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

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

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

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

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

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

\[ {}y^{\prime \prime }-\left (n \left (n +1\right ) k^{2} \mathrm {sn}\left (x | k \right )^{2}+b \right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\mathit {a1} \,x^{2}+\mathit {b1} x +\mathit {c1} \right ) y = 0 \]

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

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

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

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

\[ {}y^{\prime \prime }+a \,x^{q -1} y^{\prime }+b \,x^{q -2} y = 0 \]

\[ {}y^{\prime \prime }+y^{\prime } \sqrt {x}+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{\frac {3}{2}}}{3}} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+\frac {k^{2} \mathrm {sn}\left (x | k \right ) \mathrm {cn}\left (x | k \right ) y^{\prime }}{\mathrm {dn}\left (x | k \right )}+n^{2} y \mathrm {dn}\left (x | k \right )^{2} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x y^{\prime \prime }+a y^{\prime }+b \,x^{\mathit {a1}} y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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