\[ {}\left (y^{\prime }\right )^{2}+\frac {2 x y^{\prime }}{y}-1 = 0 \]

\[ {}y = a y^{\prime }+b \left (y^{\prime }\right )^{2} \]

\[ {}x = a y^{\prime }+b \left (y^{\prime }\right )^{2} \]

\[ {}y = \sqrt {1+\left (y^{\prime }\right )^{2}}+a y^{\prime } \]

\[ {}x = \sqrt {1+\left (y^{\prime }\right )^{2}}+a y^{\prime } \]

\[ {}y^{\prime }-\frac {\sqrt {1+\left (y^{\prime }\right )^{2}}}{x} = 0 \]

\[ {}x^{2} \left (1+\left (y^{\prime }\right )^{2}\right )^{3}-a^{2} = 0 \]

\[ {}1+\left (y^{\prime }\right )^{2} = \frac {\left (x +a \right )^{2}}{2 a x +x^{2}} \]

\[ {}y = x y^{\prime }+y^{\prime }-\left (y^{\prime }\right )^{2} \]

\[ {}y = x y^{\prime }+\sqrt {b^{2}-a^{2} \left (y^{\prime }\right )^{2}} \]

\[ {}y = x y^{\prime }+x \sqrt {1+\left (y^{\prime }\right )^{2}} \]

\[ {}y = x y^{\prime }+a x \sqrt {1+\left (y^{\prime }\right )^{2}} \]

\[ {}x -y y^{\prime } = a \left (y^{\prime }\right )^{2} \]

\[ {}x +y y^{\prime } = a \sqrt {1+\left (y^{\prime }\right )^{2}} \]

\[ {}y y^{\prime } = x +y^{2}-y^{2} \left (y^{\prime }\right )^{2} \]

\[ {}y-\frac {1}{\sqrt {1+\left (y^{\prime }\right )^{2}}} = x +\frac {y^{\prime }}{\sqrt {1+\left (y^{\prime }\right )^{2}}} \]

\[ {}y-2 x y^{\prime } = x \left (y^{\prime }\right )^{2} \]

\[ {}\frac {y-x y^{\prime }}{y^{2}+y^{\prime }} = \frac {y-x y^{\prime }}{1+x^{2} y^{\prime }} \]

\[ {}2 x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \]

\[ {}\left (x +\sqrt {y^{2}-x y}\right ) y^{\prime }-y = 0 \]

\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \]

\[ {}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0 \]

\[ {}2 x^{2} y+y^{3}+\left (x y^{2}-2 x^{3}\right ) y^{\prime } = 0 \]

\[ {}y^{2}+\left (x \sqrt {y^{2}-x^{2}}-x y\right ) y^{\prime } = 0 \]

\[ {}\frac {y \cos \left (\frac {y}{x}\right )}{x}-\left (\frac {x \sin \left (\frac {y}{x}\right )}{y}+\cos \left (\frac {y}{x}\right )\right ) y^{\prime } = 0 \]

\[ {}y+x \ln \left (\frac {y}{x}\right ) y^{\prime }-2 x y^{\prime } = 0 \]

\[ {}2 \,{\mathrm e}^{\frac {x}{y}} y+\left (y-2 x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime } = 0 \]

\[ {}x \,{\mathrm e}^{\frac {y}{x}}-y \sin \left (\frac {y}{x}\right )+x \sin \left (\frac {y}{x}\right ) y^{\prime } = 0 \]

\[ {}x^{2}+y^{2} = 2 x y y^{\prime } \]

\[ {}x \,{\mathrm e}^{\frac {y}{x}}+y = x y^{\prime } \]

\[ {}y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right ) = 0 \]

\[ {}x y-y^{2}-x^{2} y^{\prime } = 0 \]

\[ {}x +2 y-4-\left (2 x -4 y\right ) y^{\prime } = 0 \]

\[ {}3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime } = 0 \]

\[ {}x +y+1+\left (2 x +2 y+2\right ) y^{\prime } = 0 \]

\[ {}x +y-1+\left (2 x +2 y-3\right ) y^{\prime } = 0 \]

\[ {}x +y-1-\left (x -y-1\right ) y^{\prime } = 0 \]

\[ {}x +y+\left (2 x +2 y-1\right ) y^{\prime } = 0 \]

\[ {}7 y-3+\left (1+2 x \right ) y^{\prime } = 0 \]

\[ {}x +2 y+\left (3 x +6 y+3\right ) y^{\prime } = 0 \]

\[ {}x +2 y+\left (y-1\right ) y^{\prime } = 0 \]

\[ {}3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime } = 0 \]

\[ {}x +y+\left (3 x +3 y-4\right ) y^{\prime } = 0 \]

\[ {}3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime } = 0 \]

\[ {}y+7+\left (2 x +y+3\right ) y^{\prime } = 0 \]

\[ {}x +y+2-\left (x -y-4\right ) y^{\prime } = 0 \]

\[ {}3 x^{2} y+8 x y^{2}+\left (x^{3}+8 x^{2} y+12 y^{2}\right ) y^{\prime } = 0 \]

\[ {}\frac {2 x y+1}{y}+\frac {\left (-x +y\right ) y^{\prime }}{y^{2}} = 0 \]

\[ {}2 x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \]

\[ {}{\mathrm e}^{x} \sin \relax (y)+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \relax (y)\right ) y^{\prime } = 0 \]

\[ {}\cos \relax (y)-\left (x \sin \relax (y)-y^{2}\right ) y^{\prime } = 0 \]

\[ {}x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime } = 0 \]

\[ {}x^{2}-x +y^{2}-\left ({\mathrm e}^{y}-2 x y\right ) y^{\prime } = 0 \]

\[ {}2 x +y \cos \relax (x )+\left (2 y+\sin \relax (x )-\sin \relax (y)\right ) y^{\prime } = 0 \]

\[ {}x \sqrt {x^{2}+y^{2}}-\frac {x^{2} y y^{\prime }}{y-\sqrt {x^{2}+y^{2}}} = 0 \]

\[ {}4 x^{3}-\sin \relax (x )+y^{3}-\left (y^{2}+1-3 x y^{2}\right ) y^{\prime } = 0 \]

\[ {}{\mathrm e}^{x} \left (y^{3}+x y^{3}+1\right )+3 y^{2} \left (x \,{\mathrm e}^{x}-6\right ) y^{\prime } = 0 \]

\[ {}\sin \relax (x ) \cos \relax (y)+\cos \relax (x ) \sin \relax (y) y^{\prime } = 0 \]

\[ {}y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime } = 0 \]

\[ {}y^{2}+y-x y^{\prime } = 0 \]

\[ {}y \sec \relax (x )+\sin \relax (x ) y^{\prime } = 0 \]

\[ {}{\mathrm e}^{x}-\sin \relax (y)+\cos \relax (y) y^{\prime } = 0 \]

\[ {}x y+\left (x^{2}+1\right ) y^{\prime } = 0 \]

\[ {}y^{3}+x y^{2}+y+\left (x^{3}+x^{2} y+x \right ) y^{\prime } = 0 \]

\[ {}3 y-x y^{\prime } = 0 \]

\[ {}y-3 x y^{\prime } = 0 \]

\[ {}y \left (2 x^{2} y^{3}+3\right )+x \left (x^{2} y^{3}-1\right ) y^{\prime } = 0 \]

\[ {}2 x y+x^{2}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \]

\[ {}x^{2}+y \cos \relax (x )+\left (y^{3}+\sin \relax (x )\right ) y^{\prime } = 0 \]

\[ {}x^{2}+y^{2}+x +x y y^{\prime } = 0 \]

\[ {}x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime } = 0 \]

\[ {}{\mathrm e}^{x} \sin \relax (y)+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \relax (y)\right ) y^{\prime } = 0 \]

\[ {}x^{2}-y^{2}-y-\left (x^{2}-y^{2}-x \right ) y^{\prime } = 0 \]

\[ {}x^{4} y^{2}-y+\left (x^{2} y^{4}-x \right ) y^{\prime } = 0 \]

\[ {}y \left (2 x +y^{3}\right )-x \left (2 x -y^{3}\right ) y^{\prime } = 0 \]

\[ {}\arctan \left (x y\right )+\frac {x y-2 x y^{2}}{1+x^{2} y^{2}}+\frac {\left (x^{2}-2 x^{2} y\right ) y^{\prime }}{1+x^{2} y^{2}} = 0 \]

\[ {}{\mathrm e}^{x} \left (x +1\right )+\left (y \,{\mathrm e}^{y}-x \,{\mathrm e}^{x}\right ) y^{\prime } = 0 \]

\[ {}\frac {1+x y}{y}+\frac {\left (2 y-x \right ) y^{\prime }}{y^{2}} = 0 \]

\[ {}y^{2}-3 x y-2 x^{2}+\left (x y-x^{2}\right ) y^{\prime } = 0 \]

\[ {}\left (2 x +y+1\right ) y-x \left (x +2 y-1\right ) y^{\prime } = 0 \]

\[ {}y \left (2 x -y-1\right )+x \left (2 y-x -1\right ) y^{\prime } = 0 \]

\[ {}y^{2}+12 x^{2} y+\left (2 x y+4 x^{3}\right ) y^{\prime } = 0 \]

\[ {}3 \left (x +y\right )^{2}+x \left (2 x +3 y\right ) y^{\prime } = 0 \]

\[ {}y-\left (y^{2}+x^{2}+x \right ) y^{\prime } = 0 \]

\[ {}2 x y+\left (x^{2}+y^{2}+a \right ) y^{\prime } = 0 \]

\[ {}2 x y+x^{2}+b +\left (x^{2}+y^{2}+a \right ) y^{\prime } = 0 \]

\[ {}x y^{\prime }+y = x^{3} \]

\[ {}y^{\prime }+a y = b \]

\[ {}x y^{\prime }+y = y^{2} \ln \relax (x ) \]

\[ {}x^{\prime }+2 y x = {\mathrm e}^{-y^{2}} \]

\[ {}r^{\prime } = \left (r+{\mathrm e}^{-\theta }\right ) \tan \left (\theta \right ) \]

\[ {}y^{\prime }-\frac {2 x y}{x^{2}+1} = 1 \]

\[ {}y^{\prime }+y = x y^{3} \]

\[ {}\left (-x^{3}+1\right ) y^{\prime }-2 \left (x +1\right ) y = y^{\frac {5}{2}} \]

\[ {}\tan \left (\theta \right ) r^{\prime }-r = \tan ^{2}\left (\theta \right ) \]

\[ {}y^{\prime }+2 y = 3 \,{\mathrm e}^{-2 x} \]

\[ {}y^{\prime }+2 y = \frac {3 \,{\mathrm e}^{-2 x}}{4} \]

\[ {}y^{\prime }+2 y = \sin \relax (x ) \]

\[ {}y^{\prime }+y \cos \relax (x ) = {\mathrm e}^{2 x} \]

\[ {}y^{\prime }+y \cos \relax (x ) = \frac {\sin \left (2 x \right )}{2} \]