2.2.64 Problems 6301 to 6400

Table 2.129: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

6301

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

[_linear]

1.354

6302

\[ {}r^{\prime }+r \tan \left (\theta \right ) = \sec \left (\theta \right ) \]

[_linear]

1.745

6303

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

[_linear]

1.522

6304

\[ {}t +y+1-y^{\prime } = 0 \]

[[_linear, ‘class A‘]]

1.272

6305

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

[[_linear, ‘class A‘]]

1.791

6306

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

[_linear]

1.627

6307

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

[_linear]

1.894

6308

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

[_separable]

1.846

6309

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

[_linear]

3.398

6310

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

[_linear]

1.749

6311

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

[[_linear, ‘class A‘]]

1.725

6312

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

[_linear]

1.718

6313

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

[_linear]

1.817

6314

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

[_linear]

3.490

6315

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

[_linear]

2.852

6316

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

[_linear]

741.593

6317

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

[[_1st_order, _with_exponential_symmetries]]

4.872

6318

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

[_rational, _Bernoulli]

1.644

6319

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

[_linear]

1.738

6320

\[ {}x^{\prime } = \alpha -\beta \cos \left (\frac {\pi t}{12}\right )-k x \]
i.c.

[[_linear, ‘class A‘]]

2.082

6321

\[ {}u^{\prime } = \alpha \left (1-u\right )-\beta u \]

[_quadrature]

1.149

6322

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

[_linear]

1.659

6323

\[ {}x^{{10}/{3}}-2 y+x y^{\prime } = 0 \]

[_linear]

1.664

6324

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

[_separable]

13.676

6325

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

[_exact]

0.384

6326

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

[_separable]

0.283

6327

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

[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

0.330

6328

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

[_exact]

0.451

6329

\[ {}\theta r^{\prime }+3 r-\theta -1 = 0 \]

[_linear]

0.280

6330

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

[_linear]

0.269

6331

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

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

0.496

6332

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

[_exact]

7.833

6333

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

[_linear]

0.288

6334

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

[_separable]

0.329

6335

\[ {}\cos \left (\theta \right ) r^{\prime }-r \sin \left (\theta \right )+{\mathrm e}^{\theta } = 0 \]

[_linear]

0.303

6336

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

[_exact]

0.350

6337

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

[[_homogeneous, ‘class G‘], _rational]

0.292

6338

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

[_exact]

38.029

6339

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

[_separable]

2.539

6340

\[ {}y^{\prime }-4 y = 32 x^{2} \]

[[_linear, ‘class A‘]]

1.323

6341

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

[_exact, _rational]

2.050

6342

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

[_linear]

1.971

6343

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

[_separable]

3.459

6344

\[ {}t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}} = 0 \]

[_separable]

1.692

6345

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

[[_2nd_order, _with_linear_symmetries]]

0.414

6346

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

[[_2nd_order, _with_linear_symmetries]]

0.145

6347

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

[[_2nd_order, _with_linear_symmetries]]

1.738

6348

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

[[_Emden, _Fowler]]

1.370

6349

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

[[_2nd_order, _with_linear_symmetries]]

0.546

6350

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

[[_2nd_order, _with_linear_symmetries]]

0.440

6351

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

[[_2nd_order, _with_linear_symmetries]]

1.575

6352

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

[[_2nd_order, _with_linear_symmetries]]

0.805

6353

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

[[_2nd_order, _with_linear_symmetries]]

6.130

6354

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

[_separable]

0.462

6355

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

[_quadrature]

0.323

6356

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

[_separable]

0.415

6357

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

[[_Emden, _Fowler]]

0.361

6358

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.380

6359

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

[[_2nd_order, _missing_x]]

0.519

6360

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

[_Lienard]

0.393

6361

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

[[_2nd_order, _with_linear_symmetries]]

0.391

6362

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

[[_2nd_order, _with_linear_symmetries]]

0.498

6363

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

[_Hermite]

0.429

6364

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

[[_Emden, _Fowler]]

0.477

6365

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

[[_2nd_order, _with_linear_symmetries]]

0.467

6366

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

[_Lienard]

1.833

6367

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

[[_2nd_order, _with_linear_symmetries]]

0.662

6368

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

[_separable]

0.462

6369

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

[_separable]

0.485

6370

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

[[_2nd_order, _with_linear_symmetries]]

0.416

6371

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

[[_Emden, _Fowler]]

0.457

6372

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

[[_2nd_order, _with_linear_symmetries]]

0.493

6373

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

[[_2nd_order, _with_linear_symmetries]]

0.434

6374

\[ {}x^{\prime }+\sin \left (t \right ) x = 0 \]
i.c.

[_separable]

0.563

6375

\[ {}y^{\prime }-y \,{\mathrm e}^{x} = 0 \]
i.c.

[_separable]

0.571

6376

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

[[_2nd_order, _with_linear_symmetries]]

0.747

6377

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

[[_2nd_order, _with_linear_symmetries]]

0.521

6378

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

[[_2nd_order, _with_linear_symmetries]]

1.038

6379

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

[_linear]

0.510

6380

\[ {}w^{\prime }+w x = {\mathrm e}^{x} \]

[_linear]

0.485

6381

\[ {}z^{\prime \prime }+x z^{\prime }+z = x^{2}+2 x +1 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

0.391

6382

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.362

6383

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

[[_2nd_order, _with_linear_symmetries]]

0.542

6384

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.397

6385

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.490

6386

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.590

6387

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

[_Gegenbauer]

0.588

6388

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

[[_2nd_order, _missing_x]]

1.649

6389

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

[[_3rd_order, _missing_x]]

0.054

6390

\[ {}x^{\prime \prime }+42 x^{\prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.285

6391

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

[[_high_order, _missing_x]]

0.069

6392

\[ {}x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x = 0 \]

[[_3rd_order, _missing_x]]

0.056

6393

\[ {}x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x = F \cos \left (\omega t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

83.747

6394

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

[[_2nd_order, _with_linear_symmetries]]

1.770

6395

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.876

6396

\[ {}y^{\prime \prime }+16 y = 16 \cos \left (4 x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4.226

6397

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.538

6398

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

[[_linear, ‘class A‘]]

1.345

6399

\[ {}x^{2} y^{\prime }+2 x y-x +1 = 0 \]
i.c.

[_linear]

1.714

6400

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

[[_linear, ‘class A‘]]

1.612