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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}10 y^{\prime \prime }+x^{2} y^{\prime }+\frac {3 {y^{\prime }}^{2}}{y} = 0 \]

\[ {}10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )} = 0 \]

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

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

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

\[ {}y^{\prime \prime }-6 y^{2}+4 y = 0 \]

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

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

\[ {}y^{\prime \prime }+6 a^{10} y^{11}-y = 0 \]

\[ {}y^{\prime \prime }-\frac {1}{\left (a y^{2}+b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{\frac {3}{2}}} = 0 \]

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

\[ {}y^{\prime \prime }+a \,{\mathrm e}^{x} \sqrt {y} = 0 \]

\[ {}y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right ) = 0 \]

\[ {}y^{\prime \prime }+a \sin \left (y\right ) = 0 \]

\[ {}y^{\prime \prime } = \frac {f \left (\frac {y}{\sqrt {x}}\right )}{x^{\frac {3}{2}}} \]

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

\[ {}y^{\prime \prime }-7 y^{\prime }-y^{\frac {3}{2}}+12 y = 0 \]

\[ {}y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y = 0 \]

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

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

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

\[ {}y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n} = 0 \]

\[ {}y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right ) = 0 \]

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+f \left (x , y\right ) y^{\prime }+g \left (x , y\right ) = 0 \]

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

\[ {}y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b y^{\prime }+c y = 0 \]

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

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

\[ {}y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b \sin \left (y\right ) = 0 \]

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

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

\[ {}y^{\prime \prime }-\frac {D\left (f \right )\left (y\right ) {y^{\prime }}^{3}}{f \left (y\right )}+g \left (x \right ) y^{\prime }+h \left (x \right ) f \left (y\right ) = 0 \]

\[ {}y^{\prime \prime }+\phi \left (y\right ) {y^{\prime }}^{2}+f \left (x \right ) y^{\prime }+g \left (x \right ) \Phi \left (y\right ) = 0 \]

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

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

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

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

\[ {}y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r} = 0 \]

\[ {}y^{\prime \prime }+\left (y^{\prime }-\frac {y}{x}\right )^{a} f \left (x , y\right ) = 0 \]

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-f \left (y^{\prime }, a x +b y\right ) = 0 \]

\[ {}y^{\prime \prime }-y f \left (x , \frac {y^{\prime }}{y}\right ) = 0 \]

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

\[ {}8 y^{\prime \prime }+9 {y^{\prime }}^{4} = 0 \]

\[ {}a y^{\prime \prime }+h \left (y^{\prime }\right )+c y = 0 \]

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

\[ {}x y^{\prime \prime }+2 y^{\prime }+a \,x^{v} y^{n} = 0 \]

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

\[ {}x y^{\prime \prime }+a y^{\prime }+b x \,{\mathrm e}^{y} = 0 \]

\[ {}x y^{\prime \prime }+a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y} = 0 \]

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

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