\[ {}x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-8 x^{3} y = 4 x^{3} {\mathrm e}^{-x^{2}} \]

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

\[ {}\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}2 y^{\prime \prime } = {\mathrm e}^{y} \]

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

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

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

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

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

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

\[ {}\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = 0 \]

\[ {}2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 x^{2} {y^{\prime }}^{2}+36 x y y^{\prime }+6 y^{2} = 0 \]

\[ {}x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y = 0 \]

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

\[ {}x^{2} y^{\prime \prime \prime }-5 x y^{\prime \prime }+\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y = 0 \]

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

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

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

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

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

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

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

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

\[ {}\left (x^{3}+1\right ) y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+18 x y^{\prime }+6 y = 0 \]

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

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

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

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

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

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

\[ {}4 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }+y^{\prime } = 0 \]

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

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

\[ {}x^{\prime } = \frac {2 x}{t} \]

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

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

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

\[ {}x^{\prime } = {\mathrm e}^{-x} \]

\[ {}x^{\prime }+2 x = t^{2}+4 t +7 \]

\[ {}2 t x^{\prime } = x \]

\[ {}t^{2} x^{\prime \prime }-6 x = 0 \]

\[ {}2 x^{\prime \prime }-5 x^{\prime }-3 x = 0 \]

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

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

\[ {}x^{\prime } = t \cos \left (t^{2}\right ) \]

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

\[ {}x^{\prime \prime } = -3 \sqrt {t} \]

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

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

\[ {}\sqrt {t}\, x^{\prime } = \cos \left (\sqrt {t}\right ) \]

\[ {}x^{\prime } = \frac {{\mathrm e}^{-t}}{\sqrt {t}} \]

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

\[ {}x^{\prime } = \sqrt {x} \]

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

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

\[ {}u^{\prime } = \frac {1}{5-2 u} \]

\[ {}x^{\prime } = a x+b \]

\[ {}Q^{\prime } = \frac {Q}{4+Q^{2}} \]

\[ {}x^{\prime } = {\mathrm e}^{x^{2}} \]

\[ {}y^{\prime } = r \left (a -y\right ) \]

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

\[ {}\theta ^{\prime } = t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \]

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

\[ {}R^{\prime } = \left (t +1\right ) \left (1+R^{2}\right ) \]

\[ {}y^{\prime }+y+\frac {1}{y} = 0 \]

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

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

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

\[ {}x^{\prime } = 2 t x^{2} \]

\[ {}x^{\prime } = t^{2} {\mathrm e}^{-x} \]

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

\[ {}x^{\prime } = {\mathrm e}^{t +x} \]

\[ {}T^{\prime } = 2 a t \left (T^{2}-a^{2}\right ) \]

\[ {}y^{\prime } = t^{2} \tan \left (y\right ) \]

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

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

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

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

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

\[ {}x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t} = {\mathrm e}^{-t} \]

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

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

\[ {}y^{\prime } = -y^{2} {\mathrm e}^{-t^{2}} \]

\[ {}x^{\prime } = 2 t^{3} x-6 \]

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