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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y-x \sin \left (x \right )-\left (x^{2} a +12 a +4\right ) \cos \left (x \right ) = 0 \]

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y-5 x = 0 \]

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y-x^{2} \ln \left (x \right ) = 0 \]

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

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

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y-\sin \left (x \right ) x^{3} = 0 \]

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }+\left (x -9\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-9 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (-a^{2}+x^{2}\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0 \]

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

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

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

\[ {}\left (x^{2}+x -2\right ) y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }-\left (6 x^{2}+7 x \right ) y = 0 \]

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

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

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

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

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

\[ {}x \left (x -1\right ) y^{\prime \prime }+\left (\left (\operatorname {a1} +\operatorname {b1} +1\right ) x -\operatorname {d1} \right ) y^{\prime }+\operatorname {a1} \operatorname {b1} \operatorname {d1} = 0 \]

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

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

\[ {}x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{\frac {7}{3}} = 0 \]

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

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