query: Find all the functions in $\mathbb{R}$, satisfying the given equation $(x+y)(f(x)-f(y)) = (x-y)f(x+y)$ for all $x,y$ in $\mathbb{R}$.
positive_passages.docid: 129599
positive_passages.text: Functional Equation: Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $(x+y)(f(x)-f(y))=(x-y)f(x+y)$
negative_passages.docid: 62966
negative_passages.text: Find all functions $f(x)$ such that $f\left(x^2+f(y)\right)$=$y+(f(x))^2$
negative_passages.docid: 13042
negative_passages.text: Finding a function from the given functional equation .
negative_passages.docid: 24810
negative_passages.text: Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
negative_passages.docid: 133646
negative_passages.text: real analysis -functional equation
negative_passages.docid: 20568
negative_passages.text: Does the following have a solution for f(x,y)?
negative_passages.docid: 106033
negative_passages.text: Solve the system in $\mathbb{R}$
negative_passages.docid: 157744
negative_passages.text: Cauchy's functional equation with composite function: $gf(x+y)=gf(x)+gf(y)$
negative_passages.docid: 125788
negative_passages.text: A function with a property $f(x+y)=f(x)f(y)$
negative_passages.docid: 81720
negative_passages.text: $f(x) + f(x+f(y)) = y + f(f(x) + f(f(y)))$
negative_passages.docid: 11453
negative_passages.text: Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
negative_passages.docid: 24862
negative_passages.text: Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$
negative_passages.docid: 32599
negative_passages.text: Solution to the functional equation $f(x^y)=f(x)^{f(y)}$
negative_passages.docid: 42699
negative_passages.text: Solve for $f(x)$ if $f(f(x))=6x-f(x)$
negative_passages.docid: 34077
negative_passages.text: Let $f:\mathbb{R}\to\mathbb{R}$ satisfy $f\big(x-f(y)\big)=f\big(f(y)\big)+x\cdot f(y)+f(x)-1$ for all $x,y\in\mathbb{R}$.
negative_passages.docid: 118873
negative_passages.text: Prove that $f(x)=0$ for all $x\in\mathbb{R}$.
negative_passages.docid: 144090
negative_passages.text: How to solve the functional equation $f\left(x^2+f(y)\right)=y+f(x)^2$