Second order ode Frobenius with roots diﬀerence not integer

2.8.6 Second order ode Frobenius with roots diﬀerence not integer

Table 2.1267: 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 \(x=0\).	✓	✓	✓	✓	0.954

473	\begin{align} 4 x y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.856

474	\begin{align} 2 x y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.834

475	\begin{align} 2 x y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.843

476	\begin{align} 3 x y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.852

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 \(x=0\).	✓	✓	✓	✓	0.730

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 \(x=0\).	✓	✓	✓	✓	0.728

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 \(x=0\).	✓	✓	✓	✓	0.728

480	\begin{align} 3 x^{2} y^{\prime \prime }+2 x y^{\prime }+x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.690

481	\begin{align} 2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.848

482	\begin{align} 2 x y^{\prime \prime }+\left (-2 x^{2}+1\right ) y^{\prime }-4 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.749

488	\begin{align} 2 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (2 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.892

489	\begin{align} \left (5 x^{3}+2 x^{2}\right ) y^{\prime \prime }+\left (-x^{2}+3 x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.999

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 \(x=0\).	✓	✓	✓	✗	0.754

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 \(x=0\).	✓	✓	✓	✗	1.247

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 \(x=0\).	✓	✓	✓	✓	0.992

1942	\begin{align} x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.925

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 \(x=0\).	✓	✓	✓	✓	0.963

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 \(x=0\).	✓	✓	✓	✓	1.040

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 \(x=0\).	✓	✓	✓	✓	1.033

1948	\begin{align} 12 x^{2} \left (x +1\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 \(x=0\).	✓	✓	✓	✓	0.954

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 \(x=0\).	✓	✓	✓	✓	1.078

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 \(x=0\).	✓	✓	✓	✓	1.024

1951	\begin{align} 18 x^{2} \left (x +1\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 \(x=0\).	✓	✓	✓	✓	0.971

1952	\begin{align} x \left (x^{2}+x +3\right ) y^{\prime \prime }+\left (-x^{2}+x +4\right ) y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.037

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 \(x=0\).	✓	✓	✓	✓	1.083

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 \(x=0\).	✓	✓	✓	✓	0.859

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 \(x=0\).	✓	✓	✓	✓	0.925

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 \(x=0\).	✓	✓	✓	✓	0.870

1957	\begin{align} 3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.848

1958	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-2 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.862

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 \(x=0\).	✓	✓	✓	✓	0.865

1960	\begin{align} 3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.917

1961	\begin{align} 2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.938

1962	\begin{align} x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (-3 x +1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.922

1963	\begin{align} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.877

1964	\begin{align} x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (5+18 x \right ) y^{\prime }-\left (1-12 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.961

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 \(x=0\).	✓	✓	✓	✓	0.928

1966	\begin{align} x^{2} \left (8+x \right ) y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.990

1967	\begin{align} x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (4 x +3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.965

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 \(x=0\).	✓	✓	✓	✓	1.058

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 \(x=0\).	✓	✓	✓	✓	1.023

1971	\begin{align} 8 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.847

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 \(x=0\).	✓	✓	✓	✓	0.860

1974	\begin{align} x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.849

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 \(x=0\).	✓	✓	✓	✓	0.792

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 \(x=0\).	✓	✓	✓	✓	0.813

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 \(x=0\).	✓	✓	✓	✓	0.835

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 \(x=0\).	✓	✓	✓	✓	0.825

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 \(x=0\).	✓	✓	✓	✓	0.792

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 \(x=0\).	✓	✓	✓	✓	0.813

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 \(x=0\).	✓	✓	✓	✓	0.800

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 \(x=0\).	✓	✓	✓	✓	0.829

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 \(x=0\).	✓	✓	✓	✓	0.837

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 \(x=0\).	✓	✓	✓	✓	0.830

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 \(x=0\).	✓	✓	✓	✓	0.852

1990	\begin{align} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-3 x +1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.758

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 \(x=0\).	✓	✓	✓	✓	0.794

1992	\begin{align} 28 x^{2} \left (-3 x +1\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 \(x=0\).	✓	✓	✓	✓	0.855

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 \(x=0\).	✓	✓	✓	✓	1.036

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 \(x=0\).	✓	✓	✓	✓	0.823

1996	\begin{align} 3 x^{2} \left (x +1\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 \(x=0\).	✓	✓	✓	✓	0.884

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 \(x=0\).	✓	✓	✓	✓	0.958

2446	\begin{align} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-\left (t +1\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.963

2447	\begin{align} 2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.020

2448	\begin{align} 2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.062

2449	\begin{align} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.946

2450	\begin{align} 4 t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.009

2451	\begin{align} 2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.928

2463	\begin{align} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-v^{2}\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✗	1.089

2465	\begin{align} 2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✗	1.482

2643	\begin{align} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-\left (t +1\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.954

2644	\begin{align} 2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.026

2645	\begin{align} 2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.076

2646	\begin{align} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.935

2647	\begin{align} 4 t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.019

2648	\begin{align} 2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.925

2660	\begin{align} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-v^{2}\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✗	0.927

2662	\begin{align} t \left (1-t \right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) t \right ) y^{\prime }-\alpha \beta y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✗	1.506

2663	\begin{align} 2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✗	1.113

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 \(t=0\).	✓	✓	✓	✗	30.034

3350	\begin{align} 2 x y^{\prime \prime }+5 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.695

3351	\begin{align} 3 x \left (3 x +2\right ) y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.982

3352	\begin{align} x^{2} \left (x +4\right ) y^{\prime \prime }+7 x y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.960

3353	\begin{align} 2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.800

3354	\begin{align} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.949

3355	\begin{align} 9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.847

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 \(x=0\).	✓	✓	✓	✓	1.026

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 \(x=0\).	✓	✓	✓	✓	0.888

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 \(x=0\).	✓	✓	✓	✓	0.934

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 \(x=0\).	✓	✓	✓	✗	1.199

3361	\begin{align} 9 x^{2} y^{\prime \prime }+9 \left (-x^{2}+x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.969

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 \(x=0\).	✓	✓	✓	✓	0.937

3363	\begin{align} 2 x^{2} \left (-3 x +1\right ) y^{\prime \prime }+5 x y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.905

3364	\begin{align} 4 x^{2} \left (x +1\right ) y^{\prime \prime }-5 x y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.863

3365	\begin{align} x^{2} \left (x +4\right ) y^{\prime \prime }+x \left (x -1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.856

3366	\begin{align} \left (8-x \right ) x^{2} y^{\prime \prime }+6 x y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.912

3367	\begin{align} 2 x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.980

3368	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.737

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 \(x=0\).	✓	✓	✓	✓	0.734

3371	\begin{align} 2 x y^{\prime \prime }-\left (x^{3}+1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.981

3394	\begin{align} 3 x^{2} \left (x +1\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 \(x=0\).	✓	✓	✓	✗	1.255

3395	\begin{align} 9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=x^{4}+x^{2} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.056

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 \(x=0\).	✓	✓	✓	✗	1.056

3400	\begin{align} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y&=x \left (x^{2}+x +1\right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.157

3401	\begin{align} \left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y&=x^{2} \left (x +1\right )^{2} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.243

3501	\begin{align} 4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(z=0\).	✓	✓	✓	✓	0.900

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 \(z=0\).	✓	✓	✓	✓	0.944

4009	\begin{align} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-7 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.352

4010	\begin{align} 4 x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x -y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.237

4013	\begin{align} 4 x^{2} y^{\prime \prime }+3 x y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.076

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 \(x=0\).	✓	✓	✓	✓	1.058

4015	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.195

4016	\begin{align} 2 x y^{\prime \prime }+y^{\prime }-2 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.872

4017	\begin{align} 3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.058

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 \(x=0\).	✓	✓	✓	✓	1.078

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 \(x=0\).	✓	✓	✓	✗	1.166

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 \(x=0\).	✓	✓	✓	✓	0.952

4022	\begin{align} 3 x^{2} y^{\prime \prime }+x \left (3 x^{2}+1\right ) y^{\prime }-2 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.110

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 \(x=0\).	✓	✓	✓	✓	1.632

4067	\begin{align} 2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.119

4071	\begin{align} 4 x y^{\prime \prime }+3 y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.007

4072	\begin{align} x^{2} y^{\prime \prime }+\frac {3 x y^{\prime }}{2}-\frac {\left (x +1\right ) y}{2}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.967

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 \(x=0\).	✓	✓	✓	✓	1.044

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 \(x=0\).	✓	✓	✓	✓	1.174

4185	\begin{align} y^{\prime \prime }-\frac {y^{\prime }}{2 x}+\frac {y}{4 x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.216

4600	\begin{align} x^{2} y^{\prime \prime }+\left (\frac {1}{2} x +x^{2}\right ) y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.202

7164	\begin{align} x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.882

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 \(x=0\).	✓	✓	✓	✗	0.815

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 \(x=0\).	✓	✓	✓	✓	0.905

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 \(x=0\).	✓	✓	✓	✓	1.016

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 \(x=0\).	✓	✓	✓	✓	0.824

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 \(x=0\).	✓	✓	✓	✓	0.794

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 \(x=0\).	✓	✓	✓	✓	0.825

7197	\begin{align} 2 x \left (1-x \right ) y^{\prime \prime }+y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.753

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 \(x=0\).	✓	✓	✓	✓	0.825

8078	\begin{align} 4 x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.924

8079	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.757

8085	\begin{align} 2 x y^{\prime \prime }+y^{\prime }-y&=x +1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.139

8086	\begin{align} 2 x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=\infty \).	✓	✓	✓	✓	0.996

8096	\begin{align} x^{2} y^{\prime \prime }+4 \left (x +a \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.164

8107	\begin{align} 2 x y^{\prime \prime }-y^{\prime }+x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.772

8110	\begin{align} x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.041

8111	\begin{align} x y^{\prime \prime }+\left (\frac {1}{2}-x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.954

8132	\begin{align} x^{2} y^{\prime \prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.634

8134	\begin{align} x^{2} y^{\prime \prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.622

8136	\begin{align} 2 x y^{\prime \prime }+y^{\prime }-x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.757

8137	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.661

8148	\begin{align} x^{2} y^{\prime \prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.622

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 \(x=0\).	✓	✓	✓	✗	1.480

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 (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.256

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 \(x=0\).	✓	✓	✓	✓	1.016

8513	\begin{align} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.085

8514	\begin{align} 2 x y^{\prime \prime }+5 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.872

8515	\begin{align} 4 x y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.075

8516	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.869

8517	\begin{align} 3 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.107

8518	\begin{align} x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.937

8519	\begin{align} 2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.115

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 \(x=0\).	✓	✓	✓	✓	0.860

8521	\begin{align} 9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.007

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 \(x=0\).	✓	✓	✓	✓	0.984

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 \(x=0\).	✓	✓	✓	✓	0.865

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 \(x=0\).	✓	✓	✓	✓	0.875

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 \(x=0\).	✓	✓	✓	✓	0.874

8558	\begin{align} 2 x y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.119

8586	\begin{align} 2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.174

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 \(x=0\).	✓	✓	✓	✓	1.391

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 \(x=0\).	✓	✓	✓	✓	1.224

8593	\begin{align} 4 x y^{\prime \prime }+y^{\prime }+8 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.060

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 \(x=0\).	✓	✓	✓	✓	0.920

8600	\begin{align} x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.996

8603	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-6\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.981

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 \(x=0\).	✓	✓	✓	✓	0.933

8616	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-5\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.977

8988	\begin{align} \left (x^{2}+x -2\right )^{2} y^{\prime \prime }+3 \left (x +2\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=-2\).	✓	✓	✓	✓	1.674

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 \(x=0\).	✓	✓	✓	✓	1.450

8993	\begin{align} 3 x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.494

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 \(x=0\).	✓	✓	✓	✓	1.444

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 \(x=0\).	✓	✓	✓	✓	2.018

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 \(x=0\).	✓	✓	✓	✓	1.609

9396	\begin{align} x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.118

9397	\begin{align} 4 x y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.598

9398	\begin{align} 2 x y^{\prime \prime }+\left (-x +3\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.607

9399	\begin{align} 2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.682

9400	\begin{align} 2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.487

9409	\begin{align} \left (x -1\right )^{2} y^{\prime \prime }-3 \left (x -1\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✗	1.145

9410	\begin{align} 3 \left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=-1\).	✓	✓	✓	✗	1.158

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 \(x=0\).	✓	✓	✓	✓	1.697

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 \(x=0\).	✓	✓	✓	✓	1.397

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 \(x=-1\).	✓	✓	✓	✓	1.833

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 \(x=3\).	✓	✓	✓	✓	1.719

9417	\begin{align} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	2.250

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 \(x=0\).	✓	✓	✓	✗	2.865

9431	\begin{align} 2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.605

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 \(x=\infty \).	✓	✓	✓	✗	2.059

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 \(x=\infty \).	✓	✓	✓	✓	2.404

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 \(x=0\).	✓	✓	✓	✗	2.240


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 (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.875

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 \(x=0\).	✓	✓	✓	✓	1.540

9541	\begin{align} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.622

9542	\begin{align} 2 x y^{\prime \prime }+5 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.289

9543	\begin{align} 4 x y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.600

9544	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.234

9545	\begin{align} 3 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.595

9546	\begin{align} x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.381

9547	\begin{align} 2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.610

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 \(x=0\).	✓	✓	✓	✓	1.217

9549	\begin{align} 9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.452

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 \(x=0\).	✓	✓	✓	✓	1.453

9586	\begin{align} 2 x y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.595

9859	\begin{align} 2 x \left (x +1\right ) y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.835

9862	\begin{align} 4 x y^{\prime \prime }+3 y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.746

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 \(x=0\).	✓	✓	✓	✓	1.582

9864	\begin{align} 2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.855

9865	\begin{align} 8 x^{2} y^{\prime \prime }+10 x y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.648

9867	\begin{align} 2 x \left (x +3\right ) y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.799

9868	\begin{align} 2 x y^{\prime \prime }+\left (-2 x^{2}+1\right ) y^{\prime }-4 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.605

9869	\begin{align} x \left (4-x \right ) y^{\prime \prime }+\left (2-x \right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.816

9870	\begin{align} 3 x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.608

9871	\begin{align} 2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.731

9872	\begin{align} 2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-5 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.801

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 \(x=0\).	✓	✓	✓	✓	1.634

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 \(x=0\).	✓	✓	✓	✓	1.619

9875	\begin{align} -y x -\left (2 x^{2}+1\right ) y^{\prime }+2 x y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.599

9876	\begin{align} 2 x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.181

9877	\begin{align} 2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.134

9878	\begin{align} 9 x^{2} y^{\prime \prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.139

9879	\begin{align} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.174

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 \(x=0\).	✓	✓	✓	✓	1.964

9944	\begin{align} 2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.827

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 \(x=0\).	✓	✓	✓	✓	1.750

9951	\begin{align} 2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.786

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 \(x=0\).	✓	✓	✓	✓	1.654

9957	\begin{align} 2 x y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.760

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 \(x=0\).	✓	✓	✓	✓	1.633

10164	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.724

10165	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.850

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 \(x=0\).	✓	✓	✓	✗	0.733

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 \(x=0\).	✓	✓	✓	✗	0.793

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 \(x=0\).	✓	✓	✓	✗	0.739

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 \(x=0\).	✓	✓	✓	✗	0.802

10177	\begin{align} \left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.766

10178	\begin{align} \left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=2\).	✓	✓	✓	✓	0.873

10181	\begin{align} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y x&=x^{2}+2 x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.923

10182	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.736

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 \(x=0\).	✓	✓	✓	✗	0.868

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 \(x=0\).	✓	✓	✓	✗	0.851

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 \(x=0\).	✓	✓	✓	✗	0.909

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 \(x=0\).	✓	✓	✓	✗	0.796

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 \(x=0\).	✓	✓	✓	✗	0.910

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 \(x=0\).	✓	✓	✓	✓	0.865

10193	\begin{align} x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.799

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 \(x=0\).	✓	✓	✓	✓	0.711

10199	\begin{align} 4 x y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.752

10205	\begin{align} 2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (x -5\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.910

10221	\begin{align} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.556

10455	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-5\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.765

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 \(x=0\).	✓	✓	✓	✓	1.974

14749	\begin{align} 2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.467

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 \(x=0\).	✓	✓	✓	✓	1.519

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 \(x=0\).	✓	✓	✓	✓	1.437

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 \(x=0\).	✓	✓	✓	✓	1.456

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 \(x=0\).	✓	✓	✓	✓	1.460

14754	\begin{align} 2 x y^{\prime \prime }+y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.614

14755	\begin{align} 3 x y^{\prime \prime }-\left (x -2\right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.690

14977	\begin{align} 2 x y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.749

14983	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.730

15308	\begin{align} 2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }-k y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.263

15311	\begin{align} 2 x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.834

16883	\begin{align} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.813

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 \(x=0\).	✓	✓	✓	✓	0.896

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 \(x=0\).	✓	✓	✓	✓	0.906

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 \(x=0\).	✓	✓	✓	✓	0.859

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 \(x=0\).	✓	✓	✓	✓	1.051

16925	\begin{align} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✗	1.169

17709	\begin{align} 2 x y^{\prime \prime }-5 y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.199

17710	\begin{align} 5 x y^{\prime \prime }+8 y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.955

17711	\begin{align} 9 x y^{\prime \prime }+14 y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.243

17712	\begin{align} 7 x y^{\prime \prime }+10 y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.335

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 \(x=0\).	✓	✓	✓	✓	0.944

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 \(x=0\).	✓	✓	✓	✓	1.063

17723	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-k^{2}+x^{2}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.172

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 \(x=0\).	✓	✓	✓	✓	1.274

17790	\begin{align} 3 x y^{\prime \prime }+11 y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.195

17791	\begin{align} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.903

18386	\begin{align} 4 x y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.474

18388	\begin{align} 9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.539

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 \(x=0\).	✓	✓	✓	✓	0.915

19602	\begin{align} 4 x y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.894

19603	\begin{align} 2 x y^{\prime \prime }+\left (-x +3\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.892

19604	\begin{align} 2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.938

19605	\begin{align} 2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.858

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 \(x=0\).	✓	✓	✓	✓	0.977

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 \(x=0\).	✓	✓	✓	✓	0.819

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 \(x=-1\).	✓	✓	✓	✓	1.040

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 \(x=3\).	✓	✓	✓	✓	1.007

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 \(x=\infty \).	✓	✓	✓	✓	1.282

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 \(x=0\).	✓	✓	✓	✗	1.250

20903	\begin{align} 4 x y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.078

20906	\begin{align} y^{\prime \prime }+\frac {y^{\prime }}{2 x}-\frac {\left (x +1\right ) y}{2 x^{2}}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.035

20908	\begin{align} 2 x \left (x +1\right ) y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.116

21629	\begin{align} 2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.396

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 \(x=0\).	✓	✓	✓	✗	1.939

21672	\begin{align} 8 x^{2} y^{\prime \prime }+10 x y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.253

21673	\begin{align} -y+\left (x +1\right ) y^{\prime }+2 x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.418

21674	\begin{align} 4 x y^{\prime \prime }+2 y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.328

21675	\begin{align} y^{\prime \prime }+\frac {y^{\prime }}{2 x}+\frac {y}{4 x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.339

21676	\begin{align} x^{2} y^{\prime \prime }+\left (\frac {1}{2} x +x^{2}\right ) y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.398

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 \(x=0\).	✓	✓	✓	✓	1.370

21678	\begin{align} 2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.235

21679	\begin{align} 3 x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.948

21694	\begin{align} 3 x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.937

21696	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-p^{2}+x^{2}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.261

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 \(x=0\).	✓	✓	✓	✗	1.763

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 \(x=0\).	✓	✓	✓	✓	1.273

21908	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.243

22172	\begin{align} 2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.386

22182	\begin{align} x^{4} \left (x^{2}-4\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+\left (x^{2}-3 x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=2\).	✓	✓	✓	✓	1.616

22202	\begin{align} 8 x^{2} y^{\prime \prime }+10 x y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.273

22203	\begin{align} 2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.293

22204	\begin{align} 3 x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.027

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 \(x=0\).	✓	✓	✓	✗	1.965

22212	\begin{align} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.209

22213	\begin{align} 2 x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.243

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 \(x=0\).	✓	✓	✓	✓	1.121

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 \(x=0\).	✓	✓	✓	✗	1.625

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 \(x=0\).	✓	✓	✓	✓	2.132

22851	\begin{align} 2 x y^{\prime \prime }+y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.612

22860	\begin{align} -6 y x -y^{\prime }+x \left (x^{2}+2\right ) y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.759

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 \(x=0\).	✓	✓	✓	✓	1.563

22870	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-8\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.672

23670	\begin{align} 2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.870

23676	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-p^{2}+x^{2}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.831

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 \(x=0\).	✓	✓	✓	✗	1.204

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 \(x=0\).	✓	✓	✓	✓	0.711

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 \(x=0\).	✓	✓	✓	✓	0.892

23730	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-p^{2}+x^{2}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.753

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 \(x=0\).	✓	✓	✓	✓	0.709

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 \(x=0\).	✓	✓	✓	✓	0.894

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 \(x=-3\).	✓	✓	✓	✓	0.842

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 \(x=0\).	✓	✓	✓	✓	0.699

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 \(x=0\).	✓	✓	✓	✓	0.901

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 \(x=0\).	✓	✓	✓	✓	0.893

24095	\begin{align} x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.795

24099	\begin{align} 2 x y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.910

24100	\begin{align} 25 x^{2} y^{\prime \prime }+\left (2 x +4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.837

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 \(x=0\).	✓	✓	✓	✓	0.862

25339	\begin{align} 2 t y^{\prime \prime }+y^{\prime }+y t&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.971

25346	\begin{align} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.101

25348	\begin{align} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (1-t \right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.092

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 \(t=0\).	✓	✓	✓	✓	1.546

26021	\begin{align} 2 x y^{\prime \prime }+5 \left (2 x +1\right ) y^{\prime }+5 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.937

26022	\begin{align} 4 x y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.809

26023	\begin{align} 2 x \left (x -1\right ) y^{\prime \prime }+3 \left (x -1\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.845

26027	\begin{align} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.936

26028	\begin{align} 2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.806

26029	\begin{align} 2 x y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.829

26708	\begin{align} 9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.722

27076	\begin{align} 4 x y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.886

27773	\begin{align} 2 x^{2} y^{\prime \prime }+\left (-2 x^{2}+3 x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.547

27774	\begin{align} 9 x^{2} y^{\prime \prime }-\left (x^{2}-2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.423

27779	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.617

27781	\begin{align} x^{2} y^{\prime \prime }+\left (x -1\right ) y&=-1 \\ \end{align} Series expansion around \(x=0\).	✓	✗	✓	✗	0.732

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