Pexerized D'alembert functional equation $f(x+y)+g(x−y)=\lambda f(x)g(y)$
136475
d'Alembert-like functional equation: $f(x+y)+g(x-y)=\lambda f(x)g(y)$
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
145265
A non-zero function satisfying $g(x+y) = g(x)g(y)$ must be positive everywhere
131586
Hard functional equation: $ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $
15262
Prove $\exists \xi, \eta \in (0,1)$, such that $f(\xi)+f'(\eta)=\xi+\eta$.
79212
Find the general solution of $y'= a^{x + y}$ where y is the function
32599
Solution to the functional equation $f(x^y)=f(x)^{f(y)}$
111789
Solving functional differential equation $f'(x)=2f(2x)-f(x)$
26113
Proving the functional equation $\theta (x) = x^{-\frac{1}{2}} \theta (x^{-1})$ from the Poisson summation formula
44293
Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
5765
Show that $[2x]+[2y] \geq [x]+[y]+[x+y]$
129599
Functional Equation: Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $(x+y)(f(x)-f(y))=(x-y)f(x+y)$
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
106038
Burgers' equation $u_y + uu_x = 0$ with $u(x,0)=-x$
14656
The differential equation $xu_{x}+yu_{y}=2u$ satisfying the initial condition $y=xg(x),u=f(x)$
104278
Finding function $f(x)$ which satisfy given functional equation
49211
Solving $f(x+y) = f(x)f(y)f(xy)$