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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \]

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

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \]

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

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = 0 \]

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \]

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

\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+25 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}u^{\prime \prime }-\cot \left (\theta \right ) u^{\prime } = 0 \]

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 0 \]

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

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

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

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

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

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

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