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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (x^{3}+4 x \right ) y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \]

\[ {}x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y = 0 \]

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

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

\[ {}x^{3} \left (x^{2}-25\right ) \left (-2+x \right )^{2} y^{\prime \prime }+3 x \left (-2+x \right ) y^{\prime }+7 \left (5+x \right ) y = 0 \]

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

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

\[ {}x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}16 x^{2} y^{\prime \prime }+16 x y^{\prime }+\left (16 x^{2}-1\right ) y = 0 \]

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \]

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y = 0 \]

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0 \]