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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}4 y^{\prime \prime }-8 y^{\prime }+5 y = 0 \]

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }+6 y = 0 \]

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

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

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

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

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

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

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

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

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

\[ {}x^{\prime \prime }+2 x^{\prime }+6 x = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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