x^3)+f(y^3)=(x+y)(f(x^2)+f(y^2)-f(xy))$
103251
Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)
76458
Solve the following functional equation $f(xf(y))+f(yf(x))=2xy$