2.8.7 Second order ode Frobenius with repeated roots

Table 2.1221: Second order ode Frobenius with repeated roots [287]

#

ODE

solved

Maple

Mma

Sympy

time(sec)

506

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

0.359

507

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

0.381

508

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

0.460

513

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

0.432

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 \(x=0\).

0.765

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 \(x=0\).

0.736

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 \(x=0\).

0.720

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 \(x=0\).

0.620

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 \(x=0\).

0.802

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 \(x=0\).

0.728

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 \(x=0\).

0.926

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 \(x=0\).

0.794

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 \(x=0\).

0.841

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 \(x=0\).

0.772

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 \(x=0\).

0.848

2008

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

0.788

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 \(x=0\).

0.752

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 \(x=0\).

0.864

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 \(x=0\).

0.834

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 \(x=0\).

0.809

2013

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

0.488

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 \(x=0\).

0.585

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 \(x=0\).

0.504

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 \(x=0\).

0.526

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 \(x=0\).

0.573

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 \(x=0\).

0.572

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 \(x=0\).

0.609

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 \(x=0\).

0.573

2021

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

0.579

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 \(x=0\).

0.591

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 \(x=0\).

0.600

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 \(x=0\).

0.815

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 \(x=0\).

0.814

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 \(x=0\).

0.888

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 \(x=0\).

0.869

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 \(x=0\).

0.823

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 \(x=0\).

0.467

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 \(x=0\).

0.470

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 \(x=0\).

0.461

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 \(x=0\).

0.480

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 \(x=0\).

0.508

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 \(x=0\).

0.513

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 \(x=0\).

0.531

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 \(x=0\).

0.586

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 \(x=0\).

0.529

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 \(x=0\).

0.498

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 \(x=0\).

0.541

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 \(x=0\).

0.506

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 \(x=0\).

0.460

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 \(x=0\).

0.520

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 \(x=0\).

0.531

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 \(x=0\).

0.500

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 \(x=0\).

0.568

2046

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

0.539

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 \(x=0\).

0.552

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 \(x=0\).

0.646

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 \(x=0\).

0.582

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 \(x=0\).

0.504

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 \(x=0\).

0.542

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 \(x=0\).

0.483

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 \(x=0\).

0.516

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 \(x=0\).

0.483

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 \(x=0\).

0.508

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 \(x=0\).

0.517

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 \(x=0\).

0.566

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 \(x=0\).

0.502

2059

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

1.584

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 \(x=0\).

0.516

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 \(x=0\).

0.565

2443

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

1.022

2461

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

0.607

2462

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

0.545

2464

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

0.895

2467

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

0.652

2468

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

0.643

2640

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

0.958

2659

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

0.583

2661

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

0.962

2665

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

0.709

2666

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

0.691

3372

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

0.950

3373

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

0.771

3374

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

0.890

3375

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

0.833

3376

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

0.890

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 \(x=0\).

0.804

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 \(x=0\).

0.926

3389

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

0.908

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 \(x=0\).

1.175

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 \(z=0\).

1.232

3508

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

0.857

3512

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

1.148

4000

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

0.976

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 \(x=0\).

0.995

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 \(x=0\).

0.955

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 \(x=0\).

0.957

4026

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

0.920

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 \(x=0\).

1.049

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 \(x=0\).

0.894

4034

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

0.923

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 \(x=0\).

2.114

4042

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

0.911

4046

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

0.870

4047

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

0.995

4049

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

0.919

4052

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

0.946

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 \(x=0\).

0.917

4065

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

0.993

4068

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

0.795

4074

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

0.914

4181

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

1.037

4186

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

0.833

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 \(x=0\).

1.122

4596

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

0.978

4597

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

1.574

4598

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

1.367

4606

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

0.977

7179

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

1.149

7180

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

0.981

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 \(x=0\).

1.048

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 \(x=0\).

1.052

7835

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

0.766

8080

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

1.446

8081

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

1.502

8087

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

1.689

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 \(x=0\).

1.645

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 \(x=0\).

1.530

8097

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

1.582

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 \(x=0\).

1.618

8135

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

0.484

8150

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

0.495

8512

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

0.763

8527

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

0.765

8528

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

0.754

8538

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

0.625

8549

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

0.619

8553

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

0.651

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 \(x=0\).

0.863

8585

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

0.613

8590

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

0.844

8598

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

0.773

8607

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

0.755

8608

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

0.767

8613

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

0.857

8621

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

0.614

8987

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

1.168

8994

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

0.810

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 \(x=0\).

1.160

8999

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

0.984

9401

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

0.882

9404

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

1.058

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 \(x=0\).

1.177

9432

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

1.204

9434

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

1.107

9439

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

1.179

9540

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

1.127

9555

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

1.132

9556

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

1.110

9866

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

1.243

9890

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

1.062

9891

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

1.072

9892

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

1.125

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 \(x=0\).

0.946

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 \(x=0\).

1.242

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 \(x=0\).

1.195

9896

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

1.121

9897

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

1.262

9898

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

1.294

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 \(x=4\).

1.211

9901

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

0.909

9902

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

1.105

9903

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

1.277

9904

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

1.197

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 \(x=0\).

1.183

9906

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

1.166

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 \(x=0\).

1.284

9939

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

1.169

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 \(x=0\).

1.377

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 \(x=2\).

1.122

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 \(x=0\).

1.058

9958

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

1.024

9959

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

1.143

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 \(x=0\).

1.190

9963

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

1.096

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 \(x=0\).

1.110

9970

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

1.110

10198

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

0.699

10200

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

0.692

10201

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

0.752

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 \(x=0\).

0.857

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 \(x=0\).

1.026

10206

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

0.994

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 \(x=0\).

0.915

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 \(x=0\).

0.997

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 \(x=0\).

0.990

10212

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

0.717

10217

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

0.564

14767

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

0.805

14769

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

0.690

14981

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

0.701

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 \(x=0\).

0.959

16891

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

0.813

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 \(x=0\).

0.695

16897

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

0.638

16900

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

0.655

16901

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

0.523

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 \(x=0\).

0.635

16907

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

0.647

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 \(x=0\).

0.560

16912

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

0.648

16916

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

0.522

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 \(x=0\).

0.661

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 \(x=0\).

0.677

16926

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

0.637

16927

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

0.532

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 \(x=0\).

0.960

17720

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

0.627

17721

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

0.622

17726

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

0.892

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 \(x=0\).

0.945

17728

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

1.099

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 \(x=0\).

0.971

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 \(x=0\).

0.974

19606

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

0.654

19609

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

0.792

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 \(x=0\).

0.856

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 \(x=0\).

0.734

20895

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

1.019

20896

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

0.894

20904

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

0.679

20909

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

0.863

21273

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

1.243

21274

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

1.052

21634

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

1.559

21689

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

1.019

21690

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

0.877

21691

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

1.142

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 \(x=0\).

1.247

21693

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

1.178

21698

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

0.888

21702

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

1.563

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 \(x=0\).

1.673

22176

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

0.665

22205

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

0.549

22206

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

0.519

22215

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

0.615

22216

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

0.519

22221

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

0.523

22222

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

0.526

22846

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

0.846

22856

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

0.721

22859

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

0.673

22867

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

0.690

22875

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

0.591

22878

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

0.550

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 \(x=0\).

0.638

23668

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

0.862

23680

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

1.043

23682

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

0.988

23721

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

0.661

23723

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

0.829

23726

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

0.777

23727

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

0.860

23731

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

0.867

23733

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

0.746

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 \(x=0\).

0.925

23737

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

0.892

23741

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

0.720

23744

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

0.660

23746

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

0.836

23747

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

0.858

23748

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

0.854

24090

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

0.735

24091

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

0.752

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 \(x=0\).

0.867

24106

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

0.718

24107

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

0.754

24108

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

0.813

24109

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

0.922

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 \(t=0\).

0.727

25338

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

0.636

25342

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

0.829

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 \(t=0\).

0.684

25347

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

0.562

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 \(t=0\).

0.655

26036

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

0.757

26037

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

0.922