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

\[ {}3 \left (y^{\prime }\right )^{5}-y y^{\prime }+1 = 0 \]

\[ {}\left (y^{\prime }\right )^{6} = \left (y-a \right )^{4} \left (y-b \right )^{3} \]

\[ {}\left (y^{\prime }\right )^{6}+f \relax (x ) \left (y-a \right )^{4} \left (y-b \right )^{3} = 0 \]

\[ {}\left (y^{\prime }\right )^{6}+f \relax (x ) \left (y-a \right )^{5} \left (y-b \right )^{3} = 0 \]

\[ {}\left (y^{\prime }\right )^{6}+f \relax (x ) \left (y-a \right )^{5} \left (y-b \right )^{4} = 0 \]

\[ {}x^{2} \left (\left (y^{\prime }\right )^{6}+3 y^{4}+3 y^{2}+1\right ) = a^{2} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) = y \]

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

\[ {}y^{\prime } = \frac {x +y-3}{x -y-1} \]

\[ {}y^{\prime } = \frac {2 x +y-1}{4 x +2 y+5} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}8 y+10 x +\left (7 x +5 y\right ) y^{\prime } = 0 \]

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

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

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

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

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

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

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

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

\[ {}3 z^{2} z^{\prime }-a z^{3} = x +1 \]

\[ {}z^{\prime }+2 x z = 2 a \,x^{3} z^{3} \]

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

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

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

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

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

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

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

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

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

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

\[ {}\frac {x^{n} y^{\prime }}{b y^{2}-c \,x^{2 a}}-\frac {a y x^{a -1}}{b y^{2}-c \,x^{2 a}}+x^{a -1} = 0 \]

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

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

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

\[ {}8 y+10 x +\left (7 x +5 y\right ) y^{\prime } = 0 \]

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

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

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

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

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

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

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

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

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

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

\[ {}x y^{\prime }-a y+y^{2} = x^{-\frac {2 a}{3}} \]

\[ {}u^{\prime }+u^{2} = \frac {c}{x^{\frac {4}{3}}} \]

\[ {}u^{\prime }+b u^{2} = \frac {c}{x^{4}} \]

\[ {}u^{\prime }-u^{2} = \frac {2}{x^{\frac {8}{3}}} \]

\[ {}\frac {\sqrt {f \,x^{4}+c \,x^{3}+c \,x^{2}+b x +a}\, y^{\prime }}{\sqrt {a +b y+c y^{2}+c y^{3}+f y^{4}}} = -1 \]

\[ {}\left (y^{\prime }\right )^{2}-5 y^{\prime }+6 = 0 \]

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

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