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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}2 \left (x^{2}+x +1\right ) y^{\prime } = 1+8 x^{2}-\left (2 x +1\right ) y \]

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

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

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

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

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

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

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

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

\[ {}x^{3} y^{\prime } = x^{4}+y^{2} \]

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

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

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

\[ {}x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right ) = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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