2.8.5 Second order ode Frobenius with roots difference is integer

Table 2.1217: Second order ode Frobenius with roots difference is integer [462]

#

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 \(x=0\).

1.589

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 \(x=0\).

0.508

463

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

0.471

483

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

0.469

484

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

0.459

485

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

0.482

486

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

0.446

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 \(x=0\).

0.498

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 \(x=0\).

0.481

494

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

1.349

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 \(x=0\).

2.111

498

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

0.582

499

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

0.577

500

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

0.588

501

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

0.619

502

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

0.621

503

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

1.606

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 \(x=0\).

0.551

505

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

0.568

509

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

0.553

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 \(x=0\).

1.452

511

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

0.582

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 \(x=0\).

0.484

1848

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

3.314

1849

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

3.188

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 \(x=0\).

0.911

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 \(x=0\).

0.756

1853

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

3.351

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 \(x=0\).

0.902

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 \(x=0\).

0.709

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 \(x=0\).

0.759

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 \(x=0\).

0.745

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 \(x=0\).

0.743

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 \(x=0\).

0.763

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 \(x=0\).

0.793

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 \(x=0\).

1.626

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 \(x=0\).

0.878

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 \(x=0\).

1.712

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 \(x=0\).

0.788

2066

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

1.233

2067

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

0.959

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 \(x=0\).

1.460

2069

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

1.326

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 \(x=0\).

1.482

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 \(x=0\).

1.297

2072

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

1.269

2073

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

1.306

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 \(x=0\).

1.534

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 \(x=0\).

1.458

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 \(x=0\).

1.346

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 \(x=0\).

1.337

2078

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

0.746

2079

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

1.005

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 \(x=0\).

0.869

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 \(x=0\).

0.976

2082

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

1.138

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 \(x=0\).

0.961

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 \(x=0\).

0.957

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 \(x=0\).

0.968

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 \(x=0\).

1.111

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 \(x=0\).

1.648

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 \(x=0\).

1.508

2089

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

1.402

2090

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

1.238

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 \(x=0\).

1.487

2092

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

1.391

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 \(x=0\).

1.557

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 \(x=0\).

1.465

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 \(x=0\).

1.482

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 \(x=0\).

1.510

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 \(x=0\).

1.794

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 \(x=0\).

1.478

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 \(x=0\).

1.456

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 \(x=0\).

0.787

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 \(x=0\).

0.909

2102

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

1.060

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 \(x=0\).

1.455

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 \(x=0\).

1.811

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 \(x=0\).

0.888

2440

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

3.014

2453

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

0.824

2454

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

0.756

2455

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

0.846

2456

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

0.819

2457

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

0.959

2458

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

1.834

2459

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

2.589

2460

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

1.464

2469

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

1.676

2470

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

2.345

2637

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

2.679

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 \(t=0\).

1.006

2650

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

0.868

2651

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

0.815

2652

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

0.926

2653

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

0.865

2654

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

0.975

2655

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

2.295

2656

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

2.264

2657

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

1.883

2667

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

2.187

2668

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

1.854

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 \(x=0\).

1.089

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 \(x=0\).

1.240

3380

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

1.056

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 \(x=0\).

1.098

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 \(x=0\).

1.220

3383

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

1.156

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 \(x=0\).

4.566

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 \(x=0\).

4.526

3386

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

4.482

3387

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

3.653

3388

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

3.622

3390

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

3.666

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 \(x=0\).

1.545

3502

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

0.954

3505

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

0.918

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 \(x=0\).

7.136

4011

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

4.218

4027

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

4.959

4029

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

1.403

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 \(x=0\).

5.603

4032

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

4.003

4036

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

1.058

4037

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

1.119

4038

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

4.981

4039

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

5.266

4041

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

1.135

4043

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

3.660

4044

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

1.101

4045

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

1.047

4048

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

4.869

4050

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

1.059

4051

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

5.205

4053

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

1.153

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 \(x=0\).

5.202

4056

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

1.157

4057

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

4.651

4058

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

4.020

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 \(x=0\).

5.214

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 \(x=0\).

0.990

4061

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

4.048

4066

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

0.975

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 \(x=0\).

0.983

4073

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

5.321

4075

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

4.649

4179

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

1.240

4180

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

1.020

4182

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

1.465

4183

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

1.238

4188

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

1.177

4599

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

6.591

4601

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

1.316

4602

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

1.180

4603

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

5.400

4604

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

1.201

4605

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

6.554

7167

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

1.483

7170

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

1.381

7171

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

1.483

7173

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

1.300

7174

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

1.275

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 \(x=0\).

1.566

7181

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

4.133

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 \(x=0\).

5.868

7184

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

5.600

7187

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

5.742

7189

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

6.689

7192

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

1.658

7194

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

6.064

7372

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

1.112

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 \(x=0\).

1.468

7625

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

7.538

7628

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

8.275

8082

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

3.303

8083

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

1.611

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 \(x=0\).

1.746

8089

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

1.900

8093

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

1.838

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 \(x=0\).

3.973

8104

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

3.200

8106

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

3.821

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 \(x=0\).

1.927

8138

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

3.699

8140

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

3.393

8141

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

4.279

8145

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

3.412

8146

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

4.151

8149

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

3.623

8500

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

3.781

8502

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

4.336

8503

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

3.673

8506

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

3.517

8510

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

3.451

8523

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

0.777

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 \(x=0\).

0.808

8525

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

2.632

8526

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

2.526

8529

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

1.272

8530

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

1.002

8535

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

3.217

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 \(x=0\).

0.806

8539

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

3.195

8540

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

3.228

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 \(x=0\).

0.824

8543

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

4.102

8544

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

2.634

8545

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

2.493

8546

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

2.580

8547

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

2.561

8548

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

0.753

8550

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

0.797

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 \(x=0\).

0.720

8555

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

0.784

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 \(x=0\).

0.803

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 \(x=0\).

0.805

8562

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

0.957

8580

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

0.777

8581

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

2.431

8583

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

3.574

8587

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

0.786

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 \(x=0\).

0.973

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 \(x=0\).

0.811

8596

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

3.580

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 \(x=0\).

0.813

8604

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

2.516

8611

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

2.682

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 \(x=0\).

0.887

8618

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

0.927

8619

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

0.783

8620

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

2.472

8983

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

1.212

8984

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

3.563

8986

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

3.206

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 \(x=0\).

1.063

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 \(x=0\).

6.200

9000

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

1.231

9001

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

1.105

9002

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

1.227

9003

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

4.128

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 \(x=0\).

4.376

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 \(x=0\).

5.832

9390

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

4.607

9393

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

1.154

9395

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

3.866

9406

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

1.132

9407

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

1.317

9408

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

1.140

9411

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

4.680

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 \(x=0\).

1.128

9429

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

1.151

9528

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

5.204

9530

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

6.898

9531

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

5.240

9534

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

4.996

9538

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

5.140

9551

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

1.160

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 \(x=0\).

1.162

9553

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

3.914

9554

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

3.731

9557

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

1.529

9558

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

1.360

9559

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

1.216

9590

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

1.391

9597

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

6.220

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 \(x=0\).

1.207

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 \(x=0\).

1.175

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 \(x=0\).

1.381

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 \(x=0\).

1.480

9909

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

1.348

9910

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

1.500

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 \(x=0\).

1.615

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 \(x=-1\).

1.636

9913

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

1.360

9914

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

1.499

9915

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

1.598

9916

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

1.468

9917

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

1.570

9918

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

1.490

9919

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

1.481

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 \(x=0\).

1.583

9921

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

1.355

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 \(x=0\).

1.534

9923

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

3.813

9924

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

5.138

9925

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

4.171

9926

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

5.555

9927

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

5.144

9928

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

5.286

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 \(x=0\).

5.500

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 \(x=1\).

5.468

9932

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

4.955

9933

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

5.065

9934

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

5.343

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 \(x=0\).

6.185

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 \(x=0\).

5.338

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 \(x=0\).

1.437

9941

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

5.635

9945

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

5.261

9946

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

5.321

9947

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

1.368

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 \(x=0\).

1.260

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 \(x=0\).

1.390

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 \(x=0\).

1.375

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 \(x=0\).

1.358

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 \(x=0\).

1.257

9967

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

4.972

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 \(x=0\).

1.575

9969

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

1.436

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 \(x=0\).

0.782

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 \(x=0\).

0.885

10202

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

2.836

10211

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

0.799

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 \(x=0\).

0.790

10214

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

2.869

10215

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

0.905

10216

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

2.764

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 \(x=0\).

0.801

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 \(x=0\).

0.791

10220

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

0.890

10223

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

0.737

10224

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

1.936

10454

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

4.343

14756

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

0.849

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 \(x=0\).

0.855

14758

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

0.887

14759

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

0.916

14760

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

0.944

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 \(x=0\).

1.125

14762

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

0.751

14763

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

2.510

14764

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

2.543

14765

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

2.531

14766

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

2.256

14768

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

2.127

14770

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

2.489

14980

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

2.961

14982

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

2.665

15307

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

0.915

15312

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

3.154

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 \(x=0\).

0.776

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 \(x=1\).

2.855

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 \(x=0\).

2.685

16896

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

0.694

16898

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

1.951

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 \(x=0\).

0.718

16902

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

1.813

16906

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

2.023

16910

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

1.586

16911

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

0.675

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 \(x=3\).

0.812

16914

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

0.677

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 \(x=0\).

0.799

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 \(x=0\).

2.113

16921

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

1.913

16922

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

1.004

16923

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

0.844

16924

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

1.628

16928

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

2.052

16929

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

1.902

17713

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

3.621

17714

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

3.012

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 \(x=0\).

4.361

17719

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

0.959

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 \(x=0\).

0.868

17730

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

3.773

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 \(x=0\).

3.625

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 \(x=0\).

3.038

19597

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

2.678

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 \(x=0\).

0.889

19611

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

0.839

19612

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

0.976

19613

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

0.800

19614

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

2.556

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 \(x=0\).

0.842

20145

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

1.072

20894

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

0.963

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 \(x=\infty \).

5.806

20905

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

0.996

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 \(x=0\).

0.983

20910

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

1.277

21267

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

4.543

21268

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

1.148

21271

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

1.457

21272

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

1.190

21631

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

6.177

21633

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

6.893

21640

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

1.127

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 \(x=0\).

7.695

21671

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

7.970

21680

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

6.280

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 \(x=0\).

1.234

21682

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

1.221

21683

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

6.092

21685

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

1.328

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 \(x=1\).

2.819

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 \(x=0\).

1.241

21699

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

1.266

21905

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

1.690

21907

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

1.388

22171

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

2.560

22177

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

2.836

22207

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

2.533

22208

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

2.397

22209

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

0.824

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 \(x=0\).

2.994

22217

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

0.814

22218

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

2.624

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 \(x=0\).

2.667

22223

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

2.405

22224

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

0.681

22226

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

1.730

22844

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

0.658

22850

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

0.704

22852

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

0.882

22854

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

1.986

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 \(x=0\).

0.725

22857

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

0.728

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 \(x=0\).

0.729

22861

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

2.665

22862

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

0.765

22863

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

0.836

22864

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

0.819

22869

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

2.712

22871

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

2.681

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 \(x=0\).

0.736

22873

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

2.645

22877

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

1.964

23667

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

3.892

23672

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

3.326

23687

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

1.098

23720

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

3.593

23724

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

3.684

23728

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

3.502

23729

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

0.827

23738

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

0.829

23739

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

3.388

23740

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

3.381

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 \(x=0\).

0.821

24098

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

0.841

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 \(x=0\).

1.024

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 \(x=0\).

1.018

24110

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

3.353

24111

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

3.224

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 \(x=0\).

4.222

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 \(x=0\).

5.220

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 \(x=0\).

4.264

25340

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

0.644

25345

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

0.641

25349

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

0.737

25350

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

0.672

25351

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

2.827

25352

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

1.470

25354

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

0.726

26024

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

0.996

26026

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

1.003

26030

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

1.191

26031

\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 \(x=0\).

1.194

26032

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

0.903

26033

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

0.891

26034

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

1.080

26035

\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 \(x=0\).

4.045