2.2.145 Problems 14401 to 14500

Table 2.291: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

14401

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

[[_2nd_order, _with_linear_symmetries]]

19.648

14402

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

[[_3rd_order, _missing_y]]

0.793

14403

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

[[_2nd_order, _missing_y]]

1.460

14404

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

[[_2nd_order, _missing_y]]

1.729

14405

\[ {}\sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.816

14406

\[ {}\left (x^{2}-4\right ) y^{\prime \prime }+y \ln \left (x \right ) = x \,{\mathrm e}^{x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.357

14407

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

[[_2nd_order, _missing_x]]

2.168

14408

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

[[_2nd_order, _missing_x]]

2.148

14409

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

[[_Emden, _Fowler]]

1.063

14410

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

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.339

14411

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

[[_2nd_order, _missing_x]]

2.747

14412

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

[[_3rd_order, _missing_x]]

0.092

14413

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

[[_Emden, _Fowler]]

1.928

14414

\[ {}y^{\prime \prime }-4 y = 31 \]
i.c.

[[_2nd_order, _missing_x]]

3.275

14415

\[ {}y^{\prime \prime }+9 y = 27 x +18 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

3.242

14416

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

[[_2nd_order, _with_linear_symmetries]]

2.710

14417

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

[[_2nd_order, _missing_x]]

1.064

14418

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

[[_3rd_order, _missing_x]]

0.089

14419

\[ {}y^{\prime \prime \prime \prime }-16 y = 0 \]

[[_high_order, _missing_x]]

0.081

14420

\[ {}y^{\prime \prime \prime \prime }+16 y = 0 \]

[[_high_order, _missing_x]]

0.098

14421

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y = 0 \]

[[_high_order, _missing_x]]

0.099

14422

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

[[_high_order, _missing_x]]

0.089

14423

\[ {}36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y = 0 \]

[[_high_order, _missing_x]]

0.093

14424

\[ {}y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0 \]

[[_high_order, _missing_x]]

0.095

14425

\[ {}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+35 y^{\prime \prime }+16 y^{\prime }-52 y = 0 \]

[[_high_order, _missing_x]]

0.100

14426

\[ {}y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y = 0 \]

[[_high_order, _missing_x]]

0.116

14427

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

[[_2nd_order, _missing_x]]

38.749

14428

\[ {}y^{\prime \prime \prime }+\left (-3-4 i\right ) y^{\prime \prime }+\left (-4+12 i\right ) y^{\prime }+12 y = 0 \]

[[_3rd_order, _missing_x]]

0.106

14429

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

[[_high_order, _missing_x]]

0.090

14430

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

[_quadrature]

1.190

14431

\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 2 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x} \]

[[_high_order, _linear, _nonhomogeneous]]

0.188

14432

\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 24 x^{2}-6 x +14+32 \cos \left (2 x \right ) \]

[[_high_order, _missing_y]]

0.594

14433

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

[[_high_order, _linear, _nonhomogeneous]]

0.181

14434

\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = 6 x -20-120 x^{2} {\mathrm e}^{x} \]

[[_high_order, _missing_y]]

0.181

14435

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y = 36 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \]

[[_3rd_order, _linear, _nonhomogeneous]]

0.528

14436

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = \left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right ) \]

[[_3rd_order, _linear, _nonhomogeneous]]

0.267

14437

\[ {}y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y = {\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right ) \]

[[_high_order, _linear, _nonhomogeneous]]

0.266

14438

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.148

14439

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

[[_high_order, _missing_x]]

0.154

14440

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

[[_3rd_order, _with_linear_symmetries]]

0.146

14441

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

[[_high_order, _with_linear_symmetries]]

0.150

14442

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

[_quadrature]

0.259

14443

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

[[_2nd_order, _missing_x]]

0.219

14444

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

[_quadrature]

0.282

14445

\[ {}y^{\prime \prime }-9 y = 2 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.230

14446

\[ {}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.229

14447

\[ {}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{x}-3 x^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.229

14448

\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x \,{\mathrm e}^{x}-3 x^{2} \]

[[_high_order, _missing_y]]

0.317

14449

\[ {}y^{\prime } = {\mathrm e}^{x} \]
i.c.

[_quadrature]

0.571

14450

\[ {}y^{\prime }-y = 2 \,{\mathrm e}^{x} \]
i.c.

[[_linear, ‘class A‘]]

0.370

14451

\[ {}y^{\prime \prime }-9 y = x +2 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.332

14452

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

[[_2nd_order, _with_linear_symmetries]]

0.394

14453

\[ {}y^{\prime \prime }-y^{\prime }+6 y = -2 \sin \left (3 x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.639

14454

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = -x^{2}+1 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.344

14455

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

[[_3rd_order, _missing_y]]

0.444

14456

\[ {}y^{\prime }-2 y = 6 \]
i.c.

[_quadrature]

0.465

14457

\[ {}y^{\prime }+y = {\mathrm e}^{x} \]
i.c.

[[_linear, ‘class A‘]]

0.464

14458

\[ {}y^{\prime \prime }+9 y = 1 \]
i.c.

[[_2nd_order, _missing_x]]

0.325

14459

\[ {}y^{\prime \prime }+9 y = 18 \,{\mathrm e}^{3 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.380

14460

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

[[_2nd_order, _missing_x]]

0.216

14461

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

[[_2nd_order, _with_linear_symmetries]]

0.272

14462

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.359

14463

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

[[_3rd_order, _missing_x]]

0.431

14464

\[ {}y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \]
i.c.

[[_linear, ‘class A‘]]

0.774

14465

\[ {}y^{\prime \prime }-y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2.605

14466

\[ {}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (-1+x \right )^{2} & 1\le x \end {array}\right . \]
i.c.

[[_2nd_order, _missing_y]]

0.881

14467

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.032

14468

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.753

14469

\[ {}y^{\prime \prime }-4 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.996

14470

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2.645

14471

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

[[_linear, ‘class A‘]]

0.586

14472

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

[[_linear, ‘class A‘]]

0.783

14473

\[ {}y^{\prime \prime }+9 y = \delta \left (x -\pi \right )+\delta \left (x -3 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.822

14474

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.642

14475

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = \cos \left (x \right )+2 \delta \left (x -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.359

14476

\[ {}y^{\prime \prime }+4 y = \cos \left (x \right ) \delta \left (x -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.612

14477

\[ {}y^{\prime \prime }+a^{2} y = \delta \left (x -\pi \right ) f \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.616

14478

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ] \]

system_of_ODEs

0.469

14479

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}-2 y_{2} \\ y_{2}^{\prime }=y_{1}+3 y_{2} \end {array}\right ] \]

system_of_ODEs

0.548

14480

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2}+x -1 \\ y_{2}^{\prime }=3 y_{1}+2 y_{2}-5 x -2 \end {array}\right ] \]
i.c.

system_of_ODEs

0.597

14481

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=\frac {2 y_{1}}{x}-\frac {y_{2}}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}} \\ y_{2}^{\prime }=2 y_{1}+1-6 x \end {array}\right ] \]
i.c.

system_of_ODEs

0.039

14482

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\ y_{2}^{\prime }=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \end {array}\right ] \]
i.c.

system_of_ODEs

0.040

14483

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}-2 y_{2} \\ y_{2}^{\prime }=y_{2}-y_{1} \end {array}\right ] \]
i.c.

system_of_ODEs

0.829

14484

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\ y_{2}^{\prime }=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \end {array}\right ] \]
i.c.

system_of_ODEs

0.043

14485

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\ y_{2}^{\prime }=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \end {array}\right ] \]
i.c.

system_of_ODEs

0.043

14486

\[ {}\left [\begin {array}{c} y_{1}^{\prime }={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\ y_{2}^{\prime }=\frac {y_{1}}{\left (-2+x \right )^{2}} \end {array}\right ] \]
i.c.

system_of_ODEs

0.041

14487

\[ {}\left [\begin {array}{c} y_{1}^{\prime }={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\ y_{2}^{\prime }=\frac {y_{1}}{\left (-2+x \right )^{2}} \end {array}\right ] \]
i.c.

system_of_ODEs

0.042

14488

\(\left [\begin {array}{cc} -2 & -4 \\ 1 & 3 \end {array}\right ]\)

Eigenvectors

0.115

14489

\(\left [\begin {array}{cc} -3 & -1 \\ 2 & -1 \end {array}\right ]\)

Eigenvectors

0.169

14490

\(\left [\begin {array}{ccc} 1 & 0 & 1 \\ 0 & 1 & -1 \\ -2 & 0 & -1 \end {array}\right ]\)

Eigenvectors

0.306

14491

\(\left [\begin {array}{ccc} 3 & 1 & -1 \\ 1 & 3 & -1 \\ 3 & 3 & -1 \end {array}\right ]\)

Eigenvectors

0.225

14492

\(\left [\begin {array}{ccc} 7 & -1 & 6 \\ -10 & 4 & -12 \\ -2 & 1 & -1 \end {array}\right ]\)

Eigenvectors

0.279

14493

\(\left [\begin {array}{cccc} 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \end {array}\right ]\)

Eigenvectors

0.263

14494

\(\left [\begin {array}{cccc} 1 & 3 & 5 & 7 \\ 2 & 6 & 10 & 14 \\ 3 & 9 & 15 & 21 \\ 6 & 18 & 30 & 42 \end {array}\right ]\)

Eigenvectors

0.280

14495

\(\left [\begin {array}{ccccc} 1 & 3 & 5 & 2 & 4 \\ 5 & 2 & 4 & 1 & 3 \\ 4 & 1 & 3 & 5 & 2 \\ 3 & 5 & 2 & 4 & 1 \\ 2 & 4 & 1 & 3 & 5 \end {array}\right ]\)

Eigenvectors

5.074

14496

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2}+5 \,{\mathrm e}^{x} \\ y_{2}^{\prime }=y_{1}+4 y_{2}-2 \,{\mathrm e}^{-x} \end {array}\right ] \]

system_of_ODEs

1.369

14497

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{2}-2 y_{1}+\sin \left (2 x \right ) \\ y_{2}^{\prime }=-3 y_{1}+y_{2}-2 \cos \left (3 x \right ) \end {array}\right ] \]

system_of_ODEs

3.274

14498

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{2} \\ y_{2}^{\prime }=3 y_{1} \\ y_{3}^{\prime }=2 y_{3}-y_{1} \end {array}\right ] \]

system_of_ODEs

0.701

14499

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 x y_{1}-x^{2} y_{2}+4 x \\ y_{2}^{\prime }={\mathrm e}^{x} y_{1}+3 \,{\mathrm e}^{-x} y_{2}-\cos \left (3 x \right ) \end {array}\right ] \]

system_of_ODEs

0.042

14500

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ] \]

system_of_ODEs

0.456