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

\[ {}y^{\prime } = -\frac {2 x}{3}+1+y^{2}+\frac {2 x^{2} y}{3}+\frac {x^{4}}{9}+y^{3}+x^{2} y^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27} \]

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

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

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

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

\[ {}y^{\prime } = \frac {-30 x^{3} y+12 x^{6}+70 x^{\frac {7}{2}}-30 x^{3}-25 y \sqrt {x}+50 x -25 \sqrt {x}-25}{5 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \]

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

\[ {}y^{\prime } = \frac {\left (-256 x^{2} a +512+512 y^{2}+128 y a \,x^{4}+8 a^{2} x^{8}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512} \]

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

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

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

\[ {}y^{\prime } = \frac {1+y^{4}-8 a x y^{2}+16 a^{2} x^{2}+y^{6}-12 y^{4} a x +48 y^{2} a^{2} x^{2}-64 a^{3} x^{3}}{y} \]

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

\[ {}y^{\prime } = -\frac {2 a}{-y-2 a -2 a y^{4}+16 a^{2} x y^{2}-32 a^{3} x^{2}-2 a y^{6}+24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \]

\[ {}y^{\prime } = \frac {-18 x y-6 x^{3}-18 x +27 y^{3}+27 x^{2} y^{2}+9 x^{4} y+x^{6}}{27 y+9 x^{2}+27} \]

\[ {}y^{\prime } = -\frac {\left (-108 x^{\frac {3}{2}}-216-216 y^{2}+72 x^{3} y-6 x^{6}-216 y^{3}+108 x^{3} y^{2}-18 y x^{6}+x^{9}\right ) \sqrt {x}}{216} \]

\[ {}y^{\prime } = \frac {\left (a^{3}+y^{4} a^{3}+2 y^{2} a^{2} b \,x^{2}+a \,x^{4} b^{2}+y^{6} a^{3}+3 y^{4} a^{2} b \,x^{2}+3 y^{2} a \,b^{2} x^{4}+b^{3} x^{6}\right ) x}{a^{\frac {7}{2}} y} \]

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

\[ {}y^{\prime } = -\frac {i \left (32 i x +64+64 y^{4}+32 x^{2} y^{2}+4 x^{4}+64 y^{6}+48 y^{4} x^{2}+12 x^{4} y^{2}+x^{6}\right )}{128 y} \]

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

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

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

\[ {}y^{\prime } = -\frac {\left (-8-8 y^{3}+24 y^{\frac {3}{2}} {\mathrm e}^{x}-18 \,{\mathrm e}^{2 x}-8 y^{\frac {9}{2}}+36 y^{3} {\mathrm e}^{x}-54 y^{\frac {3}{2}} {\mathrm e}^{2 x}+27 \,{\mathrm e}^{3 x}\right ) {\mathrm e}^{x}}{8 \sqrt {y}} \]

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

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

\[ {}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{-\frac {2}{-y^{2}+x^{2}-1}}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{-\frac {2}{-y^{2}+x^{2}-1}}} \]

\[ {}y^{\prime } = \frac {6 x +x^{3}+x^{3} y^{2}+4 x^{2} y+y^{3} x^{3}+6 x^{2} y^{2}+12 x y+8}{x^{3}} \]

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

\[ {}y^{\prime } = \frac {\left (-256 x^{2} a y-32 a^{2} x^{6}-256 x^{2} a +512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512 y+64 a \,x^{4}+512} \]

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

\[ {}y^{\prime } = \frac {\left (-108 y x^{\frac {3}{2}}+18 x^{\frac {9}{2}}-108 x^{\frac {3}{2}}-216 y^{3}+108 x^{3} y^{2}-18 y x^{6}+x^{9}\right ) \sqrt {x}}{-216 y+36 x^{3}-216} \]

\[ {}y^{\prime } = \frac {32 x^{5} y+8 x^{3}+32 x^{5}+64 x^{6} y^{3}+48 x^{4} y^{2}+12 x^{2} y+1}{16 x^{6} \left (4 x^{2} y+1+4 x^{2}\right )} \]

\[ {}y^{\prime } = \frac {32 x^{5}+64 x^{6}+64 y^{2} x^{6}+32 x^{4} y+4 x^{2}+64 x^{6} y^{3}+48 x^{4} y^{2}+12 x^{2} y+1}{64 x^{8}} \]

\[ {}y^{\prime } = \frac {2 a \left (-y^{2}+4 a x -1\right )}{-y^{3}+4 a x y-y-2 a y^{6}+24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {2 a x}{-x^{3} y+2 a \,x^{3}+2 a y^{4} x^{3}-16 y^{2} a^{2} x^{2}+32 a^{3} x +2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \]

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

\[ {}y^{\prime } = \frac {2 a \left (y^{2} x -4 a +x \right )}{-y^{3} x^{3}+4 x^{2} a y-x^{3} y+2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \]

\[ {}y^{\prime } = -\frac {-y^{3}-y+4 y^{2} \ln \left (x \right )-4 \ln \left (x \right )^{2} y^{3}-1+6 y \ln \left (x \right )-12 \ln \left (x \right )^{2} y^{2}+8 \ln \left (x \right )^{3} y^{3}}{y x} \]

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

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

\[ {}y^{\prime } = \frac {2 y^{8}}{y^{5}+2 y^{6}+2 y^{2}+16 x y^{4}+32 y^{6} x^{2}+2+24 y^{2} x +96 y^{4} x^{2}+128 x^{3} y^{6}} \]

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

\[ {}y^{\prime } = \frac {2 y^{6} \left (1+4 y^{2} x +y^{2}\right )}{y^{3}+4 y^{5} x +y^{5}+2+24 y^{2} x +96 y^{4} x^{2}+128 x^{3} y^{6}} \]

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

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

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

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

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

\[ {}y^{\prime } = \frac {-8 x^{2} y^{3}+16 y^{2} x +16 x y^{3}-8+12 x y-6 x^{2} y^{2}+y^{3} x^{3}}{16 \left (-2+x y-2 y\right ) x} \]

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

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

\[ {}y^{\prime } = -\frac {16 x y^{3}-8 y^{3}-8 y+8 y^{2} x -2 x^{2} y^{3}-8+12 x y-6 x^{2} y^{2}+y^{3} x^{3}}{32 y x} \]

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

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

\[ {}y^{\prime } = \frac {\left (27 y^{3}+27 \,{\mathrm e}^{3 x^{2}} y+18 \,{\mathrm e}^{3 x^{2}} y^{2}+3 y^{3} {\mathrm e}^{3 x^{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y+9 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y^{2}+{\mathrm e}^{\frac {9 x^{2}}{2}} y^{3}\right ) {\mathrm e}^{3 x^{2}} x \,{\mathrm e}^{-\frac {9 x^{2}}{2}}}{243 y} \]

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

\[ {}y^{\prime } = \frac {x}{2}+1+y^{2}+\frac {x^{2} y}{4}-x y-\frac {x^{4}}{8}+\frac {x^{3}}{8}+\frac {x^{2}}{4}+y^{3}-\frac {3 x^{2} y^{2}}{4}-\frac {3 y^{2} x}{2}+\frac {3 x^{4} y}{16}+\frac {3 x^{3} y}{4}-\frac {x^{6}}{64}-\frac {3 x^{5}}{32} \]

\[ {}y^{\prime } = -\frac {x}{2}+1+y^{2}+\frac {7 x^{2} y}{2}-2 x y+\frac {13 x^{4}}{16}-\frac {3 x^{3}}{2}+x^{2}+y^{3}+\frac {3 x^{2} y^{2}}{4}-3 y^{2} x +\frac {3 x^{4} y}{16}-\frac {3 x^{3} y}{2}+\frac {x^{6}}{64}-\frac {3 x^{5}}{16} \]

\[ {}y^{\prime } = -\frac {x}{4}+1+y^{2}+\frac {7 x^{2} y}{16}-\frac {x y}{2}+\frac {5 x^{4}}{128}-\frac {5 x^{3}}{64}+\frac {x^{2}}{16}+y^{3}+\frac {3 x^{2} y^{2}}{8}-\frac {3 y^{2} x}{4}+\frac {3 x^{4} y}{64}-\frac {3 x^{3} y}{16}+\frac {x^{6}}{512}-\frac {3 x^{5}}{256} \]

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

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

\[ {}y^{\prime } = \frac {-32 x y+16 x^{3}+16 x^{2}-32 x -64 y^{3}+48 x^{2} y^{2}+96 y^{2} x -12 x^{4} y-48 x^{3} y-48 x^{2} y+x^{6}+6 x^{5}+12 x^{4}}{-64 y+16 x^{2}+32 x -64} \]

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

\[ {}y^{\prime } = \frac {-32 x y-72 x^{3}+32 x^{2}-32 x +64 y^{3}+48 x^{2} y^{2}-192 y^{2} x +12 x^{4} y-96 x^{3} y+192 x^{2} y+x^{6}-12 x^{5}+48 x^{4}}{64 y+16 x^{2}-64 x +64} \]

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

\[ {}y^{\prime } = \frac {-128 x y-24 x^{3}+32 x^{2}-128 x +512 y^{3}+192 x^{2} y^{2}-384 y^{2} x +24 x^{4} y-96 x^{3} y+96 x^{2} y+x^{6}-6 x^{5}+12 x^{4}}{512 y+64 x^{2}-128 x +512} \]

\[ {}y^{\prime } = \frac {-32 a x y-8 a^{2} x^{3}-16 a b \,x^{2}-32 a x +64 y^{3}+48 a \,x^{2} y^{2}+96 y^{2} b x +12 y a^{2} x^{4}+48 y a \,x^{3} b +48 y b^{2} x^{2}+a^{3} x^{6}+6 a^{2} x^{5} b +12 a \,x^{4} b^{2}+8 b^{3} x^{3}}{64 y+16 x^{2} a +32 b x +64} \]

\[ {}y^{\prime } = \frac {-32 x y-8 x^{3}-16 x^{2} a -32 x +64 y^{3}+48 x^{2} y^{2}+96 a x y^{2}+12 x^{4} y+48 y a \,x^{3}+48 a^{2} x^{2} y+x^{6}+6 x^{5} a +12 a^{2} x^{4}+8 a^{3} x^{3}}{64 y+16 x^{2}+32 a x +64} \]

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

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

\[ {}y^{\prime } = -\frac {216 y}{-216 y^{4}-252 y^{3}-396 y^{2}-216 y+36 x^{2}-72 x y+60 y^{5}-36 x y^{3}-72 y^{2} x -24 x y^{4}+4 y^{8}+12 y^{7}+33 y^{6}} \]

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

\[ {}y^{\prime } = -\frac {a x}{2}+1+y^{2}+\frac {x^{2} a y}{2}+b x y+\frac {a^{2} x^{4}}{16}+\frac {a \,x^{3} b}{4}+\frac {b^{2} x^{2}}{4}+y^{3}+\frac {3 a \,x^{2} y^{2}}{4}+\frac {3 y^{2} b x}{2}+\frac {3 y a^{2} x^{4}}{16}+\frac {3 y a \,x^{3} b}{4}+\frac {3 y b^{2} x^{2}}{4}+\frac {a^{3} x^{6}}{64}+\frac {3 a^{2} x^{5} b}{32}+\frac {3 a \,x^{4} b^{2}}{16}+\frac {b^{3} x^{3}}{8} \]

\[ {}y^{\prime } = -\frac {x}{2}+1+y^{2}+\frac {x^{2} y}{2}+a x y+\frac {x^{4}}{16}+\frac {a \,x^{3}}{4}+\frac {a^{2} x^{2}}{4}+y^{3}+\frac {3 x^{2} y^{2}}{4}+\frac {3 a x y^{2}}{2}+\frac {3 x^{4} y}{16}+\frac {3 y a \,x^{3}}{4}+\frac {3 a^{2} x^{2} y}{4}+\frac {x^{6}}{64}+\frac {3 x^{5} a}{32}+\frac {3 a^{2} x^{4}}{16}+\frac {a^{3} x^{3}}{8} \]

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

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

\[ {}y^{\prime } = \frac {150 x^{3}+125 \sqrt {x}+125+125 y^{2}-100 x^{3} y-500 y \sqrt {x}+20 x^{6}+200 x^{\frac {7}{2}}+500 x +125 y^{3}-150 x^{3} y^{2}-750 y^{2} \sqrt {x}+60 y x^{6}+600 y x^{\frac {7}{2}}+1500 x y-8 x^{9}-120 x^{\frac {13}{2}}-600 x^{4}-1000 x^{\frac {3}{2}}}{125 x} \]

\[ {}y^{\prime } = \frac {-150 x^{3} y+60 x^{6}+350 x^{\frac {7}{2}}-150 x^{3}-125 y \sqrt {x}+250 x -125 \sqrt {x}-125 y^{3}+150 x^{3} y^{2}+750 y^{2} \sqrt {x}-60 y x^{6}-600 y x^{\frac {7}{2}}-1500 x y+8 x^{9}+120 x^{\frac {13}{2}}+600 x^{4}+1000 x^{\frac {3}{2}}}{25 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \]

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

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

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

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

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

\[ {}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{2+2 y^{4}-4 x^{2} y^{2}+2 x^{4}+2 y^{6}-6 y^{4} x^{2}+6 x^{4} y^{2}-2 x^{6}}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{2+2 y^{4}-4 x^{2} y^{2}+2 x^{4}+2 y^{6}-6 y^{4} x^{2}+6 x^{4} y^{2}-2 x^{6}}} \]

\[ {}y^{\prime } = \frac {4 x \left (-1+a \right ) \left (a +1\right ) \left (-y^{2}+a^{2} x^{2}-x^{2}-2\right )}{-4 y^{3}+4 a^{2} x^{2} y-4 x^{2} y-8 y-a^{2} y^{6}+3 a^{4} y^{4} x^{2}-6 y^{4} a^{2} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-9 y^{2} a^{2} x^{4}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-4 a^{2} x^{6}+y^{6}+3 y^{4} x^{2}+3 x^{4} y^{2}+x^{6}} \]

\[ {}y^{\prime } = \frac {-4 \cos \left (x \right ) x +4 x^{2} \sin \left (x \right )+4 x +4+4 y^{2}+8 y \cos \left (x \right ) x -8 x y+2 x^{2} \cos \left (2 x \right )+6 x^{2}-8 x^{2} \cos \left (x \right )+4 y^{3}+12 y^{2} \cos \left (x \right ) x -12 y^{2} x +6 y x^{2} \cos \left (2 x \right )+18 x^{2} y-24 y \cos \left (x \right ) x^{2}+x^{3} \cos \left (3 x \right )+15 x^{3} \cos \left (x \right )-6 x^{3} \cos \left (2 x \right )-10 x^{3}}{4 x} \]

\[ {}y^{\prime } = -\frac {8 x \left (-1+a \right ) \left (a +1\right )}{8+x^{6}-8 y+2 x^{4}+2 y^{4}+4 a^{4} y^{2} x^{2}-6 y^{4} a^{2} x^{2}+y^{6}-8 a^{2}-4 a^{2} x^{6}+4 x^{2} y^{2}+3 a^{4} y^{4} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-9 y^{2} a^{2} x^{4}+3 x^{4} y^{2}+3 y^{4} x^{2}-2 a^{2} y^{4}-2 a^{6} x^{4}+6 a^{4} x^{4}-6 a^{2} x^{4}-a^{2} y^{6}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-8 y^{2} a^{2} x^{2}} \]

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