\[ {}x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a \right ) x^{3} y^{\prime \prime \prime }+\left (4 b^{2} c^{2} x^{2 c}+6 \left (-1+a \right )^{2}-2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )+1\right ) x^{2} y^{\prime \prime }+\left (4 \left (3 c -2 a +1\right ) b^{2} c^{2} x^{2 c}+\left (2 a -1\right ) \left (2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )-2 a \left (-1+a \right )-1\right )\right ) x y^{\prime }+\left (4 \left (-c +a \right ) \left (a -2 c \right ) b^{2} c^{2} x^{2 c}+\left (c \mu +c \nu +a \right ) \left (c \mu +c \nu -a \right ) \left (c \mu -c \nu +a \right ) \left (c \mu -c \nu -a \right )\right ) y = 0 \]

\[ {}x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a -4 c \right ) x^{3} y^{\prime \prime \prime }+\left (-2 \nu ^{2} c^{2}+2 a^{2}+4 \left (a +c -1\right )^{2}+4 \left (-1+a \right ) \left (c -1\right )-1\right ) x^{2} y^{\prime \prime }+\left (2 \nu ^{2} c^{2}-2 a^{2}-\left (2 a -1\right ) \left (2 c -1\right )\right ) \left (2 a +2 c -1\right ) x y^{\prime }+\left (\left (-\nu ^{2} c^{2}+a^{2}\right ) \left (-\nu ^{2} c^{2}+a^{2}+4 a c +4 c^{2}\right )-b^{4} c^{4} x^{4 c}\right ) y = 0 \]

\[ {}\nu ^{4} x^{4} y^{\prime \prime \prime \prime }+\left (4 \nu -2\right ) \nu ^{3} x^{3} y^{\prime \prime \prime }+\left (\nu -1\right ) \left (2 \nu -1\right ) \nu ^{2} x^{2} y^{\prime \prime }-\frac {b^{4} x^{\frac {2}{\nu }} y}{16} = 0 \]

\[ {}\left (x^{2}-1\right )^{2} y^{\prime \prime \prime \prime }+10 x \left (x^{2}-1\right ) y^{\prime \prime \prime }+\left (24 x^{2}-8-2 \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )\right ) \left (x^{2}-1\right )\right ) y^{\prime \prime }-6 x \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )-2\right ) y^{\prime }+\left (\left (\mu \left (\mu +1\right )-\nu \left (\nu +1\right )\right )^{2}-2 \mu \left (\mu +1\right )-2 \nu \left (\nu +1\right )\right ) y = 0 \]

\[ {}\left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \,{\mathrm e}^{x} y^{\prime }+y \,{\mathrm e}^{x}-\frac {1}{x^{5}} = 0 \]

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

\[ {}y^{\prime \prime \prime \prime } \sin \left (x \right )^{6}+4 y^{\prime \prime \prime } \sin \left (x \right )^{5} \cos \left (x \right )-6 y^{\prime \prime } \sin \left (x \right )^{6}-4 y^{\prime } \sin \left (x \right )^{5} \cos \left (x \right )+y \sin \left (x \right )^{6}-f = 0 \]

\[ {}f \left (y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y\right )+2 \operatorname {df} \left (y^{\prime \prime \prime }-a^{2} y^{\prime }\right ) = 0 \]

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

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

\[ {}y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime }-a x -b \sin \left (x \right )-c \cos \left (x \right ) = 0 \]

\[ {}y^{\left (6\right )}+y-\sin \left (\frac {3 x}{2}\right ) \sin \left (\frac {x}{2}\right ) = 0 \]

\[ {}y^{\left (5\right )}-a x y-b = 0 \]

\[ {}y^{\left (5\right )}+a \,x^{\nu } y^{\prime }+a \nu \,x^{\nu -1} y = 0 \]

\[ {}y^{\left (5\right )}+a y^{\prime \prime \prime \prime }-f = 0 \]

\[ {}x y^{\left (5\right )}-m n y^{\prime \prime \prime \prime }+a x y = 0 \]

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

\[ {}x y^{\left (5\right )}-\left (a A_{1} -A_{0} \right ) x -A_{1} -\left (\left (a A_{2} -A_{1} \right ) x +A_{2} \right ) y^{\prime } = 0 \]

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

\[ {}x^{10} y^{\left (5\right )}-a y = 0 \]

\[ {}x^{\frac {5}{2}} y^{\left (5\right )}-a y = 0 \]

\[ {}\left (x -a \right )^{5} \left (x -b \right )^{5} y^{\left (5\right )}-c y = 0 \]

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+d +b y^{2}+c y+a y^{3} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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