query: Find all continous functon satisfying: $\int_{0}^{x} f = f^2(x) + C$, for some constant $C$
positive_passages.docid: 26754
positive_passages.text: Find all continuous functions satisfying $\int_0^xf=(f(x))^2+C$ for some constant $C \neq 0$.
negative_passages.docid: 26388
negative_passages.text: proof that function is constant
negative_passages.docid: 105172
negative_passages.text: Prove that the entire function is constant over certain conditions.
negative_passages.docid: 129052
negative_passages.text: Find all functions satisfying $\frac{1}{f(a)}+ \frac{1}{f(b)} = \frac{1}{f(c)} $ whenever $\frac{1}{a}+ \frac{1}{b} = \frac{1}{c} $
negative_passages.docid: 77267
negative_passages.text: Given $f$ is continuous and $f(x)=f(e^{t}x)$ for all $x\in\mathbb{R}$ and $t\ge0$, show that $f$ is constant function
negative_passages.docid: 129324
negative_passages.text: Let $f:[0;1]\to\mathbb R$ be continiously differentiable
negative_passages.docid: 13927
negative_passages.text: Values of $a$ s.t. for all continuous $f$ with $f(0)=f(1)$ there exists $x$ s.t. $f(x+a) = f(x)$
negative_passages.docid: 19474
negative_passages.text: Find all solutions to the functional equation $f(x) +f(x+y)=y+2 $
negative_passages.docid: 104278
negative_passages.text: Finding function $f(x)$ which satisfy given functional equation
negative_passages.docid: 41226
negative_passages.text: Find $f:f(xf(x)+f(y))=f(x)^2+y$
negative_passages.docid: 50103
negative_passages.text: Show that a continuous function satisfying $f(2^x)=f(3^x)$ for $x\in (0,\infty)$ is a constant function
negative_passages.docid: 85208
negative_passages.text: Is there a function with infinite integral on every interval?
negative_passages.docid: 56958
negative_passages.text: bounding a $C^1$ function that upholds $f'(t)\leq 1-f(t)^2$
negative_passages.docid: 52380
negative_passages.text: How to prove the function $e^x$ is continous for all real numbers
negative_passages.docid: 90199
negative_passages.text: Prove that there exists a constant $c>0$ such that the following happens
negative_passages.docid: 132093
negative_passages.text: Solve $f(f(x))=f(x)$
negative_passages.docid: 44293
negative_passages.text: Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$