2.2.99 Problems 9801 to 9900

Table 2.199: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

9801

\[ {}t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.333

9802

\[ {}t y^{\prime \prime }+t y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.320

9803

\[ {}t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.757

9804

\[ {}t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.325

9805

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.210

9806

\[ {}\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+y = 0 \]

[_Gegenbauer]

0.434

9807

\[ {}4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.331

9808

\[ {}f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.274

9809

\[ {}z y^{\prime \prime }-2 y^{\prime }+y z = 0 \]

[_Lienard]

0.353

9810

\[ {}z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.358

9811

\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.181

9812

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.161

9813

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[_Gegenbauer]

0.332

9814

\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.242

9815

\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.306

9816

\[ {}y^{\prime \prime }+2 x y^{\prime }+4 y = 0 \]

[_erf]

0.220

9817

\[ {}y^{\prime \prime }+x y^{\prime }+3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.334

9818

\[ {}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.344

9819

\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0 \]

[_Gegenbauer]

0.316

9820

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

[_Gegenbauer]

0.233

9821

\[ {}y^{\prime \prime }+x y^{\prime }+\left (x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.374

9822

\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.425

9823

\[ {}4 y^{\prime \prime }+x y^{\prime }+4 y = 0 \]

[_Lienard]

0.341

9824

\[ {}y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.304

9825

\[ {}4 x y^{\prime \prime }-x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.312

9826

\[ {}6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.375

9827

\[ {}3 x^{2} y^{\prime \prime }-x \left (x +8\right ) y^{\prime }+6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

3.507

9828

\[ {}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.790

9829

\[ {}4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.256

9830

\[ {}x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.352

9831

\[ {}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.385

9832

\[ {}x^{2} y^{\prime \prime }+x \left (3-x \right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.370

9833

\[ {}x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.195

9834

\[ {}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.326

9835

\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.233

9836

\[ {}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.237

9837

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.220

9838

\[ {}x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.430

9839

\[ {}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.243

9840

\[ {}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.353

9841

\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.308

9842

\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.346

9843

\[ {}x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.422

9844

\[ {}4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.318

9845

\[ {}x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.335

9846

\[ {}x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.342

9847

\[ {}4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.135

9848

\[ {}x^{2} y^{\prime \prime }+x \left (4+x \right ) y^{\prime }+\left (x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.345

9849

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.374

9850

\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \]

[_Lienard]

0.217

9851

\[ {}2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.454

9852

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.168

9853

\[ {}x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.447

9854

\[ {}x^{4} y^{\prime \prime }+x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.427

9855

\[ {}x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.344

9856

\[ {}\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.464

9857

\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.232

9858

\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.232

9859

\[ {}x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (-\frac {1}{4} x -x^{2}\right ) y^{\prime }-\frac {5 x y}{16} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.436

9860

\[ {}x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.350

9861

\[ {}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.370

9862

\[ {}x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.339

9863

\[ {}2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.524

9864

\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4} = 0 \]

[_Jacobi]

0.257

9865

\[ {}2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.318

9866

\[ {}2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0 \]

[_Jacobi]

0.309

9867

\[ {}x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9} = 0 \]

[_Jacobi]

0.318

9868

\[ {}4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.215

9869

\[ {}u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.367

9870

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.136

9871

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.144

9872

\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.352

9873

\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.396

9874

\[ {}y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

0.379

9875

\[ {}y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

0.433

9876

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.115

9877

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.413

9878

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.391

9879

\[ {}y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

0.355

9880

\[ {}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0 \]

[[_Emden, _Fowler]]

0.368

9881

\[ {}\left (2-x \right ) x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.227

9882

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.363

9883

\[ {}x y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+\left (x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.161

9884

\[ {}3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.165

9885

\[ {}x \left (x +1\right ) y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.250

9886

\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.238

9887

\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.239

9888

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.352

9889

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.361

9890

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.090

9891

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.089

9892

\[ {}\left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.431

9893

\[ {}y^{\prime \prime }-x y^{\prime }-3 y = 0 \]

[_Hermite]

0.246

9894

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.329

9895

\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \]

[_Hermite]

0.326

9896

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.806

9897

\[ {}x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.189

9898

\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler]]

0.224

9899

\[ {}x y^{\prime \prime }+x y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.309

9900

\[ {}x \left (-1+x \right )^{2} y^{\prime \prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.178