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

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

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

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

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

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

\[ {}y^{\prime \prime }+3 y y^{\prime }+y^{3}+f \relax (x ) y-g \relax (x ) = 0 \]

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

\[ {}y^{\prime \prime }-3 y y^{\prime }-3 a y^{2}-4 a^{2} y-b = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}8 y^{\prime \prime }+9 \left (y^{\prime }\right )^{4} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}9 x^{2} y^{\prime \prime }+a y^{3}+2 y = 0 \]

\[ {}x^{3} \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )+12 x y+24 = 0 \]

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

\[ {}2 x^{3} y^{\prime \prime }+x^{2} \left (9+2 x y\right ) y^{\prime }+b +x y \left (a +3 x y-2 x^{2} y^{2}\right ) = 0 \]

\[ {}2 \left (-x^{k}+4 x^{3}\right ) \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )-\left (k \,x^{k -1}-12 x^{2}\right ) \left (3 y^{\prime }+y^{2}\right )+y a x +b = 0 \]

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

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

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

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

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

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

\[ {}x^{\frac {n}{n +1}} y^{\prime \prime }-y^{\frac {2 n +1}{n +1}} = 0 \]

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime } y-\left (y^{\prime }\right )^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right ) = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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