\[ {}y^{\prime } = y^{2}+a \,{\mathrm e}^{2 \lambda x} \left ({\mathrm e}^{\lambda x}+b \right )^{n}-\frac {\lambda ^{2}}{4} \]

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = y^{2}-\frac {\lambda ^{2}}{2}-\frac {3 \lambda ^{2} \tan \left (\lambda x \right )^{2}}{4}+a \cos \left (\lambda x \right )^{2} \sin \left (\lambda x \right )^{n} \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y y^{\prime }-y = A +B \,{\mathrm e}^{-\frac {2 x}{A}} \]

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

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

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

\[ {}y y^{\prime }-y = \frac {2 a^{2}}{\sqrt {8 a^{2}+x^{2}}} \]

\[ {}y y^{\prime }-y = -\frac {4 x}{25}+\frac {A}{\sqrt {x}} \]

\[ {}y y^{\prime }-y = -\frac {12 x}{49}+\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49} \]

\[ {}y y^{\prime }-y = -\frac {12 x}{49}+\frac {A \left (25 \sqrt {x}+41 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{98} \]

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

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

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

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

\[ {}y y^{\prime }-y = -\frac {3 x}{16}+\frac {3 A}{x^{\frac {1}{3}}}-\frac {12 A^{2}}{x^{\frac {5}{3}}} \]

\[ {}y y^{\prime }-y = 12 x +\frac {A}{x^{\frac {5}{2}}} \]

\[ {}y y^{\prime }-y = 2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \]

\[ {}y y^{\prime }-y = -\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49} \]

\[ {}y y^{\prime }-y = -\frac {12 x}{49}+A \sqrt {x} \]

\[ {}y y^{\prime }-y = -\frac {10 x}{49}+\frac {2 A \left (4 \sqrt {x}+61 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \]

\[ {}y y^{\prime }-y = -\frac {12 x}{49}+\frac {2 A \left (\sqrt {x}+166 A +\frac {55 A^{2}}{\sqrt {x}}\right )}{49} \]

\[ {}y y^{\prime }-y = -\frac {6 x}{25}+\frac {4 B^{2} \left (\left (2-A \right ) x^{\frac {1}{3}}-\frac {3 B \left (2 A +1\right )}{2}+\frac {B^{2} \left (1-3 A \right )}{x^{\frac {1}{3}}}-\frac {A \,B^{3}}{x^{\frac {2}{3}}}\right )}{75} \]

\[ {}y y^{\prime } = \frac {3 y}{\sqrt {a \,x^{\frac {3}{2}}+8 x}}+1 \]

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

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

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

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

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

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

\[ {}y y^{\prime }+\frac {a \left (7 x -12\right ) y}{10 x^{\frac {7}{5}}} = -\frac {a^{2} \left (-1+x \right ) \left (x -16\right )}{10 x^{\frac {9}{5}}} \]

\[ {}y y^{\prime }-\frac {a \left (1+x \right ) y}{2 x^{\frac {7}{4}}} = \frac {a^{2} \left (-1+x \right ) \left (3 x +5\right )}{4 x^{\frac {5}{2}}} \]

\[ {}y y^{\prime }-\frac {a \left (5 x -4\right ) y}{x^{4}} = \frac {a^{2} \left (-1+x \right ) \left (3 x -1\right )}{x^{7}} \]

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

\[ {}y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{\frac {6}{5}}} = -\frac {a^{2} \left (-1+x \right ) \left (9 x -4\right )}{30 x^{\frac {7}{5}}} \]

\[ {}y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{\frac {8}{5}}} = \frac {a^{2} \left (-1+x \right ) \left (3 x +7\right )}{5 x^{\frac {11}{5}}} \]

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

\[ {}y y^{\prime }+\frac {a \left (x -6\right ) y}{5 x^{\frac {7}{5}}} = \frac {2 a^{2} \left (-1+x \right ) \left (x +4\right )}{5 x^{\frac {9}{5}}} \]

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

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

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

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

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

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

\[ {}y y^{\prime }+a \left (1+2 b \sqrt {x}\right ) {\mathrm e}^{2 b \sqrt {x}} y = -a^{2} b \,x^{\frac {3}{2}} {\mathrm e}^{4 b \sqrt {x}} \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x y^{\prime \prime }+\left (x^{2} a +b x +c \right ) y^{\prime }+\left (A \,x^{2}+B x +\operatorname {C0} \right ) y = 0 \]

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

\[ {}\left (x +\gamma \right ) y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (a n \,x^{n -1}+b m \,x^{m -1}\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a p \,x^{n}+q \right ) y^{\prime }+\left (a r \,x^{n}+s \right ) y = 0 \]

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

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

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

\[ {}y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}-\frac {\lambda ^{2}}{4}\right ) y = 0 \]

\[ {}y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y = 0 \]

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

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