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

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

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

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

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

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

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

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

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

\[ {}x \left (3+5 x -12 x y^{2}+4 x^{2} y\right ) y^{\prime }+\left (3+10 x -8 x y^{2}+6 x^{2} y\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3} = 0 \]

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

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

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

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

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

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

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

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

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

\[ {}\left (5 x -y-7 x y^{3}\right ) y^{\prime }+5 y-y^{4} = 0 \]

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

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

\[ {}\left (2-10 x^{2} y^{3}+3 y^{2}\right ) y^{\prime } = x \left (1+5 y^{4}\right ) \]

\[ {}x \left (a +b x y^{3}\right ) y^{\prime }+\left (a +c \,x^{3} y\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{3} \left (1+5 x^{3} y^{7}\right ) y^{\prime }+\left (3 x^{5} y^{5}-1\right ) y^{3} = 0 \]

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

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

\[ {}f \relax (x ) y^{m} y^{\prime }+g \relax (x ) y^{m +1}+h \relax (x ) y^{n} = 0 \]

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

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

\[ {}y^{\prime } \sqrt {y} = \sqrt {x} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (y^{\prime }\right )^{2} = a^{2} \left (1-\ln \relax (y)^{2}\right ) y^{2} \]

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

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

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