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

\[ {}y^{\prime } = \frac {-8 x y-x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32} \]

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

\[ {}y^{\prime } = -\frac {i \left (16 i x^{2}+16 y^{4}+8 x^{4} y^{2}+x^{8}\right ) x}{32 y} \]

\[ {}y^{\prime } = \frac {2 y^{6}}{y^{3}+2+16 y^{2} x +32 y^{4} x^{2}} \]

\[ {}y^{\prime } = \frac {-4 a x y-a^{2} x^{3}-2 a b \,x^{2}-4 a x +8}{8 y+2 x^{2} a +4 b x +8} \]

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

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

\[ {}y^{\prime } = \frac {-4 x y-x^{3}-2 x^{2} a -4 x +8}{8 y+2 x^{2}+4 a x +8} \]

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

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

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

\[ {}y^{\prime } = \frac {-3 x^{2} y+1+y^{2} x^{6}+y^{3} x^{9}}{x^{3}} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 y^{2} x +8 y^{3}}{\left (2 x -b \right )^{3}} \]

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

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

\[ {}y^{\prime } = \frac {f_{1} \left (y^{2}-2 \ln \left (x \right )\right )}{\sqrt {y^{2}}\, x} \]

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

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

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

\[ {}y^{\prime } = -\frac {1}{-x -f_{1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}} \]

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

\[ {}y^{\prime } = \frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 y^{2} x +64 y^{3}}{\left (4 x -5\right )^{3}} \]

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

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

\[ {}y^{\prime } = \frac {x^{2}}{2}+\sqrt {x^{3}-6 y}+x^{2} \sqrt {x^{3}-6 y}+x^{3} \sqrt {x^{3}-6 y} \]

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

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

\[ {}y^{\prime } = \frac {\left (3+y\right )^{3} {\mathrm e}^{\frac {9 x^{2}}{2}} x \,{\mathrm e}^{\frac {3 x^{2}}{2}} {\mathrm e}^{-3 x^{2}}}{243 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+243 y} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {1+2 \sqrt {4 x^{2} y+1}\, x^{3}+2 x^{5} \sqrt {4 x^{2} y+1}+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3}} \]

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

\[ {}y^{\prime } = \frac {2 a +\sqrt {-y^{2}+4 a x}+x^{2} \sqrt {-y^{2}+4 a x}+x^{3} \sqrt {-y^{2}+4 a x}}{y} \]

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

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

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

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

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

\[ {}y^{\prime } = -\frac {1}{-\ln \left (x \right ) \left (y^{3}\right )^{\frac {2}{3}}-f_{1} \left (y^{3}+3 \,\operatorname {expIntegral}_{1}\left (-\ln \left (x \right )\right )\right ) \ln \left (x \right ) \left (y^{3}\right )^{\frac {1}{3}}} \]

\[ {}y^{\prime } = \frac {30 x^{3}+25 \sqrt {x}+25 y^{2}-20 x^{3} y-100 y \sqrt {x}+4 x^{6}+40 x^{\frac {7}{2}}+100 x}{25 x} \]

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

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

\[ {}y^{\prime } = \frac {b \,x^{3}+c^{2} \sqrt {a}-2 c b \,x^{2} \sqrt {a}+2 c y^{2} a^{\frac {3}{2}}+b^{2} x^{4} \sqrt {a}-2 y^{2} a^{\frac {3}{2}} b \,x^{2}+a^{\frac {5}{2}} y^{4}}{a \,x^{2} y} \]

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

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

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

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

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

\[ {}y^{\prime } = \frac {x}{2}+\frac {1}{2}+\sqrt {x^{2}+2 x +1-4 y}+x^{2} \sqrt {x^{2}+2 x +1-4 y}+x^{3} \sqrt {x^{2}+2 x +1-4 y} \]

\[ {}y^{\prime } = \frac {\cosh \left (x \right )}{\sinh \left (x \right )}+f_{1} \left (y-\ln \left (\sinh \left (x \right )\right )\right ) \]

\[ {}y^{\prime } = -\frac {x}{2}+1+\sqrt {x^{2}-4 x +4 y}+x^{2} \sqrt {x^{2}-4 x +4 y}+x^{3} \sqrt {x^{2}-4 x +4 y} \]

\[ {}y^{\prime } = \frac {1}{\sin \left (x \right )}+f_{1} \left (y-\ln \left (\sin \left (x \right )\right )+\ln \left (\cos \left (x \right )+1\right )\right ) \]

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

\[ {}y^{\prime } = \frac {\alpha ^{3}+y^{2} \alpha ^{3}+2 y \alpha ^{2} \beta x +\alpha \,\beta ^{2} x^{2}+y^{3} \alpha ^{3}+3 y^{2} \alpha ^{2} \beta x +3 y \alpha \,\beta ^{2} x^{2}+\beta ^{3} x^{3}}{\alpha ^{3}} \]

\[ {}y^{\prime } = \frac {14 x y+12+2 x +y^{3} x^{3}+6 x^{2} y^{2}}{x^{2} \left (x y+2+x \right )} \]

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

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

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

\[ {}y^{\prime } = -\frac {x}{4}+\frac {1}{4}+\sqrt {x^{2}-2 x +1+8 y}+x^{2} \sqrt {x^{2}-2 x +1+8 y}+x^{3} \sqrt {x^{2}-2 x +1+8 y} \]

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

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

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

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

\[ {}y^{\prime } = -\left (\frac {\operatorname {expIntegral}_{1}\left (-\ln \left (y-1\right )\right )}{x}-f_{1} \left (x \right )\right ) \ln \left (y-1\right ) \]

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

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

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