\[ {}y y^{\prime }+\frac {a \left (17 x +18\right ) y}{30 x^{\frac {22}{15}}} = -\frac {a^{2} \left (-1+x \right ) \left (x +4\right )}{30 x^{\frac {29}{15}}} \]

\[ {}y y^{\prime }-\frac {a \left (6 x -13\right ) y}{13 x^{\frac {5}{2}}} = -\frac {a^{2} \left (-1+x \right ) \left (x -13\right )}{26 x^{4}} \]

\[ {}y y^{\prime }+\frac {a \left (24 x +11\right ) x^{\frac {27}{20}} y}{30} = -\frac {a^{2} \left (-1+x \right ) \left (9 x +1\right )}{60 x^{\frac {17}{10}}} \]

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

\[ {}y y^{\prime }-\frac {6 a \left (1+4 x \right ) y}{5 x^{\frac {7}{5}}} = \frac {a^{2} \left (-1+x \right ) \left (27 x +8\right )}{5 x^{\frac {9}{5}}} \]

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

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

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

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

\[ {}y y^{\prime }+\frac {a \left (21 x +19\right ) y}{5 x^{\frac {7}{5}}} = -\frac {2 a^{2} \left (-1+x \right ) \left (9 x -4\right )}{5 x^{\frac {9}{5}}} \]

\[ {}y y^{\prime }-\frac {3 a y}{x^{\frac {7}{4}}} = \frac {a^{2} \left (-1+x \right ) \left (x -9\right )}{4 x^{\frac {5}{2}}} \]

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

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

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

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

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

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

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

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

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

\[ {}y y^{\prime }+\frac {a \left (\frac {\left (3 n +5\right ) x}{2}+\frac {n -1}{n +1}\right ) x^{-\frac {n +4}{n +3}} y}{n +3} = -\frac {a^{2} \left (\left (n +1\right ) x^{2}-\frac {\left (n^{2}+2 n +5\right ) x}{n +1}+\frac {4}{n +1}\right ) x^{-\frac {n +5}{n +3}}}{2 n +6} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime } = 0 \]

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

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

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

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

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

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

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

\[ {}2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0 \]

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

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

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

\[ {}4 x -y+2+\left (x +y+3\right ) y^{\prime } = 0 \]

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

\[ {}y+2 x y^{2}-x^{2} y^{3}+2 x^{2} y y^{\prime } = 0 \]

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

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

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

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

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

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

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

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

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

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

\[ {}4 x y^{\prime }+3 y+{\mathrm e}^{x} x^{4} y^{5} = 0 \]

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

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

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

\[ {}2 x^{3} y-y^{2}-\left (2 x^{4}+x y\right ) y^{\prime } = 0 \]

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

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

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

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

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

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

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

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

\[ {}y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime } = 0 \]

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

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

\[ {}x y^{\prime }-y+2 x^{2} y-x^{3} = 0 \]

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

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

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

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

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

\[ {}y^{\prime }-x^{2} y = x^{5} \]

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

\[ {}x y^{\prime }+y+x^{4} y^{4} {\mathrm e}^{x} = 0 \]

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

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

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