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

\[ {}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \]

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

\[ {}x^{3} x^{\prime \prime }+1 = 0 \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}x y^{\prime \prime }-{y^{\prime }}^{2} = 6 x^{5} \]

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

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

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

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

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

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

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

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

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

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

\[ {}y^{3} y^{\prime \prime } = -1 \]

\[ {}y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \]