Second order ode Frobenius with roots diﬀerence is integer

2.8.5 Second order ode Frobenius with roots diﬀerence is integer

Table 2.1265: Second order ode Frobenius with roots diﬀerence is integer [473]


#	ODE	solved	Maple	Mma	Sympy	time(sec)

461	\begin{align} x \left (x +1\right ) y^{\prime \prime }+2 y^{\prime }+3 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.009

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

463	\begin{align} x^{2} y^{\prime \prime }+6 \sin \left (x \right ) y^{\prime }+6 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.713

483	\begin{align} x y^{\prime \prime }+2 y^{\prime }+9 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.735

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

485	\begin{align} 4 x y^{\prime \prime }+8 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.724

486	\begin{align} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.688

487	\begin{align} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-4 x^{2}+3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.760

493	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.767

494	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.750

496	\begin{align} x \left (x -1\right ) \left (x +1\right )^{2} y^{\prime \prime }+2 x \left (x -3\right ) \left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.751

498	\begin{align} x y^{\prime \prime }+\left (-x +3\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.852

499	\begin{align} x y^{\prime \prime }+\left (5-x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.856

500	\begin{align} x y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.865

501	\begin{align} 5 x y^{\prime \prime }+\left (30+3 x \right ) y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.893

502	\begin{align} x y^{\prime \prime }-\left (x +4\right ) y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.902

503	\begin{align} 2 x y^{\prime \prime }-\left (6+2 x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.058

504	\begin{align} x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.855

505	\begin{align} x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.856

509	\begin{align} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.836

510	\begin{align} x^{2} y^{\prime \prime }+\left (2 x^{2}-3 x \right ) y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.907

511	\begin{align} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.897

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

1848	\begin{align} x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.370

1849	\begin{align} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (6 x +4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.376

1851	\begin{align} x^{2} \left (1+3 x \right ) y^{\prime \prime }+x \left (x^{2}+12 x +2\right ) y^{\prime }+2 x \left (x +3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.081

1852	\begin{align} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.932

1853	\begin{align} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.509

1968	\begin{align} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.054

1973	\begin{align} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.848

1977	\begin{align} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.862

1978	\begin{align} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.864

1981	\begin{align} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.846

1988	\begin{align} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.878

1995	\begin{align} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.012

2062	\begin{align} 2 x^{2} \left (x +2\right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.474

2063	\begin{align} x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.038

2064	\begin{align} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.514

2065	\begin{align} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.987

2066	\begin{align} x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (4 x +3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.990

2067	\begin{align} x y^{\prime \prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.139

2068	\begin{align} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.336

2069	\begin{align} x \left (x +1\right ) y^{\prime \prime }+x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.122

2070	\begin{align} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.370

2071	\begin{align} x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.016

2072	\begin{align} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (9-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.963

2073	\begin{align} x^{2} y^{\prime \prime }+10 x y^{\prime }+\left (14+x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.941

2074	\begin{align} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.375

2075	\begin{align} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.365

2076	\begin{align} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.091

2077	\begin{align} x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.095

2078	\begin{align} x \left (x +1\right ) y^{\prime \prime }-4 y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.964

2079	\begin{align} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.187

2080	\begin{align} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.045

2081	\begin{align} 3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.015

2082	\begin{align} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.137

2083	\begin{align} x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.000

2084	\begin{align} x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.000

2085	\begin{align} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.000

2086	\begin{align} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.171

2087	\begin{align} x^{2} \left (2 x +1\right ) y^{\prime \prime }-x \left (9+8 x \right ) y^{\prime }-12 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.688

2088	\begin{align} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	3.158

2089	\begin{align} x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	3.025

2090	\begin{align} x y^{\prime \prime }-5 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	2.444

2091	\begin{align} x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.644

2092	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }-\left (-x^{2}+3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.982

2093	\begin{align} 4 x^{2} y^{\prime \prime }+2 x \left (x^{2}+8\right ) y^{\prime }+\left (3 x^{2}+5\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.257

2094	\begin{align} x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.122

2095	\begin{align} x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.118

2096	\begin{align} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.229

2097	\begin{align} 9 x^{2} y^{\prime \prime }-3 x \left (2 x^{2}+11\right ) y^{\prime }+\left (10 x^{2}+13\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	4.483

2098	\begin{align} x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (-x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.096

2099	\begin{align} x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.490

2100	\begin{align} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.862

2101	\begin{align} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.991

2102	\begin{align} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.147

2103	\begin{align} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.371

2104	\begin{align} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }-x \left (x^{2}+3\right ) y^{\prime }-2 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.417

2105	\begin{align} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.928

2440	\begin{align} t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	3.770

2453	\begin{align} t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.033

2454	\begin{align} t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+y t&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.006

2455	\begin{align} t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-y t&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.007

2456	\begin{align} t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.895

2457	\begin{align} t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✗	1.076

2458	\begin{align} t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	3.208

2459	\begin{align} t^{2} y^{\prime \prime }+t y^{\prime }-\left (t +1\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	3.141

2460	\begin{align} t y^{\prime \prime }+t y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	2.605

2469	\begin{align} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	3.188

2470	\begin{align} t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	2.632

2637	\begin{align} t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	4.229

2649	\begin{align} t^{2} y^{\prime \prime }-t y^{\prime }-\left (t^{2}+\frac {5}{4}\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.875

2650	\begin{align} t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.923

2651	\begin{align} t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+y t&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.960

2652	\begin{align} t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-y t&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.044

2653	\begin{align} t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.934

2654	\begin{align} t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✗	1.120

2655	\begin{align} t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	3.721

2656	\begin{align} t^{2} y^{\prime \prime }+t y^{\prime }-\left (t +1\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	3.623

2657	\begin{align} t y^{\prime \prime }+t y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	3.019

2667	\begin{align} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	3.662

2668	\begin{align} t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	3.016

3359	\begin{align} 4 x^{2} y^{\prime \prime }+x \left (x^{2}-4\right ) y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.848

3379	\begin{align} x^{2} y^{\prime \prime }+x \left (2 x -1\right ) y^{\prime }+x \left (x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.901

3380	\begin{align} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.854

3381	\begin{align} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (3 x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.918

3382	\begin{align} x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-9 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.004

3383	\begin{align} \left (-x^{2}+x \right ) y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.886

3384	\begin{align} x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	2.881

3385	\begin{align} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x -4\right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.874

3386	\begin{align} x^{2} y^{\prime \prime }+x \left (-x^{2}+3\right ) y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.611

3387	\begin{align} x y^{\prime \prime }+3 y^{\prime }-y&=x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	2.192

3388	\begin{align} x y^{\prime \prime }+3 y^{\prime }-y&=x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	2.228

3390	\begin{align} x y^{\prime \prime }-x y^{\prime }+y&=x^{3} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	2.249

3399	\begin{align} \left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+2 y&=x^{2} \left (x +2\right )^{2} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.247

3502	\begin{align} z y^{\prime \prime }-2 y^{\prime }+9 z^{5} y&=0 \\ \end{align} Series expansion around \(z=0\).	✓	✓	✓	✓	0.743

3505	\begin{align} z y^{\prime \prime }-2 y^{\prime }+y z&=0 \\ \end{align} Series expansion around \(z=0\).	✓	✓	✓	✓	0.757

4007	\begin{align} \left (x -2\right )^{2} y^{\prime \prime }+\left (x -2\right ) {\mathrm e}^{x} y^{\prime }+\frac {4 y}{x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	5.312

4011	\begin{align} 4 x y^{\prime \prime }-x y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.935

4027	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.481

4029	\begin{align} x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.246

4031	\begin{align} x^{2} y^{\prime \prime }+\left (4 x +\frac {1}{2} x^{2}-\frac {1}{3} x^{3}\right ) y^{\prime }-\frac {7 y}{4}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.174

4032	\begin{align} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.976

4036	\begin{align} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.052

4037	\begin{align} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.255

4038	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.721

4039	\begin{align} x^{2} y^{\prime \prime }+x^{3} y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.980

4041	\begin{align} x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.145

4043	\begin{align} x y^{\prime \prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.730

4044	\begin{align} x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.168

4045	\begin{align} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.069

4048	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.879

4050	\begin{align} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.063

4051	\begin{align} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.727

4053	\begin{align} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.073

4054	\begin{align} x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.652

4056	\begin{align} 4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.050

4057	\begin{align} 4 x^{2} y^{\prime \prime }-\left (4 x +3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.296

4058	\begin{align} x y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.796

4059	\begin{align} x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.678

4060	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.911

4061	\begin{align} x y^{\prime \prime }-y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.675

4066	\begin{align} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.885

4070	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.868

4073	\begin{align} x^{2} y^{\prime \prime }-x \left (2-x \right ) y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.630

4075	\begin{align} y^{\prime \prime }+\left (1-\frac {3}{4 x^{2}}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.231

4179	\begin{align} y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }-\frac {y}{x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.195

4180	\begin{align} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.024

4182	\begin{align} y^{\prime \prime }-\frac {\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )}{x \left (-x^{2}+2\right )}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.493

4183	\begin{align} y^{\prime \prime }-\frac {3 y^{\prime }}{x \left (1-x \right )}+\frac {2 y}{x \left (1-x \right )}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.175

4188	\begin{align} y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x \left (x +1\right )}-\frac {y}{x \left (x +1\right )}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.141

4599	\begin{align} x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.457

4601	\begin{align} x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.146

4602	\begin{align} x^{2} y^{\prime \prime }+2 x y^{\prime }-\left (x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.000

4603	\begin{align} x y^{\prime \prime }-2 x y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.598

4604	\begin{align} x y^{\prime \prime }+2 y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.985

4605	\begin{align} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+2 \left (x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.460

7167	\begin{align} x y^{\prime \prime }+2 y^{\prime }+a^{3} x^{2} y&=2 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.715

7170	\begin{align} x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.783

7171	\begin{align} \left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.785

7173	\begin{align} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.762

7174	\begin{align} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.732

7176	\begin{align} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.911

7181	\begin{align} x y^{\prime \prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.159

7183	\begin{align} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.625

7184	\begin{align} \left (-x^{2}+x \right ) y^{\prime \prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.596

7187	\begin{align} x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.592

7189	\begin{align} 4 x \left (1-x \right ) y^{\prime \prime }-4 y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.763

7192	\begin{align} \left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y&=3 x^{2} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.895

7194	\begin{align} 2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.746

7372	\begin{align} x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.616

7374	\begin{align} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.827

7625	\begin{align} \left (x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }-6 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.032

7628	\begin{align} \sin \left (x \right ) y^{\prime \prime }+\cos \left (x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	3.690

8082	\begin{align} x y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.414

8083	\begin{align} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.810

8084	\begin{align} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.947

8089	\begin{align} x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.167

8093	\begin{align} \left (-x +3\right ) y-x \left (4-x \right ) y^{\prime }+2 \left (2-x \right ) x^{2} y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.035

8094	\begin{align} x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.436

8104	\begin{align} x y^{\prime \prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.225

8106	\begin{align} -y-3 x y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.257

8108	\begin{align} \sin \left (x \right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }-y \sin \left (x \right )&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.147

8138	\begin{align} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.931

8140	\begin{align} x y^{\prime \prime }+x^{3} y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.461

8141	\begin{align} x y^{\prime \prime }+x y^{\prime }-y \,{\mathrm e}^{x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.788

8145	\begin{align} x y^{\prime \prime }+x^{5} y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.451

8146	\begin{align} \sin \left (x \right ) y^{\prime \prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	3.420

8149	\begin{align} x^{2} y^{\prime \prime }+\left (x -\frac {3}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.802

8500	\begin{align} x \left (x +3\right )^{2} y^{\prime \prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.740

8502	\begin{align} y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	5.382

8503	\begin{align} \left (x^{3}+4 x \right ) y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.702

8506	\begin{align} x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.282

8510	\begin{align} x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.346

8523	\begin{align} x y^{\prime \prime }+2 y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.899

8524	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.915

8525	\begin{align} x y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.402

8526	\begin{align} y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.315

8529	\begin{align} x y^{\prime \prime }+\left (-6+x \right ) y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.431


8530	\begin{align} x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.095

8535	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.116

8536	\begin{align} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.927

8539	\begin{align} y^{\prime }+x y^{\prime \prime }+\left (x -\frac {4}{x}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.115

8540	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.089

8541	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.925

8543	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	4.999

8544	\begin{align} x y^{\prime \prime }+2 y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.401

8545	\begin{align} x y^{\prime \prime }+3 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.196

8546	\begin{align} x y^{\prime \prime }-y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.417

8547	\begin{align} x y^{\prime \prime }-5 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	3.273

8548	\begin{align} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.868

8550	\begin{align} x y^{\prime \prime }+3 y^{\prime }+x^{3} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.961

8551	\begin{align} 9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.891

8555	\begin{align} x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.935

8556	\begin{align} 16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.978

8557	\begin{align} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{4}+3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.959

8562	\begin{align} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.138

8580	\begin{align} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.918

8581	\begin{align} x y^{\prime \prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.004

8583	\begin{align} x y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.661

8587	\begin{align} x y^{\prime \prime }+2 y^{\prime }+4 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.928

8588	\begin{align} x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.160

8589	\begin{align} x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.969

8596	\begin{align} 3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	4.853

8601	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.971

8604	\begin{align} x y^{\prime \prime }+5 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.291

8611	\begin{align} x y^{\prime \prime }-5 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	3.527

8617	\begin{align} x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.077

8618	\begin{align} y-\left (x +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.149

8619	\begin{align} x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.990

8620	\begin{align} y^{\prime \prime }+\frac {y}{4 x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.277

8983	\begin{align} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.342

8984	\begin{align} 3 x^{2} y^{\prime \prime }+x^{6} y^{\prime }+2 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.543

8986	\begin{align} x y^{\prime \prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.041

8990	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.177

8997	\begin{align} 4 x^{2} y^{\prime \prime }-4 \,{\mathrm e}^{x} y^{\prime } x +3 \cos \left (x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	7.072

9000	\begin{align} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.339

9001	\begin{align} x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (-x^{3}+3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.227

9002	\begin{align} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.320

9003	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	5.208

9004	\begin{align} x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (4 x -2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	5.746

9387	\begin{align} \left (1+3 x \right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.563

9390	\begin{align} x^{2} y^{\prime \prime }+y \sin \left (x \right )&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	5.720

9393	\begin{align} x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.336

9395	\begin{align} x^{2} y^{\prime \prime }+3 x y^{\prime }+4 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.798

9406	\begin{align} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.344

9407	\begin{align} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.444

9408	\begin{align} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.295

9411	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	5.675

9412	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.263

9429	\begin{align} x y^{\prime \prime }-4 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.276

9528	\begin{align} x \left (x +3\right )^{2} y^{\prime \prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	7.011

9530	\begin{align} y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	8.538

9531	\begin{align} \left (x^{3}+4 x \right ) y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.580

9534	\begin{align} x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.138

9538	\begin{align} x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.752

9551	\begin{align} x y^{\prime \prime }+2 y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.285

9552	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.273

9553	\begin{align} x y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.902

9554	\begin{align} y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.493

9557	\begin{align} x y^{\prime \prime }+\left (-6+x \right ) y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.705

9558	\begin{align} x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.557

9559	\begin{align} y^{\prime \prime }+\frac {2 y^{\prime }}{t}+\lambda y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.370

9590	\begin{align} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.570

9597	\begin{align} \left ({\mathrm e}^{x}-1-x \right ) y^{\prime \prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	7.517

9860	\begin{align} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.447

9861	\begin{align} -\left (4 x^{2}+1\right ) y+4 x y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.415

9907	\begin{align} x^{2} y^{\prime \prime }+2 x \left (x -2\right ) y^{\prime }+2 \left (2-3 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.533

9908	\begin{align} x^{2} \left (2 x +1\right ) y^{\prime \prime }+2 x \left (1+6 x \right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.656

9909	\begin{align} x^{2} y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.505

9910	\begin{align} x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.745

9911	\begin{align} x \left (x +1\right ) y^{\prime \prime }+\left (5+x \right ) y^{\prime }-4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.131

9912	\begin{align} x \left (x +1\right ) y^{\prime \prime }+\left (5+x \right ) y^{\prime }-4 y&=0 \\ \end{align} Series expansion around \(x=-1\).	✓	✓	✓	✗	1.997

9913	\begin{align} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.580

9914	\begin{align} x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.658

9915	\begin{align} x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	1.866

9916	\begin{align} x y^{\prime \prime }+\left (3 x +4\right ) y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.671

9917	\begin{align} x y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.777

9918	\begin{align} x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.687

9919	\begin{align} x \left (x +3\right ) y^{\prime \prime }-9 y^{\prime }-6 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.694

9920	\begin{align} x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+8 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.818

9921	\begin{align} x y^{\prime \prime }+\left (x^{3}-1\right ) y^{\prime }+x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.579

9922	\begin{align} x^{2} \left (4 x -1\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.710

9923	\begin{align} x y^{\prime \prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.717

9924	\begin{align} x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (4 x +3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.530

9925	\begin{align} 2 x y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	5.211

9926	\begin{align} 4 x^{2} y^{\prime \prime }+2 x \left (2-x \right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	7.433

9927	\begin{align} x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.553

9928	\begin{align} x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+8 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.762

9929	\begin{align} x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.881

9930	\begin{align} x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	7.691

9932	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.305

9933	\begin{align} x^{2} y^{\prime \prime }-5 x y^{\prime }+\left (8+5 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.361

9934	\begin{align} x y^{\prime \prime }+\left (-x +3\right ) y^{\prime }-5 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.658

9935	\begin{align} 9 x^{2} y^{\prime \prime }-15 x y^{\prime }+7 \left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	8.044

9936	\begin{align} x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.529

9940	\begin{align} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (6 x^{2}-3 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.686

9941	\begin{align} x y^{\prime \prime }+x y^{\prime }+\left (x^{4}+1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	7.037

9945	\begin{align} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.656

9946	\begin{align} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.954

9947	\begin{align} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.681

9949	\begin{align} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (x^{2}+3\right ) y^{\prime }+6 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.437

9953	\begin{align} 4 y x -\left (x^{2}+7\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.665

9955	\begin{align} \left (x +3\right ) y-2 x \left (x +2\right ) y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.588

9964	\begin{align} 4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (x +3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.531

9965	\begin{align} x \left (-x^{2}+1\right ) y^{\prime \prime }+5 \left (-x^{2}+1\right ) y^{\prime }-4 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.470

9967	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.235

9968	\begin{align} x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+18 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.832

9969	\begin{align} x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.710

10180	\begin{align} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.656

10185	\begin{align} x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.766

10202	\begin{align} x \left (x -1\right ) y^{\prime \prime }+3 x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.639

10211	\begin{align} x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.666

10213	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.665

10214	\begin{align} \left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.661

10215	\begin{align} x^{2} y^{\prime \prime }+\left (x^{2}+6 x \right ) y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.756

10216	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}-8\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.588

10218	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.666

10219	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.656

10220	\begin{align} x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.750

10223	\begin{align} x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.628

10224	\begin{align} x^{2} y^{\prime \prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.740

10454	\begin{align} x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	6.558

14756	\begin{align} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.354

14757	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.385

14758	\begin{align} x^{2} y^{\prime \prime }+\left (x^{4}+x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.669

14759	\begin{align} x y^{\prime \prime }-y^{\prime } \left (x^{2}+2\right )+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.793

14760	\begin{align} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.630

14761	\begin{align} \left (2 x^{2}-x \right ) y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+\left (-2 x^{2}+3 x -2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.996

14762	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }+\frac {3 y}{4}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.297

14763	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	7.829

14764	\begin{align} x^{2} y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	8.034

14765	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }+8 \left (x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	7.940

14766	\begin{align} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\frac {3 y}{4}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.319

14768	\begin{align} 2 x y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.956

14770	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}-3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	7.758

14980	\begin{align} -y-3 x y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	9.038

14982	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	8.015

15307	\begin{align} x y^{\prime \prime }+4 y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.583

15312	\begin{align} x \left (x -1\right ) y^{\prime \prime }+3 x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	8.792

16839	\begin{align} \left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.955

16890	\begin{align} \left (-x^{4}+x^{3}\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+827 y&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	4.256

16894	\begin{align} \left (4 x^{2}-1\right ) y^{\prime \prime }+\left (4-\frac {2}{x}\right ) y^{\prime }+\frac {\left (-x^{2}+1\right ) y}{x^{2}+1}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.606

16896	\begin{align} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.823

16898	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x -4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.239

16899	\begin{align} \left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 x y^{\prime }+10 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.859

16902	\begin{align} y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{x^{2}}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.142

16906	\begin{align} x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.426

16910	\begin{align} \left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=3\).	✓	✓	✓	✓	2.714

16911	\begin{align} y^{\prime \prime }+\frac {2 y^{\prime }}{x +2}+y&=0 \\ \end{align} Series expansion around \(x=-2\).	✓	✓	✓	✓	0.866

16913	\begin{align} \left (x -3\right )^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=3\).	✓	✓	✓	✓	0.967

16914	\begin{align} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (-x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.823

16915	\begin{align} x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.945

16919	\begin{align} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x y^{\prime }+\left (4 x^{3}-4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.550

16921	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }-\left (2 x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.252

16922	\begin{align} x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (x +2\right )^{2}}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.177

16923	\begin{align} x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (x +2\right )^{2}}&=0 \\ \end{align} Series expansion around \(x=-2\).	✓	✓	✓	✓	1.005

16924	\begin{align} \left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=3\).	✓	✓	✓	✓	2.724

16928	\begin{align} x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.430

16929	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x -4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.214

17713	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.910

17714	\begin{align} x y^{\prime \prime }+2 x y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.976

17717	\begin{align} y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.035

17719	\begin{align} x^{2} y^{\prime \prime }+7 x y^{\prime }-7 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.079

17729	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.988

17730	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (16 x^{2}-25\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	5.209

17792	\begin{align} x^{2} y^{\prime \prime }-7 x y^{\prime }+\left (-2 x^{2}+7\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	5.084

19594	\begin{align} \left (1+3 x \right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	4.299

19597	\begin{align} x^{2} y^{\prime \prime }+y \sin \left (x \right )&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.871

19600	\begin{align} x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.806

19611	\begin{align} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.741

19612	\begin{align} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.866

19613	\begin{align} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.783

19614	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.733

19615	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.768

20145	\begin{align} \left (-x^{2}+x \right ) y^{\prime \prime }+4 y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.270

20894	\begin{align} x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.878

20902	\begin{align} x^{2} \left (x -2\right ) y^{\prime \prime }+4 \left (x -2\right ) y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=\infty \).	✓	✓	✓	✓	5.812

20905	\begin{align} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.895

20907	\begin{align} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.925

20910	\begin{align} x y^{\prime \prime }-\left (x +4\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.145

21267	\begin{align} t x^{\prime \prime }&=x \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	3.629

21268	\begin{align} t x^{\prime \prime }&=x^{\prime } \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.777

21271	\begin{align} 4 t^{2} x^{\prime \prime }+4 x^{\prime } t -x&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.944

21272	\begin{align} t^{2} x^{\prime \prime }+3 x^{\prime } t&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.760

21631	\begin{align} \left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\ \end{align} Series expansion around \(x=2\).	✓	✓	✓	✓	6.227

21633	\begin{align} \left (x -1\right ) y^{\prime \prime }+x y^{\prime }+\frac {y}{x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	7.148

21640	\begin{align} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.034

21668	\begin{align} x \left (x -1\right )^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }-\left (x^{3}+2 x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	8.177

21671	\begin{align} x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x +\left (x^{3}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	7.933

21680	\begin{align} x^{2} y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.214

21681	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.137

21682	\begin{align} x^{2} y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.094

21683	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	6.013

21685	\begin{align} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.211

21687	\begin{align} 2 \left (1-x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+\left (x -3-\left (x -1\right )^{2} {\mathrm e}^{x}\right ) y&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	2.309

21688	\begin{align} x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.101

21699	\begin{align} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=x^{3} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.144

21905	\begin{align} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.128

21907	\begin{align} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.921

22171	\begin{align} \left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\ \end{align} Series expansion around \(x=2\).	✓	✓	✓	✓	7.359

22177	\begin{align} \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x&=0 \\ \end{align} Series expansion around \(x=-1\).	✓	✓	✓	✓	8.474

22207	\begin{align} x^{2} y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	7.414

22208	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	7.266

22209	\begin{align} x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.360

22210	\begin{align} x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x +\left (x^{3}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	8.779

22217	\begin{align} x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.230

22218	\begin{align} x y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	7.856

22219	\begin{align} 4 x^{2} y^{\prime \prime }+\left (2 x^{2}+4 x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	7.816

22223	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	7.425

22224	\begin{align} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.069

22226	\begin{align} x y^{\prime \prime }-3 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	5.724

22844	\begin{align} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.502

22850	\begin{align} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.645

22852	\begin{align} x \left (1-x \right ) y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.120

22854	\begin{align} x y^{\prime \prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	8.762

22855	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.648

22857	\begin{align} x y^{\prime \prime }-y^{\prime }+4 x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.013

22858	\begin{align} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-4 x^{2}+3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.638

22861	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	11.793

22862	\begin{align} U^{\prime \prime }+\frac {2 U^{\prime }}{r}+a U&=0 \\ \end{align} Series expansion around \(r=0\).	✓	✓	✓	✗	1.828

22863	\begin{align} y^{\prime \prime }-x y^{\prime }-y&=5 \sqrt {x} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	2.213

22864	\begin{align} x y^{\prime \prime }+2 y^{\prime }+y x&=2 x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	1.937

22869	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-9\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	11.935

22871	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (3 x^{2}-4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	11.787

22872	\begin{align} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (2 x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.648

22873	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	11.882

22877	\begin{align} x y^{\prime \prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	8.344

23667	\begin{align} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.234

23672	\begin{align} x^{2} y^{\prime \prime }-\left (x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.911

23687	\begin{align} \left (x +3\right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=-3\).	✓	✓	✓	✓	0.928

23720	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-4\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.956

23724	\begin{align} x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.145

23728	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.985

23729	\begin{align} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.694

23738	\begin{align} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.678

23739	\begin{align} \left (x +1\right )^{2} y^{\prime \prime }-\left (x +3\right ) y&=0 \\ \end{align} Series expansion around \(x=-1\).	✓	✓	✓	✓	2.963

23740	\begin{align} \left (x -1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	2.898

23745	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.743

24098	\begin{align} x^{2} y^{\prime \prime }+5 x y^{\prime }-5 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.750

24101	\begin{align} x^{2} y^{\prime \prime }-\left (3 x^{4}+5 x \right ) y^{\prime }+\left (6 x^{3}+5\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.886

24103	\begin{align} x^{2} \left (x +1\right ) y^{\prime \prime }-3 x y^{\prime }+\left (3-2 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.889

24110	\begin{align} x y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.529

24111	\begin{align} x^{2} y^{\prime \prime }+2 x^{4} y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	2.474

24112	\begin{align} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }+\left (2 x -3\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.242

24113	\begin{align} 9 x^{2} y^{\prime \prime }+\left (x^{2}-15 x \right ) y^{\prime }+7 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	3.846

24114	\begin{align} x^{2} y^{\prime \prime }+\left (x^{2}-5 x \right ) y^{\prime }+\left (5-6 x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	3.338

25340	\begin{align} t^{2} y^{\prime \prime }+2 t y^{\prime }+t^{2} y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.017

25345	\begin{align} t y^{\prime \prime }-2 y^{\prime }+y t&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.036

25349	\begin{align} t^{2} y^{\prime \prime }+t^{2} y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.127

25350	\begin{align} t^{2} y^{\prime \prime }+2 t y^{\prime }-a \,t^{2} y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.086

25351	\begin{align} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	6.049

25352	\begin{align} t y^{\prime \prime }-4 y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	4.119

25354	\begin{align} t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y&=0 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	1.085

26024	\begin{align} x y^{\prime \prime }-y^{\prime } \left (x^{2}+2\right )+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.745

26026	\begin{align} x y^{\prime \prime }+\left (x^{3}-1\right ) y^{\prime }+3 x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.702

26030	\begin{align} x \left (x +1\right ) y^{\prime \prime }+\left (5+x \right ) y^{\prime }-4 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.911

26031	\begin{align} x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+8 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.925

26032	\begin{align} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.731

26033	\begin{align} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.600

26034	\begin{align} x \left (1-x \right ) y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.860

26035	\begin{align} x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.629

27073	\begin{align} x y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.339

27074	\begin{align} x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.888

27075	\begin{align} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-9\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.869

27077	\begin{align} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.694

27078	\begin{align} x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.801

27079	\begin{align} x y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.317

27081	\begin{align} x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) x y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.746

27772	\begin{align} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.503

27775	\begin{align} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.510

27776	\begin{align} x^{2} y^{\prime \prime }+2 x y^{\prime }-\left (x^{2}+2 x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.535

27777	\begin{align} x y^{\prime \prime }-x y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.860

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