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

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

\[ {}y^{\prime } \sqrt {X}+\sqrt {Y} = 0 \]

\[ {}y^{\prime } \sqrt {X} = \sqrt {Y} \]

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

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

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

\[ {}y^{\prime } \sqrt {-x^{4}+1} = \sqrt {1-y^{4}} \]

\[ {}y^{\prime } \sqrt {x^{4}+x^{2}+1} = \sqrt {1+y^{2}+y^{4}} \]

\[ {}y^{\prime } \sqrt {X} = 0 \]

\[ {}y^{\prime } \sqrt {X}+\sqrt {Y} = 0 \]

\[ {}y^{\prime } \sqrt {X} = \sqrt {Y} \]

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

\[ {}y^{\prime } \left (4 x^{3}+\operatorname {a1} x +\operatorname {a0} \right )^{\frac {2}{3}}+\left (\operatorname {a0} +\operatorname {a1} y+4 y^{3}\right )^{\frac {2}{3}} = 0 \]

\[ {}X^{\frac {2}{3}} y^{\prime } = Y^{\frac {2}{3}} \]

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

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

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

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

\[ {}\left (\operatorname {a0} +\operatorname {a1} \sin \left (x \right )^{2}\right ) y^{\prime }+\operatorname {a2} x \left (\operatorname {a3} +\operatorname {a1} \sin \left (x \right )^{2}\right )+\operatorname {a1} y \sin \left (2 x \right ) = 0 \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}y y^{\prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (3-x +y\right ) y^{\prime } = 11-4 x +3 y \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y = 0 \]

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

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

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

\[ {}3 y y^{\prime }+5 \cot \left (x \right ) \cot \left (y\right ) \cos \left (y\right )^{2} = 0 \]

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

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

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

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

\[ {}\left (5-2 x -3 y\right ) y^{\prime }+1-2 x -3 y = 0 \]

\[ {}\left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y = 0 \]

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

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

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

\[ {}\left (5+3 x -4 y\right ) y^{\prime } = 2+7 x -3 y \]

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

\[ {}\left (11-11 x -4 y\right ) y^{\prime } = 62-8 x -25 y \]

\[ {}\left (6+3 x +5 y\right ) y^{\prime } = 2+x +7 y \]

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

\[ {}\left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y = 0 \]

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

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

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