\[ {}y^{\prime } = \tan \left (x y\right ) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x y^{\prime }+n y = f \left (x \right ) g \left (x^{n} y\right ) \]

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

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

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

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

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

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

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

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

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

\[ {}\left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y = 0 \]

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

\[ {}x^{7} y y^{\prime } = 2 x^{2}+2+5 x^{3} y \]

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

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

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

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

\[ {}\left (x +2 y+2 x^{2} y^{3}+y^{4} x \right ) y^{\prime }+\left (1+y^{4}\right ) y = 0 \]

\[ {}f \left (x \right ) y^{m} y^{\prime }+g \left (x \right ) y^{1+m}+h \left (x \right ) y^{n} = 0 \]

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

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

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

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

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

\[ {}y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 x a +y^{2} = 0 \]

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

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

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

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

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

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

\[ {}9 \left (-x^{2}+1\right ) y^{4} {y^{\prime }}^{2}+6 x y^{5} y^{\prime }+4 x^{2} = 0 \]

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

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

\[ {}{y^{\prime }}^{4}-4 x^{2} y {y^{\prime }}^{2}+16 x y^{2} y^{\prime }-16 y^{3} = 0 \]

\[ {}x {y^{\prime }}^{4}-2 y {y^{\prime }}^{3}+12 x^{3} = 0 \]

\[ {}\ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) = y \]

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

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

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

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

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

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

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

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

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

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

\[ {}x {y^{\prime }}^{4}-2 y {y^{\prime }}^{3}+12 x^{3} = 0 \]

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

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

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

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

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

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

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

\[ {}y^{\prime }-f \left (x \right )^{-n +1} g^{\prime }\left (x \right ) y^{n} \left (a g \left (x \right )+b \right )^{-n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right ) = 0 \]

\[ {}y^{\prime }-a^{n} f \left (x \right )^{-n +1} g^{\prime }\left (x \right ) y^{n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right ) = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (x +2 y+2 x^{2} y^{3}+y^{4} x \right ) y^{\prime }+y^{5}+y = 0 \]

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

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

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

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

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

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

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

\[ {}y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 x a +y^{2} = 0 \]

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

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

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

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

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

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

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

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

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

\[ {}9 y^{4} \left (x^{2}-1\right ) {y^{\prime }}^{2}-6 x y^{5} y^{\prime }-4 x^{2} = 0 \]

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

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

\[ {}x^{n -1} {y^{\prime }}^{n}-n x y^{\prime }+y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {6 y}{8 y^{4}+9 y^{3}+12 y^{2}+6 y-F \left (-\frac {y^{4}}{3}-\frac {y^{3}}{2}-y^{2}-y+x \right )} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = -\frac {i \left (54 i x^{2}+81 y^{4}+18 x^{4} y^{2}+x^{8}\right ) x}{243 y} \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = -\frac {-\frac {1}{x}-\textit {\_F1} \left (y+\frac {1}{x}\right )}{x} \]

\[ {}y^{\prime } = \frac {\textit {\_F1} \left (y^{2}-2 \ln \left (x \right )\right )}{\sqrt {y^{2}}\, x} \]

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

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

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

\[ {}y^{\prime } = -\frac {1}{-x -\textit {\_F1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {1}{-x +\left (\frac {1}{y}+1\right ) x +\textit {\_F1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2}-\textit {\_F1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2} \left (\frac {1}{y}+1\right )} \]

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

\[ {}y^{\prime } = \frac {\cosh \left (x \right )}{\sinh \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sinh \left (x \right )\right )\right ) \]

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

\[ {}y^{\prime } = \frac {1}{\sin \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sin \left (x \right )\right )+\ln \left (\cos \left (x \right )+1\right )\right ) \]

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

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

\[ {}y^{\prime } = -\frac {\left (-\frac {1}{x}-\textit {\_F1} \left (y^{2}-2 x \right )\right ) x}{\sqrt {y^{2}}} \]

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

\[ {}y^{\prime } = -\frac {-x -\textit {\_F1} \left (y^{2}-2 x \right )}{\sqrt {y^{2}}\, x} \]

\[ {}y^{\prime } = -\frac {\left (-\frac {y \,{\mathrm e}^{\frac {1}{x}}}{x}-\textit {\_F1} \left (y \,{\mathrm e}^{\frac {1}{x}}\right )\right ) {\mathrm e}^{-\frac {1}{x}}}{x} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = -\frac {1296 y}{216-432 x y+216 x y^{2}-1944 y^{4}-2376 y^{2}+216 x^{3}-1296 y+216 x^{2}-1728 y^{3}-315 y^{9}-8 y^{12}-570 y^{8}-648 x^{2} y+1152 y^{4} x -882 y^{6}-612 y^{5}-324 x^{2} y^{3}-846 y^{7}-126 y^{10}-36 y^{11}-648 x^{2} y^{2}-216 y^{4} x^{2}+72 y^{8} x +216 y^{7} x +1080 y^{5} x +594 x y^{6}+1080 x y^{3}} \]

\[ {}y^{\prime } = -\frac {216 y \left (-2 y^{4}-3 y^{3}-6 y^{2}-6 y+6 x +6\right )}{-1296 x y-1944 x y^{2}+2808 y^{4}-1296 y^{2}+216 x^{3}-1296 y+1728 y^{3}-315 y^{9}-8 y^{12}-18 y^{8}-648 x^{2} y-432 y^{4} x +2484 y^{6}+4428 y^{5}-324 x^{2} y^{3}+594 y^{7}-126 y^{10}-36 y^{11}-648 x^{2} y^{2}-216 y^{4} x^{2}+72 y^{8} x +216 y^{7} x +1080 y^{5} x +594 x y^{6}-648 x y^{3}} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (a \tan \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+k \tan \left (\mu x \right ) y-d^{2}+k d \tan \left (\mu x \right ) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y y^{\prime }+\frac {a \left (7 x -12\right ) y}{10 x^{\frac {7}{5}}} = -\frac {a^{2} \left (-1+x \right ) \left (x -16\right )}{10 x^{\frac {9}{5}}} \]

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

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

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

\[ {}y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{\frac {6}{5}}} = -\frac {a^{2} \left (-1+x \right ) \left (9 x -4\right )}{30 x^{\frac {7}{5}}} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 x y^{\prime }-1 = 0 \]

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

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

\[ {}x x^{\prime } = 1-x t \]

\[ {}{y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2} = 1 \]

\[ {}6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0 \]

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

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

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

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

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

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

\[ {}y^{\prime }-2 \,{\mathrm e}^{x} y = 2 \sqrt {{\mathrm e}^{x} y} \]

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

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

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

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

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

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