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

\[ {}y^{\prime } = y^{2}+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} {\mathrm e}^{2 \lambda \,x^{2}} \]

\[ {}y^{\prime } = y^{2}-\lambda ^{2}+a \cosh \left (\lambda x \right )^{n} \sinh \left (\lambda x \right )^{-n -4} \]

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

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

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

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

\[ {}x^{2} y^{\prime } = y^{2} x^{2}+a \left (b \ln \left (x \right )+c \right )^{n}+\frac {1}{4} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = y^{2}-\lambda ^{2}+\frac {f \left (\coth \left (\lambda x \right )\right )}{\sinh \left (\lambda x \right )^{4}} \]

\[ {}y^{\prime } = y^{2}-\lambda ^{2}+\frac {f \left (\tanh \left (\lambda x \right )\right )}{\cosh \left (\lambda x \right )^{4}} \]

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

\[ {}y^{\prime } = y^{2}+\lambda ^{2}+\frac {f \left (\cot \left (\lambda x \right )\right )}{\sin \left (\lambda x \right )^{4}} \]

\[ {}y^{\prime } = y^{2}+\lambda ^{2}+\frac {f \left (\tan \left (\lambda x \right )\right )}{\cos \left (\lambda x \right )^{4}} \]

\[ {}y^{\prime } = y^{2}+\lambda ^{2}+\frac {f \left (\frac {\sin \left (\lambda x +a \right )}{\sin \left (\lambda x +b \right )}\right )}{\sin \left (\lambda x +b \right )^{4}} \]

\[ {}y y^{\prime }-y = A \,x^{k -1}-k B \,x^{k}+k \,B^{2} x^{2 k -1} \]

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

\[ {}y y^{\prime }-y = \frac {2 m -2}{\left (m -3\right )^{2}}+\frac {2 A \left (m \left (m +3\right ) \sqrt {x}+\left (4 m^{2}+3 m +9\right ) A +\frac {3 m \left (m +3\right ) A^{2}}{\sqrt {x}}\right )}{\left (m -3\right )^{2}} \]

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

\[ {}y y^{\prime }-y = -\frac {6 X}{25}+\frac {2 A \left (2 \sqrt {x}+19 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{25} \]

\[ {}y y^{\prime }-y = \frac {3 x}{8}+\frac {3 \sqrt {a^{2}+x^{2}}}{8}-\frac {a^{2}}{16 \sqrt {a^{2}+x^{2}}} \]

\[ {}y y^{\prime }-y = -\frac {5 x}{36}+\frac {A}{x^{\frac {7}{5}}} \]

\[ {}y y^{\prime }-y = -\frac {12 x}{49}+\frac {6 A \left (-3 \sqrt {x}+23 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \]

\[ {}y y^{\prime }-y = -\frac {30 x}{121}+\frac {3 A \left (21 \sqrt {x}+35 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{242} \]

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

\[ {}y y^{\prime }-y = -\frac {12 x}{49}+\frac {4 A \left (-10 \sqrt {x}+27 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{49} \]

\[ {}y y^{\prime }-y = -\frac {x}{4}+\frac {6 A \left (\sqrt {x}+8 A +\frac {5 A^{2}}{\sqrt {x}}\right )}{49} \]

\[ {}y y^{\prime }-y = -\frac {6 x}{25}+\frac {6 A \left (2 \sqrt {x}+7 A +\frac {4 A^{2}}{\sqrt {x}}\right )}{25} \]

\[ {}y y^{\prime }-y = \frac {3 x}{8}+\frac {3 \sqrt {b^{2}+x^{2}}}{8}+\frac {3 b^{2}}{16 \sqrt {b^{2}+x^{2}}} \]

\[ {}y y^{\prime }-y = \frac {9 x}{32}+\frac {15 \sqrt {b^{2}+x^{2}}}{32}+\frac {3 b^{2}}{64 \sqrt {b^{2}+x^{2}}} \]

\[ {}y y^{\prime }-y = -\frac {3 x}{32}-\frac {3 \sqrt {a^{2}+x^{2}}}{32}+\frac {15 a^{2}}{64 \sqrt {a^{2}+x^{2}}} \]

\[ {}y y^{\prime }-y = \frac {63 x}{4}+\frac {A}{x^{\frac {5}{3}}} \]

\[ {}y y^{\prime }-y = 2 x +2 A \left (-10 \sqrt {x}+19 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \]

\[ {}y y^{\prime }-y = -\frac {28 x}{121}+\frac {2 A \left (5 \sqrt {x}+106 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{121} \]

\[ {}y y^{\prime }-y = 20 x +\frac {A}{\sqrt {x}} \]

\[ {}y y^{\prime }-y = \frac {15 x}{4}+\frac {A}{x^{7}} \]

\[ {}y y^{\prime }-y = -\frac {4 x}{25}+\frac {A \left (7 \sqrt {x}+49 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{50} \]

\[ {}y y^{\prime }-y = \frac {15 x}{4}+\frac {6 A}{x^{\frac {1}{3}}}-\frac {3 A^{2}}{x^{\frac {5}{3}}} \]

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

\[ {}y y^{\prime }-y = -\frac {5 x}{36}+\frac {A}{x^{\frac {3}{5}}}-\frac {B}{x^{\frac {7}{5}}} \]

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

\[ {}y y^{\prime }-y = -\frac {12 x}{49}+3 A \left (\frac {1}{49}+B \right ) \sqrt {x}+3 A^{2} \left (\frac {4}{49}-\frac {5 B}{2}\right )+\frac {15 A^{3} \left (\frac {1}{49}-\frac {5 B}{4}\right )}{4 \sqrt {x}} \]

\[ {}y y^{\prime }-y = \frac {3 x}{4}-\frac {3 A \,x^{\frac {1}{3}}}{2}+\frac {3 A^{2}}{4 x^{\frac {1}{3}}}-\frac {27 A^{4}}{625 x^{\frac {5}{3}}} \]

\[ {}y y^{\prime }-y = -\frac {6 x}{25}+\frac {7 A \,x^{\frac {1}{3}}}{5}+\frac {31 A^{2}}{3 x^{\frac {1}{3}}}-\frac {100 A^{4}}{3 x^{\frac {5}{3}}} \]

\[ {}y y^{\prime }-y = -\frac {10 x}{49}+\frac {13 A^{2}}{5 x^{\frac {1}{5}}}-\frac {7 A^{3}}{20 x^{\frac {4}{5}}} \]

\[ {}y y^{\prime }-y = -\frac {33 x}{169}+\frac {286 A^{2}}{3 x^{\frac {5}{11}}}-\frac {770 A^{3}}{9 x^{\frac {13}{11}}} \]

\[ {}y y^{\prime }-y = -\frac {21 x}{100}+\frac {7 A^{2} \left (\frac {123}{x^{\frac {1}{7}}}+\frac {280 A}{x^{\frac {5}{7}}}-\frac {400 A^{2}}{x^{\frac {9}{7}}}\right )}{9} \]

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

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

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