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

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

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

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

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

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

\[ {}y y^{\prime }-y = A \]

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

\[ {}y y^{\prime }-y = -\frac {2 x}{9}+A +\frac {B}{\sqrt {x}} \]

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

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

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

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

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

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

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

\[ {}y y^{\prime }-y = -\frac {2 x}{9}+6 A^{2} \left (1+\frac {2 A}{\sqrt {x}}\right ) \]

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

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

\[ {}y y^{\prime }-y = \frac {4}{9} x +2 A \,x^{2}+2 A^{2} x^{3} \]

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

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

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

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

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

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

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

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

\[ {}y y^{\prime }-y = -\frac {9 x}{100}+\frac {A}{x^{\frac {5}{3}}} \]

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

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

\[ {}y y^{\prime }-y = -\frac {2 x}{9}+\frac {A}{\sqrt {x}} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y y^{\prime }-y = A \,x^{2}-\frac {9}{625 A} \]

\[ {}y y^{\prime }-y = -\frac {6}{25} x -A \,x^{2} \]

\[ {}y y^{\prime }-y = \frac {6}{25} x -A \,x^{2} \]

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

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

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

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

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

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

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

\[ {}y y^{\prime }-y = 6 x +\frac {A}{x^{4}} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y y^{\prime } = \frac {y}{\sqrt {a x +b}}+1 \]

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

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

\[ {}y y^{\prime } = a \,{\mathrm e}^{\lambda x} y+1 \]

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

\[ {}y y^{\prime } = a y \cosh \relax (x )+1 \]

\[ {}y y^{\prime } = a y \sinh \relax (x )+1 \]

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

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

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

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

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

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

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

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