Second order ode Frobenius with roots diﬀerence not integer

2.8.6 Second order ode Frobenius with roots diﬀerence not integer

Table 2.1269: Second order ode Frobenius with roots diﬀerence not integer [365]


#	ODE	solved	Maple	Mma	Sympy	time(sec)

464	\begin{align} \left (2 x^{3}+6 x^{2}\right ) y^{\prime \prime }+21 x y^{\prime }+9 \left (x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.721

473	\begin{align} 4 x y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.627

474	\begin{align} 2 x y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.622

475	\begin{align} 2 x y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.615

476	\begin{align} 3 x y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.625

477	\begin{align} 2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (2 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.486

478	\begin{align} 2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (-2 x^{2}+3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.474

479	\begin{align} 6 x^{2} y^{\prime \prime }+7 x y^{\prime }-\left (x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.507

480	\begin{align} 3 x^{2} y^{\prime \prime }+2 x y^{\prime }+x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.479

481	\begin{align} 2 x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.596

482	\begin{align} 2 x y^{\prime \prime }+\left (-2 x^{2}+1\right ) y^{\prime }-4 x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.529

488	\begin{align} 2 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-\left (2 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.628

489	\begin{align} \left (5 x^{3}+2 x^{2}\right ) y^{\prime \prime }+\left (-x^{2}+3 x \right ) y^{\prime }-\left (1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.733

490	\begin{align} 2 x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.523

497	\begin{align} x \left (1-x \right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) x \right ) y^{\prime }-\alpha \beta y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.944

1941	\begin{align} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.912

1942	\begin{align} x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (1+x \right ) y^{\prime }-\left (1-4 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.931

1943	\begin{align} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (2 x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.982

1945	\begin{align} 3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.069

1946	\begin{align} x^{2} \left (x^{2}+3 x +3\right ) y^{\prime \prime }+x \left (7 x^{2}+8 x +5\right ) y^{\prime }-\left (-9 x^{2}-2 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.044

1947	\begin{align} 4 x^{2} y^{\prime \prime }+x \left (4 x^{2}+2 x +7\right ) y^{\prime }-\left (-7 x^{2}-4 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.037

1948	\begin{align} 12 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.940

1949	\begin{align} x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.092

1950	\begin{align} 8 x^{2} y^{\prime \prime }-2 x \left (-x^{2}-4 x +3\right ) y^{\prime }+\left (x^{2}+6 x +3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.031

1951	\begin{align} 18 x^{2} \left (1+x \right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.964

1952	\begin{align} x \left (x^{2}+x +3\right ) y^{\prime \prime }+\left (-x^{2}+x +4\right ) y^{\prime }+x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.047

1953	\begin{align} 10 x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (66 x^{2}+13 x +13\right ) y^{\prime }-\left (10 x^{2}+4 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.247

1954	\begin{align} 2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.867

1955	\begin{align} x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (5+4 x \right ) y^{\prime }-\left (1-2 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.934

1956	\begin{align} 2 x^{2} y^{\prime \prime }+x \left (5+x \right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.889

1957	\begin{align} 3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.871

1958	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-2 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.869

1959	\begin{align} 9 x^{2} y^{\prime \prime }+9 x y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.869

1960	\begin{align} 3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.911

1961	\begin{align} 2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.931

1962	\begin{align} x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.929

1963	\begin{align} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.885

1964	\begin{align} x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (5+18 x \right ) y^{\prime }-\left (1-12 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.971

1965	\begin{align} 6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.910

1966	\begin{align} x^{2} \left (8+x \right ) y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }+\left (1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.067

1967	\begin{align} x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.957

1969	\begin{align} x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.996

1970	\begin{align} x^{2} \left (6+x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.976

1971	\begin{align} 8 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.800

1972	\begin{align} 8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.815

1974	\begin{align} x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.832

1975	\begin{align} 4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.800

1976	\begin{align} 3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.836

1979	\begin{align} 2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.829

1980	\begin{align} 3 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+5 x \left (x^{2}+1\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.819

1982	\begin{align} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.814

1983	\begin{align} 2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.806

1984	\begin{align} 9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.808

1985	\begin{align} 6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.839

1986	\begin{align} x^{2} \left (x^{2}+8\right ) y^{\prime \prime }+7 x \left (x^{2}+2\right ) y^{\prime }-\left (-9 x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.845

1987	\begin{align} 9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.846

1989	\begin{align} 8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.842

1990	\begin{align} 2 x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.760

1991	\begin{align} 6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.773

1992	\begin{align} 28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.804

1993	\begin{align} 9 x^{2} \left (5+x \right ) y^{\prime \prime }+9 x \left (5+9 x \right ) y^{\prime }-\left (5-8 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.014

1994	\begin{align} 8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.779

1996	\begin{align} 3 x^{2} \left (1+x \right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.813

1997	\begin{align} 4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.845

2446	\begin{align} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-\left (t +1\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.888

2447	\begin{align} 2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.951

2448	\begin{align} 2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.001

2449	\begin{align} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.874

2450	\begin{align} 4 t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.960

2451	\begin{align} 2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.862

2463	\begin{align} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-v^{2}\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✗	0.926

2465	\begin{align} 2 \sin \left (t \right ) y^{\prime \prime }+\left (-t +1\right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✗	1.207

2643	\begin{align} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-\left (t +1\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.924

2644	\begin{align} 2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.968

2645	\begin{align} 2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.057

2646	\begin{align} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.911

2647	\begin{align} 4 t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.005

2648	\begin{align} 2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.889

2660	\begin{align} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-v^{2}\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✗	0.903

2662	\begin{align} t \left (-t +1\right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) t \right ) y^{\prime }-\alpha \beta y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✗	1.464

2663	\begin{align} 2 \sin \left (t \right ) y^{\prime \prime }+\left (-t +1\right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✗	1.106

2669	\begin{align} t^{2} y^{\prime \prime }+t p \left (t \right ) y^{\prime }+q \left (t \right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✗	26.443

3350	\begin{align} 2 x y^{\prime \prime }+5 y^{\prime }+x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.069

3351	\begin{align} 3 x \left (3 x +2\right ) y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.642

3352	\begin{align} x^{2} \left (x +4\right ) y^{\prime \prime }+7 x y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.414

3353	\begin{align} 2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.204

3354	\begin{align} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.225

3355	\begin{align} 9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.132

3356	\begin{align} \left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.346

3357	\begin{align} 2 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+\left (3 x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.263

3358	\begin{align} 3 x^{2} y^{\prime \prime }+\left (-x^{2}+5 x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.288

3360	\begin{align} 4 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.538

3361	\begin{align} 9 x^{2} y^{\prime \prime }+9 \left (-x^{2}+x \right ) y^{\prime }+\left (-1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.278

3362	\begin{align} 4 x^{2} \left (1-x \right ) y^{\prime \prime }+3 x \left (2 x +1\right ) y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.298

3363	\begin{align} 2 x^{2} \left (1-3 x \right ) y^{\prime \prime }+5 x y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.284

3364	\begin{align} 4 x^{2} \left (1+x \right ) y^{\prime \prime }-5 x y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.270

3365	\begin{align} x^{2} \left (x +4\right ) y^{\prime \prime }+x \left (-1+x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.273

3366	\begin{align} \left (8-x \right ) x^{2} y^{\prime \prime }+6 x y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.296

3367	\begin{align} 2 x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.406

3368	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.072

3369	\begin{align} 3 x^{2} y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.056

3371	\begin{align} 2 x y^{\prime \prime }-\left (x^{3}+1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.559

3394	\begin{align} 3 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=-x^{3}+x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.652

3395	\begin{align} 9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=x^{4}+x^{2} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.441

3397	\begin{align} 2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=x^{3}+1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.501

3400	\begin{align} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (1+x \right ) y&=x \left (x^{2}+x +1\right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.519

3401	\begin{align} \left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y&=x^{2} \left (1+x \right )^{2} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.656

3501	\begin{align} 4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(z=0\).	✓	✓	✓	✓	1.375

3504	\begin{align} z^{2} y^{\prime \prime }-\frac {3 z y^{\prime }}{2}+\left (z +1\right ) y&=0 \\ \end{align} Series expansion around \(z=0\).	✓	✓	✓	✓	1.290

4009	\begin{align} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-7 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.792

4010	\begin{align} 4 x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x -y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.566

4013	\begin{align} 4 x^{2} y^{\prime \prime }+3 x y^{\prime }+x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.576

4014	\begin{align} 6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.564

4015	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.666

4016	\begin{align} 2 x y^{\prime \prime }+y^{\prime }-2 x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.454

4017	\begin{align} 3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.588

4018	\begin{align} 2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.622

4019	\begin{align} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-\left (5+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.731

4020	\begin{align} 3 x^{2} y^{\prime \prime }+x \left (7+3 x \right ) y^{\prime }+\left (1+6 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.579

4022	\begin{align} 3 x^{2} y^{\prime \prime }+x \left (3 x^{2}+1\right ) y^{\prime }-2 x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.636

4035	\begin{align} x^{2} y^{\prime \prime }+x \cos \left (x \right ) y^{\prime }-2 y \,{\mathrm e}^{x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.659

4067	\begin{align} 2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.566

4071	\begin{align} 4 x y^{\prime \prime }+3 y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.541

4072	\begin{align} x^{2} y^{\prime \prime }+\frac {3 x y^{\prime }}{2}-\frac {\left (1+x \right ) y}{2}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.539

4178	\begin{align} y^{\prime \prime }-\frac {\left (-3 x^{2}+x \right ) y^{\prime }}{2 x^{3}+2 x^{2}}+\frac {y}{2 x^{3}+2 x^{2}}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.460

4184	\begin{align} y^{\prime \prime }+\frac {\left (1-x \right ) y^{\prime }}{2 x}-\frac {y}{4 x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.540

4185	\begin{align} y^{\prime \prime }-\frac {y^{\prime }}{2 x}+\frac {y}{4 x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.568

4600	\begin{align} x^{2} y^{\prime \prime }+\left (\frac {1}{2} x +x^{2}\right ) y^{\prime }+x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.649

7164	\begin{align} x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.755

7166	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{2} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.635

7172	\begin{align} \left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.766

7175	\begin{align} x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (\left (1-n \right ) x -\left (6-4 n \right ) x^{2}\right ) y^{\prime }+n \left (1-n \right ) x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.891

7193	\begin{align} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.709

7195	\begin{align} 2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.686

7196	\begin{align} x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.700

7197	\begin{align} 2 x \left (1-x \right ) y^{\prime \prime }+y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.646

8077	\begin{align} 2 \left (x^{3}+x^{2}\right ) y^{\prime \prime }-\left (-3 x^{2}+x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.622

8078	\begin{align} 4 x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.743

8079	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.578

8085	\begin{align} 2 x y^{\prime \prime }+y^{\prime }-y&=1+x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.879

8086	\begin{align} 2 x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=\infty \).	✓	✓	✓	✓	0.768

8096	\begin{align} x^{2} y^{\prime \prime }+4 \left (x +a \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.912

8107	\begin{align} 2 x y^{\prime \prime }-y^{\prime }+x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.592

8110	\begin{align} x \left (x +2\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }-4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.794

8111	\begin{align} x y^{\prime \prime }+\left (\frac {1}{2}-x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.707

8132	\begin{align} x^{2} y^{\prime \prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.445

8134	\begin{align} x^{2} y^{\prime \prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.498

8136	\begin{align} 2 x y^{\prime \prime }+y^{\prime }-x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.591

8137	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.512

8148	\begin{align} x^{2} y^{\prime \prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.473

8504	\begin{align} x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.179

8508	\begin{align} \left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.010

8511	\begin{align} x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.793

8513	\begin{align} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.856

8514	\begin{align} 2 x y^{\prime \prime }+5 y^{\prime }+x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.675

8515	\begin{align} 4 x y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.852

8516	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.694

8517	\begin{align} 3 x y^{\prime \prime }+\left (-x +2\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.843

8518	\begin{align} x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.750

8519	\begin{align} 2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.872

8520	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{9}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.665

8521	\begin{align} 9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.799

8522	\begin{align} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.788

8534	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.668

8537	\begin{align} 16 x^{2} y^{\prime \prime }+16 x y^{\prime }+\left (16 x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.674

8542	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.671

8558	\begin{align} 2 x y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.876

8586	\begin{align} 2 x \left (-1+x \right ) y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.902

8591	\begin{align} 2 x \left (1-x \right ) y^{\prime \prime }-\left (1+6 x \right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.910

8592	\begin{align} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.954

8593	\begin{align} 4 x y^{\prime \prime }+y^{\prime }+8 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.851

8597	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{49}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.703

8600	\begin{align} x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.751

8603	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-6\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.748

8605	\begin{align} 9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (36 x^{4}-16\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.705

8616	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-5\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.740

8988	\begin{align} \left (x^{2}+x -2\right )^{2} y^{\prime \prime }+3 \left (x +2\right ) y^{\prime }+\left (-1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=-2\).	✓	✓	✓	✓	1.329

8991	\begin{align} 4 x^{2} y^{\prime \prime }+\left (4 x^{4}-5 x \right ) y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.109

8993	\begin{align} 3 x^{2} y^{\prime \prime }+5 x y^{\prime }+3 x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.194

8996	\begin{align} 2 x^{2} y^{\prime \prime }+\left (x^{2}+5 x \right ) y^{\prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.144

9385	\begin{align} x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.851

9394	\begin{align} 4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.326

9396	\begin{align} x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.934

9397	\begin{align} 4 x y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.366

9398	\begin{align} 2 x y^{\prime \prime }+\left (-x +3\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.365

9399	\begin{align} 2 x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.408

9400	\begin{align} 2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.220

9409	\begin{align} \left (-1+x \right )^{2} y^{\prime \prime }-3 \left (-1+x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✗	0.969

9410	\begin{align} 3 \left (1+x \right )^{2} y^{\prime \prime }-\left (1+x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=-1\).	✓	✓	✓	✗	1.010

9413	\begin{align} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.447

9414	\begin{align} \left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.190

9415	\begin{align} \left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=-1\).	✓	✓	✓	✓	1.556

9416	\begin{align} \left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=3\).	✓	✓	✓	✓	1.497

9417	\begin{align} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	2.000

9418	\begin{align} \left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }+\frac {y^{\prime }}{2}+y \,{\mathrm e}^{x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	2.339

9431	\begin{align} 2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.421

9440	\begin{align} 9 \left (x -2\right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (x -2\right ) y^{\prime }+16 y&=0 \\ \end{align} Series expansion around \(x=\infty \).	✓	✓	✓	✗	1.786

9441	\begin{align} p \left (1+p \right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=\infty \).	✓	✓	✓	✓	2.058

9532	\begin{align} x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.956


9536	\begin{align} \left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.605

9539	\begin{align} x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.313

9541	\begin{align} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.480

9542	\begin{align} 2 x y^{\prime \prime }+5 y^{\prime }+x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.058

9543	\begin{align} 4 x y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.358

9544	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.053

9545	\begin{align} 3 x y^{\prime \prime }+\left (-x +2\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.339

9546	\begin{align} x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.204

9547	\begin{align} 2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.358

9548	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{9}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.954

9549	\begin{align} 9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.256

9550	\begin{align} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.275

9586	\begin{align} 2 x y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.339

9859	\begin{align} 2 x \left (1+x \right ) y^{\prime \prime }+3 \left (1+x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.602

9862	\begin{align} 4 x y^{\prime \prime }+3 y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.544

9863	\begin{align} 2 x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (1+7 x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.426

9864	\begin{align} 2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.630

9865	\begin{align} 8 x^{2} y^{\prime \prime }+10 x y^{\prime }-\left (1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.429

9867	\begin{align} 2 x \left (x +3\right ) y^{\prime \prime }-3 \left (1+x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.598

9868	\begin{align} 2 x y^{\prime \prime }+\left (-2 x^{2}+1\right ) y^{\prime }-4 x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.417

9869	\begin{align} x \left (4-x \right ) y^{\prime \prime }+\left (-x +2\right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.695

9870	\begin{align} 3 x^{2} y^{\prime \prime }+x y^{\prime }-\left (1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.466

9871	\begin{align} 2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.640

9872	\begin{align} 2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-5 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.672

9873	\begin{align} 2 x^{2} y^{\prime \prime }-3 x \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.462

9874	\begin{align} 2 x^{2} y^{\prime \prime }+x \left (4 x -1\right ) y^{\prime }+2 \left (3 x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.433

9875	\begin{align} -x y-\left (2 x^{2}+1\right ) y^{\prime }+2 x y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.384

9876	\begin{align} 2 x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.069

9877	\begin{align} 2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.086

9878	\begin{align} 9 x^{2} y^{\prime \prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.987

9879	\begin{align} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.055

9938	\begin{align} 2 x \left (1-x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.806

9944	\begin{align} 2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-\left (1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.762

9948	\begin{align} 2 \left (5+x \right ) y-x \left (7+2 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.430

9951	\begin{align} 2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.668

9954	\begin{align} 2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (1+4 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.467

9957	\begin{align} 2 x y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.543

9961	\begin{align} 2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (1+3 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.494

10164	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.521

10165	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.586

10169	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{2} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.543

10170	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{2}+1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.579

10171	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{4} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.553

10174	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x \sin \left (x \right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.595

10177	\begin{align} \left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.618

10178	\begin{align} \left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=2\).	✓	✓	✓	✓	0.711

10181	\begin{align} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-x y&=x^{2}+2 x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.733

10182	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.530

10186	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{2}+\cos \left (x \right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.639

10187	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=\cos \left (x \right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.627

10188	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{3}+\cos \left (x \right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.683

10189	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{3} \cos \left (x \right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.605

10190	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{3} \cos \left (x \right )+\sin \left (x \right )^{2} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.701

10192	\begin{align} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.641

10193	\begin{align} x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (1+x \right ) y^{\prime }-\left (1-4 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.611

10194	\begin{align} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.529

10199	\begin{align} 4 x y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.587

10205	\begin{align} 2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (x -5\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.732

10221	\begin{align} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.398

10455	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-5\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.619

14745	\begin{align} \left (x^{2}-3 x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.809

14749	\begin{align} 2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.576

14750	\begin{align} 2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.560

14751	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+\frac {8}{9}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.567

14752	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }+\left (2 x^{2}+\frac {5}{9}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.580

14753	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.543

14754	\begin{align} 2 x y^{\prime \prime }+y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.705

14755	\begin{align} 3 x y^{\prime \prime }-\left (x -2\right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.721

14977	\begin{align} 2 x y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.743

14983	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.706

15308	\begin{align} 2 x y^{\prime \prime }+\left (1+x \right ) y^{\prime }-k y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.003

15311	\begin{align} 2 x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.756

16883	\begin{align} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.917

16903	\begin{align} 2 x^{2} y^{\prime \prime }+\left (-2 x^{3}+5 x \right ) y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.116

16905	\begin{align} \left (-3 x^{3}+3 x^{2}\right ) y^{\prime \prime }-\left (5 x^{2}+4 x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.036

16909	\begin{align} \left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.982

16917	\begin{align} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+\left (4 x^{2}+5 x \right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.202

16925	\begin{align} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✗	1.389

17709	\begin{align} 2 x y^{\prime \prime }-5 y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.652

17710	\begin{align} 5 x y^{\prime \prime }+8 y^{\prime }-x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.364

17711	\begin{align} 9 x y^{\prime \prime }+14 y^{\prime }+\left (-1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.698

17712	\begin{align} 7 x y^{\prime \prime }+10 y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.825

17715	\begin{align} y^{\prime \prime }+\frac {8 y^{\prime }}{3 x}-\left (\frac {2}{3 x^{2}}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.293

17716	\begin{align} y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.411

17723	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-k^{2}+x^{2}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.579

17725	\begin{align} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.710

17790	\begin{align} 3 x y^{\prime \prime }+11 y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.605

17791	\begin{align} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.085

18386	\begin{align} 4 x y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.633

18388	\begin{align} 9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.676

19601	\begin{align} 4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.907

19602	\begin{align} 4 x y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.951

19603	\begin{align} 2 x y^{\prime \prime }+\left (-x +3\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.955

19604	\begin{align} 2 x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.989

19605	\begin{align} 2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.868

19616	\begin{align} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.024

19617	\begin{align} \left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.852

19618	\begin{align} \left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=-1\).	✓	✓	✓	✓	1.105

19619	\begin{align} \left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=3\).	✓	✓	✓	✓	1.043

19621	\begin{align} n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=\infty \).	✓	✓	✓	✓	1.456

20149	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{2} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.067

20903	\begin{align} 4 x y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.401

20906	\begin{align} y^{\prime \prime }+\frac {y^{\prime }}{2 x}-\frac {\left (1+x \right ) y}{2 x^{2}}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.232

20908	\begin{align} 2 x \left (1+x \right ) y^{\prime \prime }+3 \left (1+x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.510

21629	\begin{align} 2 x^{2} y^{\prime \prime }+7 x \left (1+x \right ) y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.865

21662	\begin{align} -a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.269

21672	\begin{align} 8 x^{2} y^{\prime \prime }+10 x y^{\prime }+\left (-1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.778

21673	\begin{align} -y+\left (1+x \right ) y^{\prime }+2 x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.875

21674	\begin{align} 4 x y^{\prime \prime }+2 y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.839

21675	\begin{align} y^{\prime \prime }+\frac {y^{\prime }}{2 x}+\frac {y}{4 x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.811

21676	\begin{align} x^{2} y^{\prime \prime }+\left (\frac {1}{2} x +x^{2}\right ) y^{\prime }+x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.825

21677	\begin{align} 18 x^{2} y^{\prime \prime }+3 x \left (5+x \right ) y^{\prime }-\left (10 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.866

21678	\begin{align} 2 x^{2} y^{\prime \prime }+7 x \left (1+x \right ) y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.813

21679	\begin{align} 3 x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.570

21694	\begin{align} 3 x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.566

21696	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-p^{2}+x^{2}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.788

21697	\begin{align} -a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.222

21903	\begin{align} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (1+3 x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.909

21908	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.832

22172	\begin{align} 2 x^{2} y^{\prime \prime }+7 x \left (1+x \right ) y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.927

22182	\begin{align} x^{4} \left (x^{2}-4\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+\left (x^{2}-3 x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=2\).	✓	✓	✓	✓	1.116

22202	\begin{align} 8 x^{2} y^{\prime \prime }+10 x y^{\prime }+\left (-1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.936

22203	\begin{align} 2 x^{2} y^{\prime \prime }+7 x \left (1+x \right ) y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.924

22204	\begin{align} 3 x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.685

22211	\begin{align} -a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.533

22212	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.919

22213	\begin{align} 2 x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.869

22214	\begin{align} 3 x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.809

22220	\begin{align} x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.143

22225	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }+\left (-n^{2}+x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.646

22851	\begin{align} 2 x y^{\prime \prime }+y^{\prime }-x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.206

22860	\begin{align} -6 x y-y^{\prime }+x \left (x^{2}+2\right ) y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.296

22868	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.127

22870	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-8\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.223

23670	\begin{align} 2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.905

23676	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-p^{2}+x^{2}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.696

23678	\begin{align} -a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	3.026

23719	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.388

23722	\begin{align} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.085

23730	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-p^{2}+x^{2}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.615

23732	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{16}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.445

23736	\begin{align} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {2}{3}-3 x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.079

23742	\begin{align} 2 \left (x +3\right )^{2} y^{\prime \prime }-\left (x^{2}+5 x +6\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=-3\).	✓	✓	✓	✓	1.716

23743	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.451

23749	\begin{align} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.066

23750	\begin{align} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{4}-4 x \right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.109

24095	\begin{align} x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.739

24099	\begin{align} 2 x y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.351

24100	\begin{align} 25 x^{2} y^{\prime \prime }+\left (2 x +4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.758

24102	\begin{align} 6 x^{2} y^{\prime \prime }+\left (x^{3}+11 x \right ) y^{\prime }+\left (-2 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.257

25339	\begin{align} 2 t y^{\prime \prime }+y^{\prime }+t y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.428

25346	\begin{align} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.534

25348	\begin{align} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (-t +1\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.525

25357	\begin{align} t y^{\prime \prime }+2 \left (i t -k \right ) y^{\prime }-2 i k y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.757

26021	\begin{align} 2 x y^{\prime \prime }+5 \left (2 x +1\right ) y^{\prime }+5 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.739

26022	\begin{align} 4 x y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.698

26023	\begin{align} 2 x \left (-1+x \right ) y^{\prime \prime }+3 \left (-1+x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.700

26027	\begin{align} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.669

26028	\begin{align} 2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.621

26029	\begin{align} 2 x y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.674

26708	\begin{align} 9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.718

27076	\begin{align} 4 x y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.773

27773	\begin{align} 2 x^{2} y^{\prime \prime }+\left (-2 x^{2}+3 x \right ) y^{\prime }-\left (1+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.964

27774	\begin{align} 9 x^{2} y^{\prime \prime }-\left (x^{2}-2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.773

27779	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.120

27781	\begin{align} x^{2} y^{\prime \prime }+\left (-1+x \right ) y&=-1 \\ \end{align} Series expansion around \(x=0\).	✓	✗	✓	✗	1.410

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