2.8.6 Second order ode Frobenius with roots difference not integer

Table 2.1219: Second order ode Frobenius with roots difference not integer [359]

#

ODE

solved

Maple

Mma

Sympy

time(sec)

464

\begin{align*} \left (2 x^{3}+6 x^{2}\right ) y^{\prime \prime }+21 y^{\prime } x +9 \left (x^{2}-1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.665

473

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

0.569

474

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

0.557

475

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

0.564

476

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

0.582

477

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

0.449

478

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

0.447

479

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

0.448

480

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

0.439

481

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

0.557

482

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

0.479

488

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

0.568

489

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

0.653

490

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

0.472

497

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

0.897

1941

\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.868

1942

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

0.804

1943

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

0.850

1945

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

0.950

1946

\begin{align*} x^{2} \left (x^{2}+3 x +3\right ) y^{\prime \prime }+x \left (7 x^{2}+8 x +5\right ) y^{\prime }-\left (-9 x^{2}-2 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.892

1947

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

0.894

1948

\begin{align*} 12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.813

1949

\begin{align*} x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.956

1950

\begin{align*} 8 x^{2} y^{\prime \prime }-2 x \left (-x^{2}-4 x +3\right ) y^{\prime }+\left (x^{2}+6 x +3\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.889

1951

\begin{align*} 18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.839

1952

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

0.904

1953

\begin{align*} 10 x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (66 x^{2}+13 x +13\right ) y^{\prime }-\left (10 x^{2}+4 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.936

1954

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

0.738

1955

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

0.799

1956

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

0.751

1957

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

0.729

1958

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

0.736

1959

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

0.748

1960

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

0.787

1961

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

0.790

1962

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

0.782

1963

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

0.739

1964

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

0.830

1965

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

0.768

1966

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

0.859

1967

\begin{align*} x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (4 x +3\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.837

1969

\begin{align*} x^{2} \left (2+x \right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.879

1970

\begin{align*} x^{2} \left (6+x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.858

1971

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

0.701

1972

\begin{align*} 8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.700

1974

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

0.705

1975

\begin{align*} 4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.692

1976

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

0.704

1979

\begin{align*} 2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.725

1980

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

0.713

1982

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

0.696

1983

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

0.704

1984

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

0.707

1985

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

0.737

1986

\begin{align*} x^{2} \left (x^{2}+8\right ) y^{\prime \prime }+7 x \left (x^{2}+2\right ) y^{\prime }-\left (-9 x^{2}+2\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.716

1987

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

0.719

1989

\begin{align*} 8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.734

1990

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

0.652

1991

\begin{align*} 6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.673

1992

\begin{align*} 28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.695

1993

\begin{align*} 9 x^{2} \left (x +5\right ) y^{\prime \prime }+9 x \left (5+9 x \right ) y^{\prime }-\left (5-8 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.874

1994

\begin{align*} 8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.672

1996

\begin{align*} 3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.720

1997

\begin{align*} 4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.736

2446

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

0.839

2447

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

0.828

2448

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

0.886

2449

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

0.820

2450

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

0.832

2451

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

0.818

2463

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

0.828

2465

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

1.125

2643

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

0.885

2644

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

0.901

2645

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

0.955

2646

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

0.871

2647

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

0.899

2648

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

0.860

2660

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

0.823

2662

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

1.337

2663

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

0.934

2669

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

30.868

3350

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

0.915

3351

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

1.300

3352

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

1.143

3353

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

1.030

3354

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

1.091

3355

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

1.009

3356

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

1.151

3357

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

1.089

3358

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

1.131

3360

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

1.384

3361

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

1.116

3362

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

1.089

3363

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

1.115

3364

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

1.106

3365

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

1.104

3366

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

1.140

3367

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

1.189

3368

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

0.928

3369

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

0.928

3371

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

1.269

3394

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

1.430

3395

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

1.233

3397

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

1.249

3400

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

1.357

3401

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

1.452

3501

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

1.074

3504

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

1.004

4009

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

1.257

4010

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

1.522

4013

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

1.185

4014

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.106

4015

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

1.218

4016

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

0.937

4017

\begin{align*} 3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.098

4018

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

1.158

4019

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

1.290

4020

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

1.094

4022

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

1.392

4035

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

1.672

4067

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

1.238

4071

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

1.179

4072

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

1.059

4178

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

0.990

4184

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

1.221

4185

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

1.235

4600

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

1.463

7164

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

1.699

7166

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

1.496

7172

\begin{align*} \left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.662

7175

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

1.838

7193

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

1.539

7195

\begin{align*} 2 \left (1-x \right ) x y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.490

7196

\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.539

7197

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

1.459

8077

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

1.680

8078

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

1.739

8079

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

1.624

8085

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

2.833

8086

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

1.740

8096

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

1.924

8107

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

1.564

8110

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

1.801

8111

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

1.738

8132

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

1.525

8134

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

1.518

8136

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

1.563

8137

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

1.553

8148

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

1.528

8504

\begin{align*} x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}-25\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.316

8508

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

1.132

8511

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

0.915

8513

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

0.937

8514

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

0.753

8515

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

0.930

8516

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

0.770

8517

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

0.939

8518

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

0.854

8519

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

0.972

8520

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

0.761

8521

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

0.887

8522

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

0.875

8534

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

0.766

8537

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

0.762

8542

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

0.760

8558

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

0.930

8586

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

0.992

8591

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

1.012

8592

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

1.039

8593

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

0.925

8597

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

0.771

8600

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

0.852

8603

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

0.829

8605

\begin{align*} 9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (36 x^{4}-16\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.772

8616

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

0.826

8988

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

1.564

8991

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

1.283

8993

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

1.299

8996

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

1.361

9385

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

1.799

9394

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

1.391

9396

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

0.990

9397

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

1.388

9398

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

1.388

9399

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

1.464

9400

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

1.323

9409

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

1.019

9410

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

1.024

9413

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

1.510

9414

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

1.221

9415

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

1.730

9416

\begin{align*} \left (x^{2}-x -6\right ) y^{\prime \prime }+\left (3 x +5\right ) y^{\prime }+y&=0 \\ \end{align*}
Series expansion around \(x=3\).

1.548

9417

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

2.039

9418

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

2.179

9431

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

1.439

9440

\begin{align*} 9 \left (x -2\right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (x -2\right ) y^{\prime }+16 y&=0 \\ \end{align*}
Series expansion around \(x=\infty \).

1.873

9441

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

1.999

9532

\begin{align*} x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}-25\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

2.010

9536

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

1.675

9539

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

1.331

9541

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

1.447

9542

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

1.111

9543

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

1.446

9544

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

1.113

9545

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

1.409

9546

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

1.267

9547

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

1.504

9548

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

1.102

9549

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

1.338

9550

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

1.332

9586

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

1.393

9859

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

1.495

9862

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

1.466

9863

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

1.351

9864

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

1.519

9865

\begin{align*} 8 x^{2} y^{\prime \prime }+10 y^{\prime } x -\left (x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.376

9867

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

1.499

9868

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

1.332

9869

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

1.600

9870

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

1.382

9871

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

1.523

9872

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

1.576

9873

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

1.431

9874

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

1.360

9875

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

1.317

9876

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

0.988

9877

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

1.022

9878

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

0.927

9879

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

1.009

9938

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

1.678

9944

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

1.546

9948

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

1.371

9951

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

1.513

9954

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

1.422

9957

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

1.470

9961

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

1.401

10164

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

0.868

10165

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

0.977

10169

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

0.849

10170

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

0.930

10171

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

0.865

10174

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

0.935

10177

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

0.918

10178

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

1.044

10181

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

1.090

10182

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

0.867

10186

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

1.015

10187

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

0.991

10188

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

1.076

10189

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

0.935

10190

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

1.088

10192

\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.016

10193

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

0.961

10194

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

0.849

10199

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

0.903

10205

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

1.089

10221

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

0.665

10455

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

0.905

14745

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

1.144

14749

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

0.877

14750

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

0.849

14751

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

0.868

14752

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

0.843

14753

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

0.839

14754

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

0.996

14755

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

1.026

14977

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

1.026

14983

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

1.035

15308

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

1.326

15311

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

1.077

16883

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

0.751

16903

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

0.701

16905

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

0.739

16909

\begin{align*} \left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.697

16917

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

0.893

16925

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

0.974

17709

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

1.198

17710

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

0.901

17711

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

1.300

17712

\begin{align*} 7 y^{\prime \prime } x +10 y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.139

17715

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

0.847

17716

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

0.964

17723

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

0.993

17725

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

1.145

17790

\begin{align*} 3 y^{\prime \prime } x +11 y^{\prime }-y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.047

17791

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

0.780

18386

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

1.276

18388

\begin{align*} 9 \left (1-x \right ) x y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.291

19601

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

0.954

19602

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

0.983

19603

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

0.986

19604

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

1.036

19605

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

1.017

19616

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

1.075

19617

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

0.907

19618

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

1.150

19619

\begin{align*} \left (x^{2}-x -6\right ) y^{\prime \prime }+\left (3 x +5\right ) y^{\prime }+y&=0 \\ \end{align*}
Series expansion around \(x=3\).

1.110

19621

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

1.355

20149

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

1.028

20903

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

1.177

20906

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

1.087

20908

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

1.222

21629

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

1.474

21662

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

2.170

21672

\begin{align*} 8 x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (x -1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.316

21673

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

1.606

21674

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

1.516

21675

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

1.496

21676

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

1.512

21677

\begin{align*} 18 x^{2} y^{\prime \prime }+3 x \left (x +5\right ) y^{\prime }-\left (10 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.447

21678

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

1.350

21679

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

1.055

21694

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

1.037

21696

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

1.418

21697

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

2.047

21903

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

1.910

21908

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

1.872

22172

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

0.941

22182

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

0.997

22202

\begin{align*} 8 x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (x -1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.842

22203

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

0.860

22204

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

0.618

22211

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

1.616

22212

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

0.829

22213

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

0.805

22214

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

0.727

22220

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

1.093

22225

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

0.895

22851

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

0.661

22860

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

0.744

22868

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

0.684

22870

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

0.737

23670

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

0.888

23676

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

0.967

23678

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

1.369

23719

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

0.773

23722

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

1.046

23730

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

0.855

23732

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

0.774

23736

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

1.043

23742

\begin{align*} 2 \left (x +3\right )^{2} y^{\prime \prime }-\left (x^{2}+5 x +6\right ) y^{\prime }-y&=0 \\ \end{align*}
Series expansion around \(x=-3\).

0.928

23743

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

0.770

23749

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

1.034

23750

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

1.052

24095

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

0.891

24099

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

1.032

24100

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

0.909

24102

\begin{align*} 6 x^{2} y^{\prime \prime }+\left (x^{3}+11 x \right ) y^{\prime }+\left (-2 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.959

25339

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

0.607

25346

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

0.728

25348

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

0.720

25357

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

1.027

26021

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

1.131

26022

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

1.047

26023

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

1.082

26027

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

1.104

26028

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

0.977

26029

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

1.095