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

\[ {}r^{\prime \prime }-6 r^{\prime }+9 r = 0 \]

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

\[ {}y^{\prime \prime } = -4 y \]

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

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

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

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

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

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

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

\[ {}x^{\prime \prime }+42 x^{\prime }+x = 0 \]

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

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

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

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

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

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

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

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

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

\[ {}\frac {x^{\prime \prime }}{2} = -48 x \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}9 y^{\prime \prime }-6 y^{\prime }+y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+16 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+10 y = 0 \]

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