\[ {}r^{\prime \prime } = \frac {h^{2}}{r^{3}}-\frac {k}{r^{2}} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}u^{\prime \prime }-\frac {a^{2} u}{x^{\frac {2}{3}}} = 0 \]

\[ {}u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]

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

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

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

\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0 \]

\[ {}y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}} \]

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \]

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 8 x^{4} \]

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

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 2 x^{3} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y = 0 \]

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

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

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

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

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