Solving functional equation $f(x)f(y) = f(x+y)$
22303
How do I prove that $f(x)f(y)=f(x+y)$ implies that $f(x)=e^{cx}$, assuming f is continuous and not zero?
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
47212
Solving functional equation
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
20568
Does the following have a solution for f(x,y)?
15025
Solve $xu_x+(x+y)u_y=1$ when $u(1,y)=y$
4178
Solve $f(x)f(2x^2) = f(2x^3+x)$
156778
Finding functions satisfying $f(f(x))+f(x)+x=0$
146719
Functional equation $f(r \cos \varphi)+f(r \sin \varphi)=f(r)$
110704
Find all functions $f$ such that $f(x)+f(\frac{1}{1-x})=x$
59063
$f(f(x))=f(x)$ question
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)
29647
Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
65418
Solve these functional equations: $\int_0^1\!{f(x)^2\, \mathrm{dx}}= \int_0^1\!{f(x)^3\, \mathrm{dx}}= \int_0^1\!{f(x)^4\, \mathrm{dx}}$
62111
Functional Equation $f(mn)=f(m)f(n)$.
44293
Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
37976
Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$