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

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

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

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

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

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

\[ {}y^{\prime \prime } = -\frac {\cos \relax (x ) y^{\prime }}{\sin \relax (x )}-\frac {\left (v \left (v +1\right ) \sin \relax (x )^{2}-n^{2}\right ) y}{\sin \relax (x )^{2}} \]

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

\[ {}y^{\prime \prime } = -\frac {\cos \relax (x ) y^{\prime }}{\sin \relax (x )}-\frac {\left (-17 \sin \relax (x )^{2}-1\right ) y}{4 \sin \relax (x )^{2}} \]

\[ {}y^{\prime \prime } = -\frac {\sin \relax (x ) y^{\prime }}{\cos \relax (x )}-\frac {\left (2 x^{2}+x^{2} \sin \relax (x )^{2}-24 \cos \relax (x )^{2}\right ) y}{4 x^{2} \cos \relax (x )^{2}}+\sqrt {\cos \relax (x )} \]

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

\[ {}y^{\prime \prime } = -\frac {4 \sin \left (3 x \right ) y}{\sin \relax (x )^{3}} \]

\[ {}y^{\prime \prime } = -\frac {\left (4 v \left (v +1\right ) \sin \relax (x )^{2}-\cos \relax (x )^{2}+2-4 n^{2}\right ) y}{4 \sin \relax (x )^{2}} \]

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

\[ {}y^{\prime \prime } = -\frac {\left (-a \cos \relax (x )^{2} \sin \relax (x )^{2}-m \left (m -1\right ) \sin \relax (x )^{2}-n \left (n -1\right ) \cos \relax (x )^{2}\right ) y}{\cos \relax (x )^{2} \sin \relax (x )^{2}} \]

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

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

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

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

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

\[ {}y^{\prime \prime } = \frac {a f^{\prime }\relax (x ) y^{\prime }}{f \relax (x )}-\frac {b f \relax (x )^{2 a +1} y}{f \relax (x )} \]

\[ {}y^{\prime \prime } = -\frac {\left (2 f \relax (x ) {g^{\prime }\relax (x )}^{2} g \relax (x )-\left (g \relax (x )^{2}-1\right ) \left (f \relax (x ) g^{\prime \prime }\relax (x )+2 f^{\prime }\relax (x ) g^{\prime }\relax (x )\right )\right ) y^{\prime }}{f \relax (x ) g^{\prime }\relax (x ) \left (g \relax (x )^{2}-1\right )}-\frac {\left (\left (g \relax (x )^{2}-1\right ) \left (f^{\prime }\relax (x ) \left (f \relax (x ) g^{\prime \prime }\relax (x )+2 f^{\prime }\relax (x ) g^{\prime }\relax (x )\right )-f \relax (x ) f^{\prime \prime }\relax (x ) g^{\prime }\relax (x )\right )-\left (2 f^{\prime }\relax (x ) g \relax (x )+v \left (v +1\right ) f \relax (x ) g^{\prime }\relax (x )\right ) f \relax (x ) {g^{\prime }\relax (x )}^{2}\right ) y}{f \relax (x )^{2} g^{\prime }\relax (x ) \left (g \relax (x )^{2}-1\right )} \]

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

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

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

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

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

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

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

\[ {}y^{\prime \prime \prime }-a^{2} y^{\prime }-{\mathrm e}^{2 a x} \sin \relax (x )^{2} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime \prime }+\operatorname {a2} y^{\prime \prime }+\operatorname {a1} y^{\prime }+\operatorname {a0} y = 0 \]

\[ {}y^{\prime \prime \prime }-6 x y^{\prime \prime }+2 \left (4 x^{2}+2 a -1\right ) y^{\prime }-8 a x y = 0 \]

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

\[ {}y^{\prime \prime \prime }-y^{\prime \prime } \sin \relax (x )-2 \cos \relax (x ) y^{\prime }+\sin \relax (x ) y-\ln \relax (x ) = 0 \]

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

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

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

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

\[ {}4 y^{\prime \prime \prime }-8 y^{\prime \prime }-11 y^{\prime }-3 y+18 \,{\mathrm e}^{x} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime }-\ln \relax (x ) = 0 \]

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

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

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

\[ {}x^{2} y^{\prime \prime \prime }-2 \left (n +1\right ) x y^{\prime \prime }+\left (x^{2} a +6 n \right ) y^{\prime }-2 a x y = 0 \]

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

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

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

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

\[ {}\left (x^{2}+1\right ) y^{\prime \prime \prime }+8 x y^{\prime \prime }+10 y^{\prime }-3+\frac {1}{x^{2}}-2 \ln \relax (x ) = 0 \]

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

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

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

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

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

\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y-6 x^{3} \left (x -1\right ) \ln \relax (x )+x^{3} \left (x +8\right ) = 0 \]

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

\[ {}x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+\left (x^{2}+8\right ) x y^{\prime }-2 \left (x^{2}+4\right ) y = 0 \]

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+\left (a \,x^{3}-12\right ) y = 0 \]

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

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

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

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

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

\[ {}2 \left (x -\operatorname {a1} \right ) \left (x -\operatorname {a2} \right ) \left (x -\operatorname {a3} \right ) y^{\prime \prime \prime }+\left (9 x^{2}-6 \left (\operatorname {a1} +\operatorname {a2} +\operatorname {a3} \right ) x +3 \operatorname {a1} \operatorname {a2} +3 \operatorname {a1} \operatorname {a3} +3 \operatorname {a2} \operatorname {a3} \right ) y^{\prime \prime }-2 \left (\left (n^{2}+n -3\right ) x +b \right ) y^{\prime }-n \left (n +1\right ) y = 0 \]

\[ {}\left (1+x \right ) x^{3} y^{\prime \prime \prime }-\left (4 x +2\right ) x^{2} y^{\prime \prime }+\left (10 x +4\right ) x y^{\prime }-4 \left (3 x +1\right ) y = 0 \]

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

\[ {}\left (x^{2}+1\right ) x^{3} y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-4 \left (3 x^{2}+1\right ) y = 0 \]

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

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