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

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

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

\[ {}y^{\prime } = y^{3}+{\mathrm e}^{-5 t} \]

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

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

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

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

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

\[ {}y^{\prime } = \operatorname {f0} \left (x \right )+\operatorname {f1} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\operatorname {f3} \left (x \right ) y^{3} \]

\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}-a y^{3} \]

\[ {}x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3} = 0 \]

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

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

\[ {}x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3} = 0 \]

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

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

\[ {}y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1} = 0 \]

\[ {}y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {a f \left (x \right )+b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )} = 0 \]

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

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

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

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

\[ {}y^{\prime }-y^{3}-a \,{\mathrm e}^{x} y^{2} = 0 \]

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

\[ {}y^{\prime }+3 a y^{3}+6 a x y^{2} = 0 \]

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

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

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

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

\[ {}y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1} = 0 \]

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

\[ {}y^{\prime }-\left (a \,x^{n}+b x \right ) y^{3}-c y^{2} = 0 \]

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

\[ {}y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {a f \left (x \right )+b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )} = 0 \]

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

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

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

\[ {}x^{2} y^{\prime }+a \,x^{2} y^{3}+b y^{2} = 0 \]

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

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

\[ {}x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3} = 0 \]

\[ {}x^{1+2 n} y^{\prime }-a y^{3}-b \,x^{3 n} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = -\frac {x \left (-513-432 x +1008 x^{5} y-648 x^{2} y^{3}-864 x^{4}+864 y^{2} x^{5}-288 y x^{8}+288 y x^{7}-540 y^{2}-576 x^{5}-648 y^{3} x^{4}+432 y^{2} x^{7}-756 x^{3}-378 y-1134 x^{2}-456 x^{6}-972 x^{4} y^{2}-216 y^{3}-144 x^{7}-594 x^{2} y-96 x^{8}+720 x^{3} y+432 x^{3} y^{2}+64 x^{9}-216 y^{2} x^{6}-216 x^{6} y^{3}-288 y x^{6}-216 x^{4} y-1296 x^{2} y^{2}\right )}{216 \left (x^{2}+1\right )^{4}} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = 2 y^{3}+t^{2} \]

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