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

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

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

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

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

\[ {}y^{\prime } = -\frac {1}{-\left (y^{3}\right )^{\frac {2}{3}} x -f_{1} \left (y^{3}-3 \ln \left (x \right )\right ) \left (y^{3}\right )^{\frac {1}{3}} x} \]

\[ {}y^{\prime } = -\frac {1}{-\ln \left (x \right ) \left (y^{3}\right )^{\frac {2}{3}}-f_{1} \left (y^{3}+3 \,\operatorname {expIntegral}_{1}\left (-\ln \left (x \right )\right )\right ) \ln \left (x \right ) \left (y^{3}\right )^{\frac {1}{3}}} \]

\[ {}y^{\prime } = -\frac {i \left (32 i x +64+64 y^{4}+32 y^{2} x^{2}+4 x^{4}+64 y^{6}+48 x^{2} y^{4}+12 x^{4} y^{2}+x^{6}\right )}{128 y} \]

\[ {}y^{\prime } = -\frac {i \left (i x +1+x^{4}+2 y^{2} x^{2}+y^{4}+x^{6}+3 x^{4} y^{2}+3 x^{2} y^{4}+y^{6}\right )}{y} \]

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

\[ {}y^{\prime \prime }-\left (4 a^{2} b^{2} x^{2} {\mathrm e}^{2 b \,x^{2}}-1\right ) y = 0 \]

\[ {}y^{\prime \prime }-\left (n \left (n +1\right ) \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )+B \right ) y = 0 \]

\[ {}y^{\prime \prime }-\left (\frac {p^{\prime \prime \prime \prime }\left (x \right )}{30}+\frac {7 p^{\prime \prime }\left (x \right )}{3}+a p \left (x \right )+b \right ) y = 0 \]

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

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

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

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

\[ {}y^{\prime \prime }+\frac {\left (11 \operatorname {WeierstrassP}\left (x , a , b\right ) \operatorname {WeierstrassPPrime}\left (x , a , b\right )-6 \operatorname {WeierstrassP}\left (x , a , b\right )^{2}+\frac {a}{2}\right ) y^{\prime }}{\operatorname {WeierstrassPPrime}\left (x , a , b\right )+\operatorname {WeierstrassP}\left (x , a , b\right )^{2}}+\frac {\left (\operatorname {WeierstrassPPrime}\left (x , a , b\right )^{2}-\operatorname {WeierstrassP}\left (x , a , b\right )^{2} \operatorname {WeierstrassPPrime}\left (x , a , b\right )-\operatorname {WeierstrassP}\left (x , a , b\right ) \left (6 \operatorname {WeierstrassP}\left (x , a , b\right )^{2}-\frac {a}{2}\right )\right ) y}{\operatorname {WeierstrassPPrime}\left (x , a , b\right )+\operatorname {WeierstrassP}\left (x , a , b\right )^{2}} = 0 \]

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+\left (a \,x^{\operatorname {a1}}+b \right ) x y^{\prime }+\left (A \,x^{2 \operatorname {a1}}+B \,x^{\operatorname {a1}}+C \,x^{\operatorname {b1}}+\operatorname {DD} \right ) y = 0 \]

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

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

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

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

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

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

\[ {}y^{\prime \prime } = -\frac {\left (x^{2} \left (\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right )+\left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )+\left (x^{2}-\operatorname {a3} \right ) \left (x^{2}-\operatorname {a1} \right )\right )-\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )\right ) y^{\prime }}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )}-\frac {\left (A \,x^{2}+B \right ) y}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )} \]

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

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

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

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

\[ {}y^{\prime \prime } = \frac {2 \,\operatorname {JacobiSN}\left (x , k\right ) \operatorname {JacobiCN}\left (x , k\right ) \operatorname {JacobiDN}\left (x , k\right ) y^{\prime }-2 \left (1-2 \left (k^{2}+1\right ) \operatorname {JacobiSN}\left (a , k\right )^{2}+3 k^{2} \operatorname {JacobiSN}\left (a , k\right )^{4}\right ) y}{\operatorname {JacobiSN}\left (x , k\right )^{2}-\operatorname {JacobiSN}\left (a , k\right )} \]

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

\[ {}y^{\prime \prime \prime }-3 \left (2 \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )+a \right ) y^{\prime }+b y = 0 \]

\[ {}y^{\prime \prime \prime }+\left (-n^{2}+1\right ) \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y^{\prime }+\frac {\left (\left (-n^{2}+1\right ) \operatorname {WeierstrassPPrime}\left (x , \operatorname {g2} , \operatorname {g3}\right )-a \right ) y}{2} = 0 \]

\[ {}y^{\prime \prime \prime }-\left (4 n \left (n +1\right ) \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )+a \right ) y^{\prime }-2 n \left (n +1\right ) \operatorname {WeierstrassPPrime}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y = 0 \]

\[ {}y^{\prime \prime \prime }+\left (A \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )+a \right ) y^{\prime }+B \operatorname {WeierstrassPPrime}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y = 0 \]

\[ {}y^{\prime \prime \prime }-\left (3 k^{2} \operatorname {JacobiSN}\left (z , x\right )^{2}+a \right ) y^{\prime }+\left (b +c \operatorname {JacobiSN}\left (z , x\right )^{2}-3 k^{2} \operatorname {JacobiSN}\left (z , x\right ) \operatorname {JacobiCN}\left (z , x\right ) \operatorname {JacobiDN}\left (z , x\right )\right ) y = 0 \]

\[ {}y^{\prime \prime \prime }-\left (6 k^{2} \sin \left (x \right )^{2}+a \right ) y^{\prime }+b y = 0 \]

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

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

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

\[ {}27 y^{\prime \prime \prime }-36 n^{2} \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y^{\prime }-2 n \left (n +3\right ) \left (4 n -3\right ) \operatorname {WeierstrassPPrime}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y = 0 \]

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

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

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

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

\[ {}x^{3} y^{\prime \prime \prime }+\left (x +3\right ) x^{2} y^{\prime \prime }+5 \left (x -6\right ) x y^{\prime }+\left (4 x +30\right ) y = 0 \]

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

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

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

\[ {}y^{\prime \prime \prime \prime }+a \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y^{\prime \prime }+b \operatorname {WeierstrassPPrime}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y^{\prime }+\left (c \left (6 \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )^{2}-\frac {\operatorname {g2}}{2}\right )+d \right ) y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-\left (12 k^{2} \operatorname {JacobiSN}\left (z , x\right )^{2}+a \right ) y^{\prime \prime }+b y^{\prime }+\left (\alpha \operatorname {JacobiSN}\left (z , x\right )^{2}+\beta \right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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