2.8.5 Second order ode Frobenius with roots difference is integer

Table 2.1189: 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 \(x=0\).

1.541

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 \(x=0\).

0.481

463

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

0.485

483

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

0.452

484

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

0.447

485

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

0.457

486

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

0.426

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 \(x=0\).

0.476

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 \(x=0\).

0.467

494

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

1.300

496

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

1.892

498

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

0.549

499

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

0.555

500

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

0.558

501

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

0.589

502

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

0.595

503

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

1.558

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 \(x=0\).

0.573

505

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

0.543

509

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

0.541

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 \(x=0\).

1.400

511

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

0.564

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 \(x=0\).

0.469

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 \(x=0\).

3.092

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 \(x=0\).

2.972

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 \(x=0\).

0.887

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 \(x=0\).

0.729

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 \(x=0\).

2.983

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 \(x=0\).

0.872

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 \(x=0\).

0.687

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 \(x=0\).

0.737

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 \(x=0\).

0.732

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 \(x=0\).

0.723

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 \(x=0\).

0.737

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 \(x=0\).

0.762

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 \(x=0\).

3.283

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 \(x=0\).

0.863

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 \(x=0\).

3.116

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 \(x=0\).

0.787

2066

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

2.841

2067

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

2.097

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 \(x=0\).

3.107

2069

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

2.934

2070

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

3.146

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 \(x=0\).

2.862

2072

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

2.872

2073

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

2.812

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 \(x=0\).

3.160

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 \(x=0\).

3.116

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 \(x=0\).

2.925

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 \(x=0\).

2.906

2078

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

0.826

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 \(x=0\).

0.988

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 \(x=0\).

0.881

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 \(x=0\).

0.852

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 \(x=0\).

0.938

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 \(x=0\).

0.849

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 \(x=0\).

0.825

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 \(x=0\).

0.830

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 \(x=0\).

0.948

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 \(x=0\).

1.358

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 \(x=0\).

2.927

2089

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

2.823

2090

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

2.283

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 \(x=0\).

2.901

2092

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

2.747

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 \(x=0\).

3.017

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 \(x=0\).

2.872

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 \(x=0\).

2.886

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 \(x=0\).

2.872

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 \(x=0\).

4.507

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 \(x=0\).

2.928

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 \(x=0\).

2.937

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 \(x=0\).

0.736

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 \(x=0\).

0.810

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 \(x=0\).

0.866

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 \(x=0\).

1.054

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 \(x=0\).

3.187

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 \(x=0\).

0.746

2440

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

3.356

2453

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

0.747

2454

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

0.772

2455

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

0.844

2456

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

0.748

2457

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

0.900

2458

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

3.039

2459

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

2.980

2460

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

2.523

2469

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

2.918

2470

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

2.528

2637

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

3.793

2649

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

0.725

2650

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

0.780

2651

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

0.822

2652

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

0.886

2653

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

0.780

2654

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

0.959

2655

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

3.470

2656

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

3.421

2657

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

2.872

2667

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

3.372

2668

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

2.882

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 \(x=0\).

0.599

3379

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

0.687

3380

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

0.635

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 \(x=0\).

0.650

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 \(x=0\).

0.744

3383

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

0.651

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 \(x=0\).

1.911

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 \(x=0\).

1.901

3386

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

1.761

3387

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

1.609

3388

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

1.556

3390

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

1.559

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 \(x=0\).

0.942

3502

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

0.535

3505

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

0.561

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 \(x=0\).

3.337

4011

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

2.102

4027

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

2.535

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 \(x=0\).

0.968

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 \(x=0\).

2.763

4032

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

2.154

4036

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

0.708

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 \(x=0\).

0.764

4038

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

2.430

4039

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

2.601

4041

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

0.766

4043

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

1.880

4044

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

0.688

4045

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

0.704

4048

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

2.446

4050

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

0.705

4051

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

2.589

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 \(x=0\).

0.767

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 \(x=0\).

2.560

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 \(x=0\).

0.776

4057

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

2.364

4058

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

2.060

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 \(x=0\).

2.504

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 \(x=0\).

0.631

4061

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

2.112

4066

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

0.576

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 \(x=0\).

0.589

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 \(x=0\).

2.392

4075

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

2.168

4179

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

0.757

4180

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

0.623

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 \(x=0\).

0.954

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 \(x=0\).

0.760

4188

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

0.713

4599

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

3.405

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 \(x=0\).

0.833

4602

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

0.734

4603

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

2.786

4604

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

0.730

4605

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

3.488

7167

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

1.280

7170

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

1.145

7171

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

1.269

7173

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

1.063

7174

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

1.081

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 \(x=0\).

1.256

7181

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

3.776

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 \(x=0\).

5.069

7184

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

4.956

7187

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

5.018

7189

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

5.583

7192

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

1.487

7194

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

5.356

7372

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

0.980

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 \(x=0\).

1.421

7625

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

6.769

7628

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

7.347

8082

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

1.109

8083

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

0.605

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 \(x=0\).

0.727

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 \(x=0\).

0.845

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 \(x=0\).

0.806

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 \(x=0\).

1.509

8104

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

1.000

8106

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

1.397

8108

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

0.740

8138

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

1.336

8140

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

1.153

8141

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

1.751

8145

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

1.099

8146

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

1.640

8149

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

1.278

8500

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

2.214

8502

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

2.560

8503

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

2.294

8506

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

2.165

8510

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

2.141

8523

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

0.561

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 \(x=0\).

0.578

8525

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

1.727

8526

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

1.609

8529

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

0.944

8530

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

0.684

8535

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

1.962

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 \(x=0\).

0.576

8539

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

1.935

8540

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

1.957

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 \(x=0\).

0.581

8543

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

2.571

8544

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

1.704

8545

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

1.609

8546

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

1.599

8547

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

1.635

8548

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

0.525

8550

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

0.540

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 \(x=0\).

0.501

8555

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

0.565

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 \(x=0\).

0.568

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 \(x=0\).

0.559

8562

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

0.691

8580

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

0.563

8581

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

1.513

8583

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

2.227

8587

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

0.560

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 \(x=0\).

0.702

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 \(x=0\).

0.569

8596

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

2.237

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 \(x=0\).

0.582

8604

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

1.619

8611

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

1.661

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 \(x=0\).

0.623

8618

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

0.674

8619

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

0.549

8620

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

1.542

8983

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

0.886

8984

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

2.378

8986

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

2.089

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 \(x=0\).

0.769

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 \(x=0\).

3.543

9000

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

0.926

9001

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

0.769

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 \(x=0\).

0.909

9003

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

2.616

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 \(x=0\).

2.837

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 \(x=0\).

3.684

9390

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

3.077

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 \(x=0\).

0.857

9395

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

2.731

9406

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

0.832

9407

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

0.993

9408

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

0.813

9411

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

3.104

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 \(x=0\).

0.849

9429

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

0.845

9528

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

3.513

9530

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

3.938

9531

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

3.603

9534

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

3.441

9538

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

3.464

9551

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

0.839

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 \(x=0\).

0.848

9553

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

2.708

9554

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

2.599

9557

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

1.145

9558

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

1.025

9559

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

0.896

9590

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

1.042

9597

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

4.225

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 \(x=0\).

0.973

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 \(x=0\).

0.977

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 \(x=0\).

1.104

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 \(x=0\).

1.167

9909

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

1.082

9910

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

1.207

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 \(x=0\).

1.309

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 \(x=-1\).

1.313

9913

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

1.093

9914

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

1.136

9915

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

1.306

9916

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

1.178

9917

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

1.273

9918

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

1.212

9919

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

1.198

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 \(x=0\).

1.283

9921

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

1.055

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 \(x=0\).

1.263

9923

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

2.862

9924

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

3.675

9925

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

3.127

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 \(x=0\).

3.912

9927

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

3.764

9928

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

3.885

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 \(x=0\).

3.900

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 \(x=1\).

3.928

9932

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

3.497

9933

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

3.665

9934

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

3.874

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 \(x=0\).

4.536

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 \(x=0\).

3.781

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 \(x=0\).

1.155

9941

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

3.931

9945

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

3.927

9946

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

3.898

9947

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

1.095

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 \(x=0\).

1.020

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 \(x=0\).

1.106

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 \(x=0\).

1.110

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 \(x=0\).

1.084

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 \(x=0\).

1.005

9967

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

3.539

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 \(x=0\).

1.255

9969

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

1.149

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 \(x=0\).

0.885

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 \(x=0\).

0.955

10202

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

4.248

10211

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

0.856

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 \(x=0\).

0.855

10214

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

4.410

10215

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

1.067

10216

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

4.097

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 \(x=0\).

0.879

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 \(x=0\).

0.865

10220

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

1.066

10223

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

0.906

10224

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

3.045

10454

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

4.829

14756

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

0.813

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 \(x=0\).

0.789

14758

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

0.859

14759

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

0.923

14760

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

0.885

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 \(x=0\).

1.085

14762

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

0.704

14763

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

4.357

14764

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

4.403

14765

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

4.338

14766

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

3.562

14768

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

3.592

14770

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

4.282

14980

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

4.775

14982

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

4.361

15307

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

0.851

15312

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

4.939

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 \(x=0\).

0.547

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 \(x=1\).

2.212

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 \(x=0\).

2.071

16896

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

0.698

16898

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

1.495

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 \(x=0\).

0.740

16902

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

1.400

16906

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

1.425

16910

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

1.403

16911

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

0.782

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 \(x=3\).

0.806

16914

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

0.670

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 \(x=0\).

0.756

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 \(x=0\).

1.430

16921

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

1.272

16922

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

0.843

16923

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

0.788

16924

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

1.096

16928

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

1.323

16929

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

1.225

17713

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

2.633

17714

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

2.155

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 \(x=0\).

3.086

17719

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

0.671

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 \(x=0\).

0.637

17730

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

2.759

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 \(x=0\).

2.530

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 \(x=0\).

5.834

19597

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

5.225

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 \(x=0\).

0.962

19611

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

0.924

19612

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

1.016

19613

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

1.026

19614

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

5.144

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 \(x=0\).

0.918

20145

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

2.017

20894

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

0.574

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 \(x=\infty \).

4.241

20905

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

0.634

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 \(x=0\).

0.660

20910

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

0.832

21267

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

3.239

21268

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

0.616

21271

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

0.716

21272

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

0.619

21631

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

4.985

21633

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

5.342

21640

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

0.708

21668

\begin{align*} x \left (-1+x \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 \(x=0\).

5.640

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 \(x=0\).

6.243

21680

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

5.537

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 \(x=0\).

0.862

21682

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

0.763

21683

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

4.979

21685

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

0.886

21687

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

1.906

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 \(x=0\).

0.825

21699

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

0.877

21905

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

0.980

21907

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

0.768

22171

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

6.300

22177

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

6.823

22207

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

6.418

22208

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

6.270

22209

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

0.976

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 \(x=0\).

7.146

22217

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

0.961

22218

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

6.571

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 \(x=0\).

6.620

22223

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

6.233

22224

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

0.822

22226

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

4.961

22844

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

1.454

22850

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

1.410

22852

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

1.839

22854

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

8.426

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 \(x=0\).

1.373

22857

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

1.744

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 \(x=0\).

1.405

22861

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

10.772

22862

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

1.590

22863

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

1.981

22864

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

1.679

22869

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

10.739

22871

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

10.563

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 \(x=0\).

1.360

22873

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

10.725

22877

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

8.990

23667

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

2.045

23672

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

1.694

23687

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

0.778

23720

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

1.737

23724

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

1.883

23728

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

1.724

23729

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

0.543

23738

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

0.535

23739

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

1.764

23740

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

1.717

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 \(x=0\).

0.573

24098

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

0.509

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 \(x=0\).

0.598

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 \(x=0\).

0.631

24110

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

1.694

24111

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

1.609

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 \(x=0\).

2.075

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 \(x=0\).

2.531

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 \(x=0\).

2.084

25340

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

0.810

25345

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

0.840

25349

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

0.899

25350

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

0.875

25351

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

4.581

25352

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

3.253

25354

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

0.882