2.2.165 Problems 16401 to 16500

Table 2.331: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

16401

\[ {}4 x^{2} y^{\prime \prime }+y = x^{3} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.330

16402

\[ {}9 x^{2} y^{\prime \prime }+27 x y^{\prime }+10 y = \frac {1}{x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

6.957

16403

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

[[_Emden, _Fowler]]

3.623

16404

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.263

16405

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

1.254

16406

\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 x y^{\prime } = 0 \]

[[_3rd_order, _missing_y]]

0.115

16407

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

[[_3rd_order, _missing_y]]

0.111

16408

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

[[_3rd_order, _with_linear_symmetries]]

0.111

16409

\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 x y^{\prime } = -8 \]

[[_3rd_order, _missing_y]]

0.293

16410

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

1.229

16411

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.054

16412

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

1.688

16413

\[ {}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2.251

16414

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

2.618

16415

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

2.768

16416

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

10.577

16417

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.298

16418

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

[[_2nd_order, _with_linear_symmetries]]

2.881

16419

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

1.602

16420

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

[[_Emden, _Fowler]]

1.675

16421

\[ {}x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 x y^{\prime }+125 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

0.126

16422

\[ {}x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-12 x^{2} y^{\prime \prime }-12 x y^{\prime }+48 y = 0 \]

[[_high_order, _with_linear_symmetries]]

0.138

16423

\[ {}x^{4} y^{\prime \prime \prime \prime }+14 x^{3} y^{\prime \prime \prime }+55 x^{2} y^{\prime \prime }+65 x y^{\prime }+15 y = 0 \]

[[_high_order, _exact, _linear, _homogeneous]]

0.148

16424

\[ {}x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+35 x y^{\prime }+45 y = 0 \]

[[_high_order, _with_linear_symmetries]]

0.146

16425

\[ {}x^{4} y^{\prime \prime \prime \prime }+10 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+21 x y^{\prime }+4 y = 0 \]

[[_high_order, _with_linear_symmetries]]

0.143

16426

\[ {}x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 x y^{\prime }+58 y = 0 \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

0.327

16427

\[ {}6 x^{2} y^{\prime \prime }+5 x y^{\prime }-y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

1.013

16428

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+7 y = 0 \]

[[_Emden, _Fowler]]

0.467

16429

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

[[_2nd_order, _with_linear_symmetries]]

0.465

16430

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

[[_2nd_order, _with_linear_symmetries]]

0.631

16431

\[ {}y^{\prime \prime }+3 y^{\prime }-18 y = 0 \]

[[_2nd_order, _missing_x]]

0.550

16432

\[ {}y^{\prime \prime }-11 y^{\prime }+30 y = 0 \]

[[_2nd_order, _missing_x]]

0.539

16433

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

[[_2nd_order, _missing_x]]

0.389

16434

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

[[_2nd_order, _with_linear_symmetries]]

0.596

16435

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

[[_2nd_order, _with_linear_symmetries]]

0.412

16436

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

[[_2nd_order, _missing_y]]

0.383

16437

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

[[_2nd_order, _with_linear_symmetries]]

0.416

16438

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.478

16439

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

[_Hermite]

0.349

16440

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.422

16441

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

[[_2nd_order, _with_linear_symmetries]]

0.402

16442

\[ {}y^{\prime \prime }-4 x^{2} y = 0 \]
i.c.

[[_Emden, _Fowler]]

0.259

16443

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

[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.427

16444

\[ {}y^{\prime \prime }+x y^{\prime } = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _missing_y]]

0.422

16445

\[ {}y^{\prime \prime }+y^{\prime }+x y = \cos \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.457

16446

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

[[_2nd_order, _missing_x], _Van_der_Pol]

0.281

16447

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

[[_2nd_order, _missing_x]]

0.277

16448

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

[[_2nd_order, _with_linear_symmetries]]

0.340

16449

\[ {}y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.358

16450

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.378

16451

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

[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.401

16452

\[ {}y^{\prime \prime }-y \cos \left (x \right ) = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.511

16453

\[ {}x^{2} y^{\prime \prime }+6 y = 0 \]

[[_Emden, _Fowler]]

0.450

16454

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

[[_2nd_order, _with_linear_symmetries]]

0.113

16455

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

[[_2nd_order, _with_linear_symmetries]]

0.474

16456

\[ {}\left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (x +5\right ) y^{\prime }+10 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.615

16457

\[ {}2 x y^{\prime \prime }-5 y^{\prime }-3 y = 0 \]

[[_Emden, _Fowler]]

0.737

16458

\[ {}5 x y^{\prime \prime }+8 y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.538

16459

\[ {}9 x y^{\prime \prime }+14 y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.753

16460

\[ {}7 x y^{\prime \prime }+10 y^{\prime }+\left (-x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.748

16461

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

[[_2nd_order, _with_linear_symmetries]]

1.283

16462

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

[[_2nd_order, _with_linear_symmetries]]

1.348

16463

\[ {}y^{\prime \prime }+\frac {8 y^{\prime }}{3 x}-\left (\frac {2}{3 x^{2}}-1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.684

16464

\[ {}y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}} = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.749

16465

\[ {}y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.582

16466

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

[[_2nd_order, _with_linear_symmetries]]

0.728

16467

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }-7 y = 0 \]

[[_Emden, _Fowler]]

0.718

16468

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.497

16469

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.496

16470

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

[[_Emden, _Fowler]]

0.243

16471

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

[_Bessel]

0.689

16472

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

[_Gegenbauer]

0.633

16473

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.772

16474

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.562

16475

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

[_Jacobi]

0.666

16476

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

[_Laguerre]

0.819

16477

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

[[_2nd_order, _with_linear_symmetries]]

0.700

16478

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (16 x^{2}-25\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.516

16479

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 0 \]

[[_2nd_order, _missing_x]]

0.884

16480

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

[[_2nd_order, _missing_x]]

0.874

16481

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

[[_2nd_order, _missing_x]]

2.071

16482

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.092

16483

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

[_Lienard]

0.152

16484

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 0 \]

[[_2nd_order, _missing_x]]

0.878

16485

\[ {}6 y^{\prime \prime }+5 y^{\prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

0.891

16486

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

[[_2nd_order, _missing_x]]

0.981

16487

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

[[_2nd_order, _missing_x]]

0.869

16488

\[ {}y^{\prime \prime }-10 y^{\prime }+34 y = 0 \]

[[_2nd_order, _missing_x]]

2.880

16489

\[ {}2 y^{\prime \prime }-5 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

0.898

16490

\[ {}15 y^{\prime \prime }-11 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

0.891

16491

\[ {}20 y^{\prime \prime }+y^{\prime }-y = 0 \]

[[_2nd_order, _missing_x]]

0.918

16492

\[ {}12 y^{\prime \prime }+8 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

0.893

16493

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

[[_3rd_order, _missing_x]]

0.050

16494

\[ {}9 y^{\prime \prime \prime }+36 y^{\prime \prime }+40 y^{\prime } = 0 \]

[[_3rd_order, _missing_x]]

0.061

16495

\[ {}9 y^{\prime \prime \prime }+12 y^{\prime \prime }+13 y^{\prime } = 0 \]

[[_3rd_order, _missing_x]]

0.059

16496

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = -t \]

[[_2nd_order, _with_linear_symmetries]]

1.226

16497

\[ {}y^{\prime \prime }+5 y^{\prime } = 5 t^{2} \]

[[_2nd_order, _missing_y]]

2.428

16498

\[ {}y^{\prime \prime }-4 y^{\prime } = -3 \sin \left (t \right ) \]

[[_2nd_order, _missing_y]]

2.661

16499

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15.820

16500

\[ {}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.414