¿How to solve this functional equation: $xf(y)+yf(x)=(x+y)f(x)f(y)$? Need some help!
50833
Find all $f:\mathbb R\to\mathbb R$ such that $\forall x,y\in\mathbb R$ the given equality holds: $xf(y)+yf(x)=(x+y)f(x)f(y)$.
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
37976
Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$
25953
Solving a functional relation $f\left( x \cdot f(y)\right)=x^2 \cdot y^a$
26219
Suppose f is a function such that f'(x) = 1/x for all x > 0. Prove that if f(1) = 0, then f(xy) = f(x) + f(y) for all x,y > 0
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
79212
Find the general solution of $y'= a^{x + y}$ where y is the function
157744
Cauchy's functional equation with composite function: $gf(x+y)=gf(x)+gf(y)$
104209
Functional equation - Cyclic Substitutions
44670
Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(x+y)=f(x)+f(y)$
132093
Solve $f(f(x))=f(x)$
131586
Hard functional equation: $ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $
20568
Does the following have a solution for f(x,y)?
49794
Solve $f(x^2+y+f(y))=2y+f(x)^2$ over $\mathbb{R}$
32432
Strategies to find the set of functions $f:\mathbb R\to\mathbb R$ satisfing the functional equation: $f(x^3)+f(y^3)=(x+y)(f(x^2)+f(y^2)-f(xy))$
64339
Find $f$ where $f'(x) = f(1+x)$
48652
Solve the functional equation $2f(x)=f(ax)$ for some $a$.