2.2.184 Problems 18301 to 18400

Table 2.369: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

18301

\[ {}y^{\prime \prime }-4 y = {\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

1.197

18302

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.193

18303

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 10 x^{3} {\mathrm e}^{-2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.247

18304

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

[[_2nd_order, _with_linear_symmetries]]

1.166

18305

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

[[_2nd_order, _with_linear_symmetries]]

1.151

18306

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 6 \,{\mathrm e}^{5 x} \]

[[_2nd_order, _with_linear_symmetries]]

1.135

18307

\[ {}y^{\prime \prime }-y^{\prime }+y = x^{3}-3 x^{2}+1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

32.030

18308

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

[[_3rd_order, _linear, _nonhomogeneous]]

0.117

18309

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.556

18310

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

[[_high_order, _missing_y]]

0.111

18311

\[ {}y^{\left (6\right )}-y = x^{10} \]

[[_high_order, _linear, _nonhomogeneous]]

0.167

18312

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.621

18313

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.985

18314

\[ {}y^{\prime \prime \prime }-y^{\prime \prime } = 12 x -2 \]

[[_3rd_order, _missing_y]]

0.094

18315

\[ {}y^{\prime \prime \prime }+y^{\prime \prime } = 9 x^{2}-2 x +1 \]

[[_3rd_order, _missing_y]]

0.103

18316

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.226

18317

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = {\mathrm e}^{2 x} \left (x^{3}-5 x^{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.302

18318

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.358

18319

\[ {}y^{\prime \prime \prime }-8 y = 16 x^{2} \]

[[_3rd_order, _with_linear_symmetries]]

0.105

18320

\[ {}y^{\prime \prime \prime \prime }-y = -x^{3}+1 \]

[[_high_order, _linear, _nonhomogeneous]]

0.107

18321

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

[[_3rd_order, _missing_y]]

0.090

18322

\[ {}y^{\prime \prime \prime \prime } = \frac {1}{x^{3}} \]

[[_high_order, _quadrature]]

0.175

18323

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime } = x +1 \]

[[_3rd_order, _missing_y]]

0.100

18324

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

[[_3rd_order, _missing_y]]

0.094

18325

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = {\mathrm e}^{2 x} \]

[[_3rd_order, _with_linear_symmetries]]

0.113

18326

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 12 \,{\mathrm e}^{-x} \]

[[_3rd_order, _with_linear_symmetries]]

0.120

18327

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.392

18328

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

[_separable]

0.365

18329

\[ {}y^{\prime }+y = 1 \]

[_quadrature]

0.343

18330

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

[_separable]

0.273

18331

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

[_separable]

0.061

18332

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

[_quadrature]

0.293

18333

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

[[_linear, ‘class A‘]]

0.467

18334

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

[[_2nd_order, _with_linear_symmetries]]

0.358

18335

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.059

18336

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.335

18337

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

[[_2nd_order, _with_linear_symmetries]]

0.368

18338

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

[[_Emden, _Fowler]]

0.236

18339

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

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

0.476

18340

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

[[_2nd_order, _with_linear_symmetries]]

0.390

18341

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

[[_2nd_order, _with_linear_symmetries]]

0.110

18342

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

[[_2nd_order, _with_linear_symmetries]]

0.634

18343

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

[[_2nd_order, _missing_y]]

0.145

18344

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

[[_2nd_order, _with_linear_symmetries]]

1.444

18345

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

[[_2nd_order, _with_linear_symmetries]]

0.470

18346

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

[[_2nd_order, _with_linear_symmetries]]

1.018

18347

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

[[_2nd_order, _with_linear_symmetries]]

1.171

18348

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

[[_2nd_order, _with_linear_symmetries]]

0.542

18349

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

[[_2nd_order, _with_linear_symmetries]]

0.112

18350

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

[[_2nd_order, _with_linear_symmetries]]

0.724

18351

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

[[_2nd_order, _with_linear_symmetries]]

0.723

18352

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

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

0.684

18353

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.655

18354

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

[[_2nd_order, _with_linear_symmetries]]

0.708

18355

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

[[_2nd_order, _with_linear_symmetries]]

0.720

18356

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

[_Lienard]

0.434

18357

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

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

0.102

18358

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

[[_2nd_order, _with_linear_symmetries]]

0.104

18359

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

[[_2nd_order, _with_linear_symmetries]]

0.666

18360

\[ {}4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.717

18361

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

[_Lienard]

0.588

18362

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

[[_2nd_order, _with_linear_symmetries]]

0.741

18363

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

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

0.504

18364

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

[_Bessel]

1.211

18365

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

[[_2nd_order, _with_linear_symmetries]]

0.668

18366

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

[_Jacobi]

0.732

18367

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.596

18368

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

[[_2nd_order, _with_linear_symmetries]]

0.768

18369

\[ {}\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.748

18370

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.469

18371

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

[_Gegenbauer]

0.807

18372

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

[_Bessel]

0.180

18373

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

[[_linear, ‘class A‘]]

0.381

18374

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

[[_2nd_order, _missing_x]]

0.204

18375

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

[[_2nd_order, _missing_x]]

0.340

18376

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

[[_2nd_order, _missing_y]]

0.321

18377

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x} \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.409

18378

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

[[_2nd_order, _missing_x]]

0.181

18379

\[ {}x y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-\left (4 x +9\right ) y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.215

18380

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.361

18381

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

[[_Emden, _Fowler]]

1.633

18382

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.445

18383

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.414

18384

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

[[_2nd_order, _with_linear_symmetries]]

0.332

18385

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

[[_2nd_order, _missing_y]]

0.320

18386

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.413

18387

\[ {}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=3 x+y \end {array}\right ] \]
i.c.

system_of_ODEs

0.559

18388

\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=3 x+2 y \end {array}\right ] \]

system_of_ODEs

0.463

18389

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

system_of_ODEs

0.588

18390

\[ {}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=y \end {array}\right ] \]

system_of_ODEs

0.405

18391

\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=y \end {array}\right ] \]

system_of_ODEs

0.297

18392

\[ {}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-2 x+3 y \end {array}\right ] \]

system_of_ODEs

0.442

18393

\[ {}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=5 x+2 y \end {array}\right ] \]

system_of_ODEs

0.581

18394

\[ {}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=y-x \end {array}\right ] \]

system_of_ODEs

0.457

18395

\[ {}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ] \]

system_of_ODEs

0.461

18396

\[ {}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=3 y \end {array}\right ] \]

system_of_ODEs

0.407

18397

\[ {}\left [\begin {array}{c} x^{\prime }=-4 x-y \\ y^{\prime }=x-2 y \end {array}\right ] \]

system_of_ODEs

0.431

18398

\[ {}\left [\begin {array}{c} x^{\prime }=7 x+6 y \\ y^{\prime }=2 x+6 y \end {array}\right ] \]

system_of_ODEs

0.485

18399

\[ {}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=4 x+5 y \end {array}\right ] \]

system_of_ODEs

0.571

18400

\[ {}\left [\begin {array}{c} x^{\prime }=x+y-5 t +2 \\ y^{\prime }=4 x-2 y-8 t -8 \end {array}\right ] \]

system_of_ODEs

0.540