2.8.5 Second order ode Frobenius with roots difference is integer

Table 2.1183: Second order ode Frobenius with roots difference is integer [454]

#

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 \(x=0\).

1.607

462

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

0.492

463

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

0.464

483

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

0.457

484

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

0.452

485

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

0.463

486

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

0.431

487

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

0.478

493

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

0.471

494

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

1.355

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 \(x=0\).

2.025

498

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

0.556

499

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

0.573

500

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

0.578

501

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

0.673

502

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

0.655

503

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

1.706

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 \(x=0\).

0.586

505

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

0.618

509

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

0.609

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 \(x=0\).

1.539

511

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

0.625

512

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

0.521

1848

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

1.940

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 \(x=0\).

1.824

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 \(x=0\).

0.737

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 \(x=0\).

0.647

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 \(x=0\).

1.825

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 \(x=0\).

0.760

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 \(x=0\).

0.586

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 \(x=0\).

0.636

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 \(x=0\).

0.626

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 \(x=0\).

0.602

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 \(x=0\).

0.634

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 \(x=0\).

0.657

2062

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

1.942

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 \(x=0\).

0.757

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 \(x=0\).

1.909

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 \(x=0\).

0.734

2066

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

1.627

2067

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

1.220

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 \(x=0\).

1.839

2069

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

1.708

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 \(x=0\).

1.901

2071

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

1.652

2072

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

1.645

2073

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

1.608

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 \(x=0\).

1.896

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 \(x=0\).

1.862

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 \(x=0\).

1.719

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 \(x=0\).

1.719

2078

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

0.686

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 \(x=0\).

0.891

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 \(x=0\).

0.780

2081

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

0.744

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 \(x=0\).

0.904

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 \(x=0\).

0.749

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 \(x=0\).

0.731

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 \(x=0\).

0.736

2086

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

0.849

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 \(x=0\).

1.239

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 \(x=0\).

1.715

2089

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

1.582

2090

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

1.354

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 \(x=0\).

1.599

2092

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

1.569

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 \(x=0\).

1.734

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 \(x=0\).

1.621

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 \(x=0\).

1.630

2096

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

1.648

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 \(x=0\).

2.222

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 \(x=0\).

1.651

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 \(x=0\).

1.644

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 \(x=0\).

0.627

2101

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

0.682

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 \(x=0\).

0.773

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 \(x=0\).

0.974

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 \(x=0\).

1.890

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 \(x=0\).

0.641

2440

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

2.154

2453

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

0.674

2454

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

0.633

2455

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

0.700

2456

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

0.654

2457

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

0.780

2458

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

1.855

2459

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

1.811

2460

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

1.547

2469

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

1.809

2470

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

1.575

2637

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

1.784

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 \(t=0\).

0.552

2650

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

0.595

2651

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

0.552

2652

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

0.614

2653

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

0.598

2654

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

0.699

2655

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

1.508

2656

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

1.462

2657

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

1.259

2667

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

1.428

2668

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

1.251

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 \(x=0\).

0.802

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 \(x=0\).

0.905

3380

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

0.798

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 \(x=0\).

0.838

3382

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

0.929

3383

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

0.866

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 \(x=0\).

3.118

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 \(x=0\).

3.185

3386

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

3.057

3387

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

2.721

3388

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

2.687

3390

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

2.665

3399

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

1.214

3502

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

0.340

3505

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

0.439

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 \(x=0\).

2.103

4011

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

1.251

4027

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

1.454

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 \(x=0\).

0.720

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 \(x=0\).

1.733

4032

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

1.191

4036

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

0.530

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 \(x=0\).

0.574

4038

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

1.457

4039

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

1.562

4041

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

0.573

4043

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

1.090

4044

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

0.497

4045

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

0.527

4048

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

1.446

4050

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

0.534

4051

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

1.501

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 \(x=0\).

0.582

4054

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

1.538

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 \(x=0\).

0.587

4057

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

1.401

4058

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

1.237

4059

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

1.520

4060

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

0.471

4061

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

1.175

4066

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

0.451

4070

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

0.477

4073

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

1.536

4075

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

1.344

4179

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

0.579

4180

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

0.476

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 \(x=0\).

0.707

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 \(x=0\).

0.572

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 \(x=0\).

0.526

4599

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

1.510

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 \(x=0\).

0.934

4602

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

0.823

4603

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

1.306

4604

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

0.821

4605

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

1.477

7167

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

0.637

7170

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

0.639

7171

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

0.667

7173

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

0.589

7174

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

0.582

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 \(x=0\).

0.723

7181

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

1.510

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 \(x=0\).

2.050

7184

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

2.029

7187

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

2.011

7189

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

2.265

7192

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

0.756

7194

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

2.202

7372

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

0.493

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 \(x=0\).

0.684

7625

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

2.852

7628

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

3.308

8082

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

1.080

8083

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

0.619

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 \(x=0\).

0.704

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 \(x=0\).

0.835

8093

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

0.776

8094

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

1.439

8104

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

0.998

8106

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

1.367

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 \(x=0\).

0.819

8138

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

1.356

8140

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

1.155

8141

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

1.790

8145

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

1.112

8146

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

1.668

8149

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

1.296

8500

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

2.547

8502

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

2.839

8503

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

2.499

8506

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

2.438

8510

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

2.414

8523

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

0.612

8524

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

0.624

8525

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

1.994

8526

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

1.822

8529

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

1.017

8530

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

0.740

8535

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

2.142

8536

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

0.623

8539

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

2.148

8540

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

2.155

8541

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

0.630

8543

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

2.861

8544

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

1.873

8545

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

1.765

8546

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

1.801

8547

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

1.851

8548

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

0.570

8550

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

0.598

8551

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

0.554

8555

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

0.627

8556

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

0.628

8557

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

0.638

8562

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

0.752

8580

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

0.599

8581

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

1.700

8583

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

2.517

8587

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

0.612

8588

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

0.753

8589

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

0.613

8596

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

2.517

8601

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

0.648

8604

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

1.805

8611

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

1.842

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 \(x=0\).

0.681

8618

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

0.738

8619

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

0.599

8620

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

1.715

8983

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

0.760

8984

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

1.386

8986

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

1.232

8990

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

0.615

8997

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

2.934

9000

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

0.746

9001

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

0.581

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 \(x=0\).

0.724

9003

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

1.489

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 \(x=0\).

2.239

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 \(x=0\).

2.581

9390

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

1.991

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 \(x=0\).

0.647

9395

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

1.733

9406

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

0.694

9407

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

0.875

9408

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

0.635

9411

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

2.111

9412

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

0.724

9429

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

0.677

9528

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

2.483

9530

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

2.825

9531

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

2.534

9534

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

2.411

9538

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

2.345

9551

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

0.689

9552

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

0.707

9553

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

1.874

9554

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

1.701

9557

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

0.964

9558

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

0.836

9559

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

0.753

9590

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

0.860

9597

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

2.981

9860

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

0.810

9861

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

0.780

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 \(x=0\).

0.961

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 \(x=0\).

1.028

9909

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

0.945

9910

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

1.015

9911

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

1.095

9912

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

1.086

9913

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

0.956

9914

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

0.959

9915

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

1.099

9916

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

0.967

9917

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

1.051

9918

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

1.005

9919

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

1.005

9920

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

1.069

9921

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

0.809

9922

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

1.077

9923

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

1.894

9924

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

2.480

9925

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

2.113

9926

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

2.701

9927

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

2.519

9928

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

2.658

9929

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

2.680

9930

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

2.776

9932

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

2.457

9933

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

2.724

9934

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

2.750

9935

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

2.984

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 \(x=0\).

2.607

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 \(x=0\).

1.039

9941

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

2.712

9945

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

2.605

9946

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

2.714

9947

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

0.971

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 \(x=0\).

0.846

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 \(x=0\).

0.939

9955

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

0.994

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 \(x=0\).

0.974

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 \(x=0\).

0.842

9967

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

2.376

9968

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

1.056

9969

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

0.970

10180

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

0.523

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 \(x=0\).

0.590

10202

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

1.450

10211

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

0.505

10213

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

0.512

10214

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

1.469

10215

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

0.599

10216

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

1.360

10218

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

0.517

10219

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

0.515

10220

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

0.599

10223

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

0.463

10224

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

1.023

10454

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

1.653

14756

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

0.580

14757

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

0.595

14758

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

0.591

14759

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

0.627

14760

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

0.680

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 \(x=0\).

0.785

14762

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

0.522

14763

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

2.370

14764

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

2.366

14765

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

2.335

14766

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

1.994

14768

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

1.948

14770

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

2.300

14980

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

3.122

14982

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

2.658

15307

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

0.507

15312

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

1.507

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 \(x=0\).

0.607

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 \(x=1\).

2.256

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 \(x=0\).

2.336

16896

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

0.551

16898

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

1.648

16899

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

0.599

16902

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

1.580

16906

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

1.804

16910

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

1.470

16911

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

0.576

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 \(x=3\).

0.683

16914

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

0.553

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 \(x=0\).

0.674

16919

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

1.894

16921

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

1.673

16922

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

0.858

16923

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

0.726

16924

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

1.419

16928

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

1.770

16929

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

1.715

17713

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

2.687

17714

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

2.274

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 \(x=0\).

3.233

17719

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

0.744

17729

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

0.694

17730

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

2.871

17792

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

2.872

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 \(x=0\).

7.649

19597

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

6.543

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 \(x=0\).

1.070

19611

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

1.025

19612

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

1.147

19613

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

1.164

19614

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

6.592

19615

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

1.030

20145

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

0.621

20894

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

0.615

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 \(x=\infty \).

5.746

20905

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

0.666

20907

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

0.683

20910

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

0.883

21267

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

4.394

21268

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

0.669

21271

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

0.794

21272

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

0.668

21631

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

7.242

21633

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

7.770

21640

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

0.815

21668

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

8.074

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 \(x=0\).

8.515

21680

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

7.356

21681

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

0.901

21682

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

0.903

21683

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

7.213

21685

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

1.029

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 \(x=1\).

2.121

21688

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

0.929

21699

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

0.951

21905

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

1.082

21907

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

0.873

22171

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

1.525

22177

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

1.693

22207

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

1.435

22208

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

1.318

22209

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

0.607

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 \(x=0\).

1.847

22217

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

0.581

22218

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

1.534

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 \(x=0\).

1.522

22223

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

1.311

22224

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

0.485

22226

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

1.098

22844

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

0.450

22850

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

0.462

22852

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

0.595

22854

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

0.932

22855

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

0.488

22857

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

0.450

22858

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

0.484

22861

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

1.157

22862

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

0.498

22863

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

0.547

22864

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

0.551

22869

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

1.196

22871

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

1.147

22872

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

0.486

22873

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

1.232

22877

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

0.916

23667

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

1.848

23672

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

1.393

23687

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

0.801

23720

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

1.393

23724

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

1.508

23728

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

1.406

23729

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

0.601

23738

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

0.603

23739

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

1.449

23740

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

1.442

23745

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

0.675

24098

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

1.337

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 \(x=0\).

1.413

24103

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

1.479

24110

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

2.097

24111

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

2.046

24112

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

3.254

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 \(x=0\).

3.479

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 \(x=0\).

3.316

25340

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

0.556

25345

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

0.559

25349

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

0.663

25350

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

0.610

25351

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

1.974

25352

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

1.368

25354

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

0.640