2.2.154 Problems 15301 to 15400

Table 2.309: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

15301

\[ {}y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y = 0 \]

[[_high_order, _missing_x]]

0.082

15302

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

[[_high_order, _missing_x]]

0.089

15303

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

[[_high_order, _missing_x]]

0.117

15304

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

[[_high_order, _missing_x]]

0.095

15305

\[ {}4 y^{\prime \prime \prime \prime }+15 y^{\prime \prime }-4 y = 0 \]

[[_high_order, _missing_x]]

0.089

15306

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+16 y^{\prime }-16 y = 0 \]

[[_high_order, _missing_x]]

0.092

15307

\[ {}y^{\left (6\right )}+16 y^{\prime \prime \prime }+64 y = 0 \]

[[_high_order, _missing_x]]

0.107

15308

\[ {}x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y = 0 \]

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

0.959

15309

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.657

15310

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

[[_2nd_order, _missing_y]]

0.619

15311

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

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

1.122

15312

\[ {}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 0 \]

[[_Emden, _Fowler]]

0.940

15313

\[ {}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = 0 \]

[[_Emden, _Fowler]]

0.995

15314

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

[[_Emden, _Fowler]]

0.373

15315

\[ {}x^{2} y^{\prime \prime }-19 y^{\prime } x +100 y = 0 \]

[[_Emden, _Fowler]]

0.982

15316

\[ {}x^{2} y^{\prime \prime }-5 y^{\prime } x +29 y = 0 \]

[[_Emden, _Fowler]]

1.171

15317

\[ {}x^{2} y^{\prime \prime }-y^{\prime } x +10 y = 0 \]

[[_Emden, _Fowler]]

1.019

15318

\[ {}x^{2} y^{\prime \prime }+5 y^{\prime } x +29 y = 0 \]

[[_Emden, _Fowler]]

1.111

15319

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

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

0.930

15320

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.198

15321

\[ {}4 x^{2} y^{\prime \prime }+37 y = 0 \]

[[_Emden, _Fowler]]

0.584

15322

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

[[_2nd_order, _missing_y]]

0.585

15323

\[ {}x^{2} y^{\prime \prime }+y^{\prime } x -25 y = 0 \]

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

0.866

15324

\[ {}4 x^{2} y^{\prime \prime }+8 y^{\prime } x +5 y = 0 \]

[[_Emden, _Fowler]]

1.136

15325

\[ {}3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y = 0 \]

[[_Emden, _Fowler]]

0.914

15326

\[ {}x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y = 0 \]
i.c.

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

1.422

15327

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

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

1.393

15328

\[ {}x^{2} y^{\prime \prime }-11 y^{\prime } x +36 y = 0 \]
i.c.

[[_Emden, _Fowler]]

1.509

15329

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

[[_Emden, _Fowler]]

1.767

15330

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

[[_Emden, _Fowler]]

1.975

15331

\[ {}x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y = 0 \]
i.c.

[[_Emden, _Fowler]]

1.907

15332

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

[[_3rd_order, _with_linear_symmetries]]

0.148

15333

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

[[_3rd_order, _with_linear_symmetries]]

0.149

15334

\[ {}x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 y^{\prime } x -18 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

0.161

15335

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 y^{\prime } x -8 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

0.145

15336

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 y^{\prime } x +16 y = 0 \]

[[_high_order, _with_linear_symmetries]]

0.169

15337

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y = 0 \]

[[_high_order, _exact, _linear, _homogeneous]]

0.165

15338

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

[[_high_order, _with_linear_symmetries]]

0.156

15339

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0 \]

[[_high_order, _exact, _linear, _homogeneous]]

0.175

15340

\[ {}y^{\prime \prime }+4 y = 24 \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.993

15341

\[ {}y^{\prime \prime }+4 y = 24 \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.962

15342

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

[[_2nd_order, _with_linear_symmetries]]

0.674

15343

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

[[_2nd_order, _with_linear_symmetries]]

0.701

15344

\[ {}y^{\prime \prime }-9 y = 36 \]
i.c.

[[_2nd_order, _missing_x]]

1.350

15345

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -6 \,{\mathrm e}^{4 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.746

15346

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 7 \,{\mathrm e}^{5 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.921

15347

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 169 \sin \left (2 x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.236

15348

\[ {}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 10 x +12 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

2.288

15349

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

[[_high_order, _missing_x]]

0.158

15350

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

[[_2nd_order, _with_linear_symmetries]]

0.462

15351

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = {\mathrm e}^{5 x} \]

[[_2nd_order, _with_linear_symmetries]]

0.604

15352

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.717

15353

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 35 \,{\mathrm e}^{5 x}+12 \,{\mathrm e}^{4 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.667

15354

\[ {}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 1 \]

[[_2nd_order, _with_linear_symmetries]]

1.416

15355

\[ {}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = x \]

[[_2nd_order, _with_linear_symmetries]]

1.370

15356

\[ {}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 22 x +24 \]

[[_2nd_order, _with_linear_symmetries]]

1.445

15357

\[ {}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

1.383

15358

\[ {}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = x \]

[[_2nd_order, _with_linear_symmetries]]

1.262

15359

\[ {}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = 1 \]

[[_2nd_order, _with_linear_symmetries]]

1.256

15360

\[ {}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = 4 x^{2}+2 x +3 \]

[[_2nd_order, _with_linear_symmetries]]

1.388

15361

\[ {}y^{\prime \prime }+9 y = 52 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

0.673

15362

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x} \]

[[_2nd_order, _with_linear_symmetries]]

0.609

15363

\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = 30 \,{\mathrm e}^{-4 x} \]

[[_2nd_order, _with_linear_symmetries]]

0.538

15364

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

[[_2nd_order, _missing_y]]

1.212

15365

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -5 \,{\mathrm e}^{3 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.748

15366

\[ {}y^{\prime \prime }+9 y = 10 \cos \left (2 x \right )+15 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.951

15367

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 25 \sin \left (6 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.904

15368

\[ {}y^{\prime \prime }+3 y^{\prime } = 26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right ) \]

[[_2nd_order, _missing_y]]

1.739

15369

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.573

15370

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -4 \cos \left (x \right )+7 \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.911

15371

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -200 \]

[[_2nd_order, _missing_x]]

0.437

15372

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.458

15373

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 18 x^{2}+3 x +4 \]

[[_2nd_order, _with_linear_symmetries]]

0.597

15374

\[ {}y^{\prime \prime }+9 y = 9 x^{4}-9 \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.631

15375

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.896

15376

\[ {}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.916

15377

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.677

15378

\[ {}y^{\prime \prime }+9 y = 54 x^{2} {\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.775

15379

\[ {}y^{\prime \prime } = 6 x \,{\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _quadrature]]

1.446

15380

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.165

15381

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left (12 x -4\right ) {\mathrm e}^{-5 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.655

15382

\[ {}y^{\prime \prime }+9 y = 39 x \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.033

15383

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

[[_2nd_order, _with_linear_symmetries]]

0.496

15384

\[ {}y^{\prime \prime }+4 y^{\prime } = 20 \]

[[_2nd_order, _missing_x]]

1.197

15385

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

[[_2nd_order, _missing_y]]

1.125

15386

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.807

15387

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 10 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

0.639

15388

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = \left (72 x^{2}-1\right ) {\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.581

15389

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 4 x \,{\mathrm e}^{6 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.521

15390

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{5 x} \]

[[_2nd_order, _with_linear_symmetries]]

0.607

15391

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{-5 x} \]

[[_2nd_order, _with_linear_symmetries]]

0.608

15392

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 24 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.704

15393

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 8 \,{\mathrm e}^{-3 x} \]

[[_2nd_order, _with_linear_symmetries]]

0.605

15394

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.727

15395

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{-x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.663

15396

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 100 \]

[[_2nd_order, _missing_x]]

0.624

15397

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{-x} \]

[[_2nd_order, _with_linear_symmetries]]

0.703

15398

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 10 x^{2}+4 x +8 \]

[[_2nd_order, _with_linear_symmetries]]

0.702

15399

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.979

15400

\[ {}y^{\prime \prime }+y = 6 \cos \left (x \right )-3 \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.955