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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }-18 y = 0 \]

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

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

\[ {}x \left (-x^{2}+1\right ) y^{\prime \prime }-\left (x^{2}+7\right ) y^{\prime }+4 x y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-9 x y^{\prime }+25 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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