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

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

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

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

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

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

\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0 \]

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+x y^{\prime }-4 y = 6 \,{\mathrm e}^{x} \]

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

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

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

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

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

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

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

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

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

\[ {}6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0 \]

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

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

\[ {}3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y = 0 \]

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

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

\[ {}3 x^{2} y^{\prime \prime }+x \left (7+3 x \right ) y^{\prime }+\left (1+6 x \right ) y = 0 \]

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-\left (-1+2 \sqrt {5}\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0 \]

\[ {}x^{2} y^{\prime \prime }+\left (-2 x^{5}+9 x \right ) y^{\prime }+\left (10 x^{4}+5 x^{2}+25\right ) y = 0 \]

\[ {}x^{2} y^{\prime \prime }+\left (4 x +\frac {1}{2} x^{2}-\frac {1}{3} x^{3}\right ) y^{\prime }-\frac {7 y}{4} = 0 \]

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

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

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

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

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

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

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

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

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+7 x \,{\mathrm e}^{x} y^{\prime }+9 \left (1+\tan \left (x \right )\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-6 x y^{\prime }-4 y = 0 \]

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

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

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

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

\[ {}\left (4 x^{2}+1\right ) y^{\prime \prime }-8 y = 0 \]

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

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

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

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

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

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

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

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

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

\[ {}4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0 \]

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

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

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

\[ {}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \]

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

\[ {}2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0 \]

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

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

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