query: Solving the functional equation $f(x^2+f(y))=(f(x))^2+y$
positive_passages.docid: 144090
positive_passages.text: How to solve the functional equation $f\left(x^2+f(y)\right)=y+f(x)^2$
negative_passages.docid: 157744
negative_passages.text: Cauchy's functional equation with composite function: $gf(x+y)=gf(x)+gf(y)$
negative_passages.docid: 81720
negative_passages.text: $f(x) + f(x+f(y)) = y + f(f(x) + f(f(y)))$
negative_passages.docid: 133646
negative_passages.text: real analysis -functional equation
negative_passages.docid: 88683
negative_passages.text: Functional equation $f\left(\frac{x+y}{2}\right)+f\left(\frac{2xy}{x+y}\right)=f(x)+f(y)$ implies $2f(\sqrt{xy})=f(x)+f(y)$
negative_passages.docid: 101289
negative_passages.text: Studying the equation $\ln(x)- 1+ x^2=0$
negative_passages.docid: 55286
negative_passages.text: Functional equation: $f: \mathbb{R} \rightarrow \mathbb{R}$, $f((x + 1) f(y)) = y (f(x) + 1)$
negative_passages.docid: 64339
negative_passages.text: Find $f$ where $f'(x) = f(1+x)$
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: 148227
negative_passages.text: Rewriting of functional equation $f(xy)=f(x)+f(y)$
negative_passages.docid: 137015
negative_passages.text: Solutions for $a^2+b^2+c^2=d^2$
negative_passages.docid: 74100
negative_passages.text: How do you solve $f'(x) = f(f(x))$?
negative_passages.docid: 133164
negative_passages.text: Rational solutions for $x^2+y^2=3$
negative_passages.docid: 125788
negative_passages.text: A function with a property $f(x+y)=f(x)f(y)$
negative_passages.docid: 28286
negative_passages.text: About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
negative_passages.docid: 34343
negative_passages.text: Determine all $f : \mathbb R \rightarrow \mathbb R$ such that $f(f(x) + y) = f(x^2 - y) + 4yf(x)$.
negative_passages.docid: 129599
negative_passages.text: Functional Equation: Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $(x+y)(f(x)-f(y))=(x-y)f(x+y)$