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

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

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

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

\[ {}\left (y^{\prime \prime }\right )^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right ) \]

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

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

\[ {}y^{\prime \prime }+y = -\cos \relax (x ) \]

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{x} \]

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 12 x^{2} \]

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = x^{2}+2 x +1 \]

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

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

\[ {}9 \left (y^{\prime }\right )^{2}+3 x y^{4} y^{\prime }+y^{5} = 0 \]

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

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

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

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

\[ {}4 x^{5} \left (y^{\prime }\right )^{2}+12 x^{4} y y^{\prime }+9 = 0 \]

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

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

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

\[ {}16 x \left (y^{\prime }\right )^{2}+8 y y^{\prime }+y^{6} = 0 \]

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

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

\[ {}9 x y^{4} \left (y^{\prime }\right )^{2}-3 y^{5} y^{\prime }-1 = 0 \]

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

\[ {}x^{6} \left (y^{\prime }\right )^{2} = 16 y+8 x y^{\prime } \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+10 x y^{\prime }+20 y = 0 \]

\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+3 x y^{\prime }+7 y = 0 \]

\[ {}2 y^{\prime \prime }+9 x y^{\prime }-36 y = 0 \]

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

\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+3 x y^{\prime }-8 y = 0 \]

\[ {}\left (9 x^{2}+1\right ) y^{\prime \prime }-18 y = 0 \]

\[ {}\left (3 x^{2}+1\right ) y^{\prime \prime }+13 x y^{\prime }+7 y = 0 \]

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

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

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

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

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

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

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

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

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

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

\[ {}8 x^{2} y^{\prime \prime }+10 x y^{\prime }-\left (x +1\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]

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

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

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

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

\[ {}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y = 0 \]

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

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

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

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

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

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