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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{4} y^{\prime }+a^{2}+x^{4} y^{2} = 0 \]

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

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

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

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

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

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

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

\[ {}x^{5} y^{\prime } = 1-3 x^{4} y \]

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

\[ {}x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3} = 0 \]

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

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

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

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

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

\[ {}x^{k} y^{\prime } = a \,x^{m}+b y^{n} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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