Second order ode Frobenius with repeated roots

2.8.7 Second order ode Frobenius with repeated roots

Table 2.1269: Second order ode Frobenius with repeated roots [290]


#	ODE	solved	Maple	Mma	Sympy	time(sec)

506	\begin{align} x y^{\prime \prime }+y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.546

507	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.602

508	\begin{align} x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.701

513	\begin{align} x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.659

1850	\begin{align} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x^{2}-6 x +1\right ) y^{\prime }+\left (x^{2}+6 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.924

1998	\begin{align} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.876

1999	\begin{align} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.846

2000	\begin{align} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.715

2001	\begin{align} x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.763

2002	\begin{align} x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.983

2003	\begin{align} x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (7 x^{2}+6 x +3\right ) y^{\prime }+\left (-3 x^{2}+6 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.149

2004	\begin{align} x^{2} \left (x^{2}+2 x +1\right ) y^{\prime \prime }+x \left (4 x^{2}+3 x +1\right ) y^{\prime }-x \left (1-2 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.111

2005	\begin{align} 4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.169

2006	\begin{align} x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.985

2007	\begin{align} 9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.069

2008	\begin{align} x^{2} y^{\prime \prime }+x \left (x^{2}+x +1\right ) y^{\prime }+x \left (2-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.155

2009	\begin{align} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.036

2010	\begin{align} 4 x^{2} y^{\prime \prime }+2 x \left (x^{2}+x +4\right ) y^{\prime }+\left (3 x^{2}+5 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.152

2011	\begin{align} 16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.117

2012	\begin{align} 9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.000

2013	\begin{align} 4 x^{2} y^{\prime \prime }+\left (1+4 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.710

2014	\begin{align} 36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.855

2015	\begin{align} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x +3\right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.737

2016	\begin{align} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.776

2017	\begin{align} 25 x^{2} y^{\prime \prime }+x \left (15+x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.836

2018	\begin{align} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.837

2019	\begin{align} x^{2} \left (9+4 x \right ) y^{\prime \prime }+3 x y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.859

2020	\begin{align} x^{2} y^{\prime \prime }-x \left (3-2 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.826

2021	\begin{align} x^{2} \left (1-4 x \right ) y^{\prime \prime }+3 x \left (1-6 x \right ) y^{\prime }+\left (1-12 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.867

2022	\begin{align} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3+5 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.796

2023	\begin{align} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.797

2024	\begin{align} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.990

2025	\begin{align} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.951

2026	\begin{align} x^{2} \left (1+4 x \right ) y^{\prime \prime }-x \left (1-4 x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.126

2027	\begin{align} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.084

2028	\begin{align} x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.017

2029	\begin{align} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.768

2030	\begin{align} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.842

2031	\begin{align} 4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.732

2032	\begin{align} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.657

2033	\begin{align} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.691

2034	\begin{align} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.681

2035	\begin{align} 4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.706

2036	\begin{align} 3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.727

2037	\begin{align} 4 x^{2} \left (4 x^{2}+1\right ) y^{\prime \prime }+32 x^{3} y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.796

2038	\begin{align} 9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.773

2039	\begin{align} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (7 x^{2}+3\right ) y^{\prime }+\left (-3 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.863

2040	\begin{align} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }+\left (12 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.706

2041	\begin{align} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.716

2042	\begin{align} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-9 x^{2}+5\right ) y^{\prime }+\left (-3 x^{2}+4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.722

2043	\begin{align} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (-x^{2}+14\right ) y^{\prime }+2 \left (x^{2}+9\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.730

2044	\begin{align} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (7 x^{2}+3\right ) y^{\prime }+\left (8 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.700

2045	\begin{align} x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 x y^{\prime }+\left (1+4 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.777

2046	\begin{align} x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.865

2047	\begin{align} x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.787

2048	\begin{align} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x^{2} y^{\prime }+\left (1-5 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.835

2049	\begin{align} x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.779

2050	\begin{align} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.707

2051	\begin{align} 9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.750

2052	\begin{align} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.658

2053	\begin{align} 4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.746

2054	\begin{align} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.643

2055	\begin{align} 9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (4 x +3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.688

2056	\begin{align} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.639

2057	\begin{align} 16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.681

2058	\begin{align} x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (-3 x +4\right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.644

2059	\begin{align} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.725

2060	\begin{align} x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.680

2061	\begin{align} 9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.735

2443	\begin{align} \left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+{\mathrm e}^{t} y^{\prime }+y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✗	1.566

2461	\begin{align} t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 y t&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.766

2462	\begin{align} t^{2} y^{\prime \prime }+t y^{\prime }+t^{2} y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.649

2464	\begin{align} t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.153

2467	\begin{align} t y^{\prime \prime }+y^{\prime }-4 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.846

2468	\begin{align} t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.808

2640	\begin{align} \left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+{\mathrm e}^{t} y^{\prime }+y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✗	1.233

2659	\begin{align} t^{2} y^{\prime \prime }+t y^{\prime }+t^{2} y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.690

2661	\begin{align} t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.116

2665	\begin{align} t y^{\prime \prime }+y^{\prime }-4 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.861

2666	\begin{align} t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.785

3372	\begin{align} x y^{\prime \prime }+y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.694

3373	\begin{align} x y^{\prime \prime }+y^{\prime }+2 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.665

3374	\begin{align} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 \left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.804

3375	\begin{align} x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.691

3376	\begin{align} x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.746

3377	\begin{align} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }+9 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.660

3378	\begin{align} x^{2} y^{\prime \prime }+x \left (x^{2}-1\right ) y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.664

3389	\begin{align} x y^{\prime \prime }+y^{\prime }-2 y x&=x^{2} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.702

3393	\begin{align} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }+y&=-2 x^{2}+x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.000

3507	\begin{align} z \left (1-z \right ) y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y&=0 \\ \end{align} Series expansion around \(z=0\).	✓	✓	✓	✓	1.043

3508	\begin{align} z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}&=0 \\ \end{align} Series expansion around \(z=0\).	✓	✓	✓	✓	0.745

3512	\begin{align} z y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y&=0 \\ \end{align} Series expansion around \(z=0\).	✓	✓	✓	✓	0.963

4000	\begin{align} x y^{\prime \prime }-\left (x -1\right ) y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.898

4023	\begin{align} 4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.852

4024	\begin{align} x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.845

4025	\begin{align} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.885

4026	\begin{align} x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.808

4028	\begin{align} x^{2} y^{\prime \prime }-\left (-x^{2}+x \right ) y^{\prime }+\left (x^{3}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.922

4033	\begin{align} x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.867

4034	\begin{align} 4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.881

4040	\begin{align} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+7 \,{\mathrm e}^{x} y^{\prime } x +9 \left (1+\tan \left (x \right )\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.019

4042	\begin{align} x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.869

4046	\begin{align} 4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.869

4047	\begin{align} x y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.993

4049	\begin{align} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.892

4052	\begin{align} x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.835

4055	\begin{align} x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.809

4065	\begin{align} x y^{\prime \prime }+y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.848

4068	\begin{align} x y^{\prime \prime }+y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.984

4074	\begin{align} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 \left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.872

4181	\begin{align} y^{\prime \prime }-2 y^{\prime }+\left (\frac {1}{4 x^{2}}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.072

4186	\begin{align} y^{\prime \prime }-\frac {y^{\prime }}{x}+\left (1+\frac {1}{x^{2}}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.841

4187	\begin{align} y^{\prime \prime }+\frac {\left (1-5 x \right ) y^{\prime }}{-x^{2}+x}-\frac {4 y}{-x^{2}+x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.065

4596	\begin{align} x y^{\prime \prime }+y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.777

4597	\begin{align} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+k y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.264

4598	\begin{align} x^{2} y^{\prime \prime }+\left (-2 x^{2}+x \right ) y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.074

4606	\begin{align} x y^{\prime \prime }+y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.792

7179	\begin{align} x y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.560

7180	\begin{align} x y^{\prime \prime }+y^{\prime }+p x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.490

7185	\begin{align} x \left (-x^{2}+1\right ) y^{\prime \prime }+\left (-3 x^{2}+1\right ) y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.549

7188	\begin{align} x \left (-x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.542

7835	\begin{align} \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.730

8080	\begin{align} x y^{\prime \prime }+y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.615

8081	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.634

8087	\begin{align} x^{3} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=\infty \).	✓	✓	✓	✓	0.851

8090	\begin{align} x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (x y^{\prime }-y\right )&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.819

8095	\begin{align} 4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.796

8097	\begin{align} x y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime }+b x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.819

8103	\begin{align} x \left (x +2\right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.852

8135	\begin{align} y^{\prime \prime }+\frac {y^{\prime }}{x}-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.648

8150	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.547

8512	\begin{align} x y^{\prime \prime }+y^{\prime }+10 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.908

8527	\begin{align} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.942

8528	\begin{align} x y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.898

8538	\begin{align} x y^{\prime \prime }+y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.716

8549	\begin{align} 4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.744

8553	\begin{align} x y^{\prime \prime }+y^{\prime }-7 x^{3} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.800

8582	\begin{align} x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.010

8585	\begin{align} x y^{\prime \prime }+y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.746

8590	\begin{align} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.040

8598	\begin{align} x y^{\prime \prime }+y^{\prime }+\frac {y}{4}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.963

8607	\begin{align} 4 x y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.938

8608	\begin{align} x y^{\prime \prime }+y^{\prime }+36 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.940

8613	\begin{align} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.071

8621	\begin{align} x y^{\prime \prime }+y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.755

8987	\begin{align} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	1.370

8994	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.967

8998	\begin{align} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+3 \left (x^{2}+x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.260

8999	\begin{align} x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.118

9401	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.032

9404	\begin{align} x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (4 x +4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.253

9405	\begin{align} 4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.315

9432	\begin{align} x y^{\prime \prime }-\left (x -1\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.362

9434	\begin{align} x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.256

9439	\begin{align} x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=\infty \).	✓	✓	✓	✓	1.336

9540	\begin{align} x y^{\prime \prime }+y^{\prime }+10 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.306

9555	\begin{align} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.286

9556	\begin{align} x y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.265

9866	\begin{align} 2 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.545

9890	\begin{align} x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.186

9891	\begin{align} 4 x^{2} y^{\prime \prime }+\left (1-2 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.214

9892	\begin{align} x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.306

9893	\begin{align} x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (4 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.095

9894	\begin{align} x \left (x +1\right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.536

9895	\begin{align} x^{2} y^{\prime \prime }-x \left (1+3 x \right ) y^{\prime }+\left (1-6 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.357

9896	\begin{align} x^{2} y^{\prime \prime }+x \left (x -1\right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.299

9897	\begin{align} x \left (x -2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.543

9898	\begin{align} x \left (x -2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=2\).	✓	✓	✓	✓	1.531

9899	\begin{align} 4 \left (x -4\right )^{2} y^{\prime \prime }+\left (x -4\right ) \left (x -8\right ) y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=4\).	✓	✓	✓	✓	1.409

9901	\begin{align} x y^{\prime \prime }+y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.075

9902	\begin{align} x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.322

9903	\begin{align} x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }+\left (1+3 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.481

9904	\begin{align} 4 x^{2} y^{\prime \prime }+8 x \left (x +1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.463

9905	\begin{align} x^{2} y^{\prime \prime }+3 x \left (x +1\right ) y^{\prime }+\left (-3 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.363

9906	\begin{align} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.374

9937	\begin{align} x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (x^{3}+x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.552

9939	\begin{align} x y^{\prime \prime }+y^{\prime }+\left (x +1\right ) x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.391

9942	\begin{align} x \left (x -2\right )^{2} y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.673

9943	\begin{align} x \left (x -2\right )^{2} y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=2\).	✓	✓	✓	✓	1.366

9956	\begin{align} x^{2} y^{\prime \prime }-x \left (x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.292

9958	\begin{align} x^{2} y^{\prime \prime }+x \left (x^{2}-3\right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.285

9959	\begin{align} 4 x^{2} y^{\prime \prime }-x^{2} y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.392

9962	\begin{align} 4 x^{2} y^{\prime \prime }+3 x^{2} y^{\prime }+\left (1+3 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.386

9963	\begin{align} x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.296

9966	\begin{align} x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.328

9970	\begin{align} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 \left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.272

10198	\begin{align} -y+y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.589

10200	\begin{align} -y+y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.584

10201	\begin{align} x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.628

10203	\begin{align} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.720

10204	\begin{align} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.687

10206	\begin{align} 2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=\sin \left (x \right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.842

10207	\begin{align} 2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=x \sin \left (x \right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.796

10208	\begin{align} 2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=\sin \left (x \right ) \cos \left (x \right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.851

10209	\begin{align} 2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=x^{3}+x \sin \left (x \right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.843

10212	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.596

10217	\begin{align} x^{2} y^{\prime \prime }-9 x y^{\prime }+25 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.477

14767	\begin{align} x y^{\prime \prime }+y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.486

14769	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.215


14981	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }-x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.208

15305	\begin{align} x \left (1-x \right ) y^{\prime \prime }+\left (1-5 x \right ) y^{\prime }-4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.731

16891	\begin{align} y^{\prime \prime }+\frac {y^{\prime }}{x -3}+\frac {y}{x -4}&=0 \\ \end{align} Series expansion around \(x=3\).	✓	✓	✓	✓	0.889

16893	\begin{align} y^{\prime \prime }+\left (\frac {1}{x}-\frac {1}{3}\right ) y^{\prime }+\left (\frac {1}{x}-\frac {1}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.924

16897	\begin{align} 4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.744

16900	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }+\frac {y}{1-x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.775

16901	\begin{align} y^{\prime \prime }+\frac {y^{\prime }}{x}+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.647

16904	\begin{align} x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.785

16907	\begin{align} 4 x^{2} y^{\prime \prime }+8 x^{2} y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.792

16908	\begin{align} x^{2} y^{\prime \prime }+\left (-x^{4}+x \right ) y^{\prime }+3 x^{3} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.779

16912	\begin{align} 4 y^{\prime \prime }+\frac {\left (4 x -3\right ) y}{\left (x -1\right )^{2}}&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	0.804

16916	\begin{align} y^{\prime \prime }+\frac {y^{\prime }}{x}+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.648

16918	\begin{align} x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+9 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.792

16920	\begin{align} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }+\left (1-4 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.777

16926	\begin{align} 4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.750

16927	\begin{align} y^{\prime \prime }+\frac {y^{\prime }}{x}+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.648

17718	\begin{align} y^{\prime \prime }-\left (\frac {1}{x}+2\right ) y^{\prime }+\left (x +\frac {1}{x^{2}}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.073

17720	\begin{align} x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.719

17721	\begin{align} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.727

17726	\begin{align} x \left (1-x \right ) y^{\prime \prime }+y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.021

17727	\begin{align} x \left (1-x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.071

17728	\begin{align} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+k y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.261

17793	\begin{align} x \left (1-x \right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+10 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.122

17794	\begin{align} x \left (x +1\right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }-10 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.122

19606	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.593

19609	\begin{align} x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (4 x +4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.708

19610	\begin{align} 4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.764

19620	\begin{align} x \left (1-x \right ) y^{\prime \prime }+\left (-3 x +1\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.668

20895	\begin{align} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.875

20896	\begin{align} x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.808

20904	\begin{align} y^{\prime \prime }+\frac {y}{4 x^{2}}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.639

20909	\begin{align} x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.809

21273	\begin{align} t^{2} x^{\prime \prime }-3 x^{\prime } t +\left (4-t \right ) x&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✗	0.867

21274	\begin{align} t^{2} x^{\prime \prime }+x^{\prime } t +x t^{2}&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.714

21634	\begin{align} \left (x -1\right ) y^{\prime \prime }+x y^{\prime }+\frac {y}{x}&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	1.362

21689	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.868

21690	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.769

21691	\begin{align} x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (1-2 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.007

21692	\begin{align} x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (x^{2}+x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.103

21693	\begin{align} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=\infty \).	✓	✓	✓	✗	1.063

21698	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.779

21702	\begin{align} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y p&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.357

21904	\begin{align} x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+\left (x +4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.030

22176	\begin{align} \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.167

22205	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.963

22206	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.846

22215	\begin{align} -y+y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.162

22216	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+x^{3} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.118

22221	\begin{align} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.859

22222	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.004

22846	\begin{align} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	2.076

22856	\begin{align} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.822

22859	\begin{align} x y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.749

22867	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.826

22875	\begin{align} x y^{\prime \prime }+y^{\prime }-i x y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.451

22878	\begin{align} x y^{\prime \prime }+y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.381

22881	\begin{align} x \left (1-x \right ) y^{\prime \prime }+\left (-3 x +1\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.650

23668	\begin{align} x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.705

23680	\begin{align} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y p&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.859

23682	\begin{align} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y&=0 \\ \end{align} Series expansion around \(x=-1\).	✓	✓	✓	✓	0.808

23721	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.550

23723	\begin{align} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.677

23726	\begin{align} x^{2} y^{\prime \prime }+3 x \left (1-x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.685

23727	\begin{align} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.700

23731	\begin{align} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.716

23733	\begin{align} x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.648

23734	\begin{align} x^{2} y^{\prime \prime }-\left (x^{3}+x^{2}+x \right ) y^{\prime }+\left (1+4 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.807

23737	\begin{align} \left (x -1\right ) y^{\prime \prime }+\left (2-x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	0.727

23741	\begin{align} x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.653

23744	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.553

23746	\begin{align} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.682

23747	\begin{align} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.684

23748	\begin{align} x y^{\prime \prime }-\left (x -1\right ) y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.706

24090	\begin{align} x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.670

24091	\begin{align} x y^{\prime \prime }+y^{\prime }-x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.655

24105	\begin{align} x^{2} y^{\prime \prime }+\left (-4 x^{3}+x \right ) y^{\prime }-x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.727

24106	\begin{align} x^{2} y^{\prime \prime }-5 x y^{\prime }+\left (-x^{2}+9\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.636

24107	\begin{align} x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.667

24108	\begin{align} x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (2 x +4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.743

24109	\begin{align} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.776

25335	\begin{align} y^{\prime \prime }+\frac {\left (1-t \right ) y^{\prime }}{t}+\frac {\left (1-\cos \left (t \right )\right ) y}{t^{3}}&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✗	1.159

25338	\begin{align} t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+4 y t&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.007

25342	\begin{align} t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.366

25343	\begin{align} t^{2} y^{\prime \prime }+3 t \left (1+3 t \right ) y^{\prime }+\left (-t^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.026

25347	\begin{align} t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.904

25356	\begin{align} t^{2} \left (t +1\right ) y^{\prime \prime }-t \left (2 t +1\right ) y^{\prime }+\left (2 t +1\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.999

26036	\begin{align} x y^{\prime \prime }+y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.491

26037	\begin{align} x y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.582

27072	\begin{align} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.721

27080	\begin{align} \left (2-x \right ) x y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.711

27778	\begin{align} x y^{\prime \prime }+y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.310

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