2.8.7 Second order ode Frobenius with repeated roots

Table 2.1193: Second order ode Frobenius with repeated roots [285]

#

ODE

solved

Maple

Mma

Sympy

time(sec)

506

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

0.352

507

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

0.370

508

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

0.450

513

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

0.421

1850

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

0.744

1998

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

0.717

1999

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

0.697

2000

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

0.601

2001

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

0.661

2002

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

0.813

2003

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

0.901

2004

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

0.931

2005

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

0.911

2006

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

0.835

2007

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

0.914

2008

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

0.994

2009

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

0.820

2010

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

0.973

2011

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

0.898

2012

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

0.847

2013

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

0.609

2014

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

0.726

2015

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

0.648

2016

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

0.656

2017

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

0.700

2018

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

0.681

2019

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

0.729

2020

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

0.702

2021

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

0.840

2022

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

0.693

2023

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

0.699

2024

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

0.834

2025

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

0.820

2026

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

0.894

2027

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

0.931

2028

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

0.842

2029

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

0.604

2030

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

0.571

2031

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

0.612

2032

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

0.562

2033

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

0.603

2034

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

0.593

2035

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

0.618

2036

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

0.619

2037

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

0.594

2038

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

0.636

2039

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

0.616

2040

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

0.591

2041

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

0.593

2042

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

0.625

2043

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

0.619

2044

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

0.608

2045

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

0.684

2046

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

0.712

2047

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

0.663

2048

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

0.737

2049

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

0.675

2050

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

0.611

2051

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

0.681

2052

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

0.586

2053

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

0.668

2054

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

0.551

2055

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

0.594

2056

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

0.548

2057

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

0.583

2058

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

0.560

2059

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

0.621

2060

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

0.589

2061

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

0.629

2443

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

1.346

2461

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

0.664

2462

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

0.552

2464

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

0.954

2467

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

0.694

2468

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

0.621

2640

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

1.014

2659

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

0.599

2661

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

1.018

2665

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

0.749

2666

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

0.650

3372

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

0.514

3373

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

0.405

3374

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

0.524

3375

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

0.491

3376

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

0.533

3377

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

0.461

3378

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

0.477

3389

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

0.512

3393

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

0.769

3507

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

0.800

3508

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

0.543

3512

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

0.740

4000

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

0.632

4023

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

0.678

4024

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

0.635

4025

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

0.628

4026

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

0.610

4028

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

0.671

4033

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

0.612

4034

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

0.622

4040

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

1.226

4042

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

0.608

4046

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

0.604

4047

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

0.621

4049

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

0.603

4052

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

0.623

4055

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

0.622

4065

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

0.576

4068

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

0.597

4074

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

0.548

4181

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

0.681

4186

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

0.514

4187

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

0.687

4596

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

0.608

4597

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

1.025

4598

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

0.849

4606

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

0.585

7179

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

1.001

7180

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

0.856

7185

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

0.895

7188

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

0.892

7835

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

1.182

8080

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

0.336

8081

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

0.359

8087

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

0.640

8090

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

0.661

8095

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

0.397

8097

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

0.435

8103

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

0.653

8135

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

0.320

8150

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

0.309

8512

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

0.550

8527

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

0.560

8528

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

0.543

8538

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

0.429

8549

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

0.447

8553

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

0.447

8582

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

0.625

8585

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

0.431

8590

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

0.618

8598

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

0.551

8607

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

0.561

8608

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

0.558

8613

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

0.622

8621

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

0.431

8987

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

0.875

8994

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

0.609

8998

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

0.888

8999

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

0.732

9401

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

0.661

9404

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

0.807

9405

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

0.922

9432

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

0.911

9434

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

0.829

9439

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

0.879

9540

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

0.856

9555

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

0.864

9556

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

0.835

9866

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

1.066

9890

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

0.911

9891

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

0.915

9892

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

0.946

9893

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

0.793

9894

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

1.148

9895

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

1.038

9896

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

0.958

9897

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

1.053

9898

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

1.131

9899

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

1.041

9901

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

0.764

9902

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

0.921

9903

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

1.099

9904

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

1.019

9905

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

1.013

9906

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

0.950

9937

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

1.058

9939

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

0.915

9942

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

1.151

9943

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

0.918

9956

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

0.860

9958

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

0.799

9959

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

0.954

9962

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

0.990

9963

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

0.858

9966

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

0.878

9970

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

0.887

10198

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

0.900

10200

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

0.864

10201

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

0.932

10203

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

0.928

10204

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

0.899

10206

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

1.154

10207

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

1.119

10208

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

1.164

10209

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

1.191

10212

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

0.904

10217

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

0.633

14767

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

0.810

14769

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

0.653

14981

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

0.644

15305

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

0.933

16891

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

0.539

16893

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

0.613

16897

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

0.499

16900

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

0.721

16901

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

0.374

16904

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

0.735

16907

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

0.540

16908

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

0.449

16912

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

0.772

16916

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

0.355

16918

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

0.646

16920

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

0.642

16926

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

0.454

16927

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

0.333

17718

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

0.687

17720

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

0.443

17721

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

0.451

17726

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

0.639

17727

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

0.670

17728

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

0.852

17793

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

0.663

17794

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

0.653

19606

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

0.787

19609

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

0.875

19610

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

0.956

19620

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

0.911

20895

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

0.641

20896

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

0.570

20904

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

0.420

20909

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

0.603

21273

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

0.703

21274

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

0.566

21634

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

1.015

21689

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

0.659

21690

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

0.606

21691

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

0.746

21692

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

0.841

21693

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

0.749

21698

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

0.579

21702

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

1.171

21904

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

0.868

22176

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

0.899

22205

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

0.756

22206

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

0.643

22215

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

0.945

22216

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

0.954

22221

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

0.663

22222

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

0.760

22846

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

1.795

22856

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

1.610

22859

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

1.611

22867

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

1.547

22875

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

1.509

22878

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

1.343

22881

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

1.439

23668

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

0.598

23680

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

0.782

23682

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

0.704

23721

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

0.443

23723

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

0.577

23726

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

0.568

23727

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

0.587

23731

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

0.608

23733

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

0.518

23734

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

0.660

23737

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

0.612

23741

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

0.511

23744

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

0.440

23746

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

0.570

23747

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

0.591

23748

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

0.595

24090

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

0.474

24091

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

0.436

24105

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

0.508

24106

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

0.455

24107

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

0.486

24108

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

0.529

24109

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

0.575

25335

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

0.969

25338

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

0.819

25342

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

1.164

25343

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

0.875

25347

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

0.827

25356

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

0.923