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

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

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

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

\[ {}2 y^{\prime \prime } = {\mathrm e}^{y} \]

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

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

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

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

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

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

\[ {}\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = 0 \]

\[ {}2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 x^{2} \left (y^{\prime }\right )^{2}+36 x y y^{\prime }+6 y^{2} = 0 \]

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

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

\[ {}x^{2} y^{\prime \prime \prime }-5 x y^{\prime \prime }+\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y = 0 \]

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

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

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

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

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