query: Solutions of $x^{y} = y^{x}$
positive_passages.docid: 5595
positive_passages.text: $x^y = y^x$ for integers $x$ and $y$
negative_passages.docid: 73073
negative_passages.text: Differentiating $y=x^{2}$
negative_passages.docid: 103993
negative_passages.text: Find all real solutions for $x$ in $2(2^x−1)x^2+(2^{x^2}−2)x=2^{x+1}−2$.
negative_passages.docid: 112390
negative_passages.text: Solutions of $x^2 \equiv 1 \pmod N$
negative_passages.docid: 102777
negative_passages.text: Is $G^{(X, Y)} = (G^X)^Y?$ ($A^B$ just means that $B$ is mapped to $A$)
negative_passages.docid: 25730
negative_passages.text: Solve $u_x + u_y + u = e^{x+2y}$
negative_passages.docid: 101019
negative_passages.text: $x^3-9=y^2$ find integral solutions
negative_passages.docid: 88333
negative_passages.text: Find all integral solutions of $y^2=x^3+7$
negative_passages.docid: 40063
negative_passages.text: $x^2+y^2=z^n$: Find solutions without Pythagoras!
negative_passages.docid: 90261
negative_passages.text: Find all solutions of the equation $n^m=x^2+py^2$ which satisfy the following properties
negative_passages.docid: 20491
negative_passages.text: How to solve this equation $x^{2}=2^{x}$?
negative_passages.docid: 57811
negative_passages.text: Properties of the solution of the Ordinary Differential Equation $y' = y(y-1)(y-2)$ as per the Initial conditions?
negative_passages.docid: 128425
negative_passages.text: How to obtain numerical solutions of a two-variable equation?
negative_passages.docid: 13120
negative_passages.text: Find all integer solutions to $x^2+y^2+z^2=2xyz$
negative_passages.docid: 13572
negative_passages.text: $x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
negative_passages.docid: 67158
negative_passages.text: Solve $y'-\int_0^xy(t)dt=2$
negative_passages.docid: 49794
negative_passages.text: Solve $f(x^2+y+f(y))=2y+f(x)^2$ over $\mathbb{R}$