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

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

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

\[ {}y^{\prime \prime } = y^{\prime } \ln \left (y^{\prime }\right ) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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