2.2.34 Problems 3301 to 3400

Table 2.69: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

3301

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

1.488

3302

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

[[_1st_order, _with_linear_symmetries]]

2.029

3303

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

2.950

3304

\[ {}8 x +1 = y {y^{\prime }}^{2} \]

[[_homogeneous, ‘class C‘], _rational, _dAlembert]

0.972

3305

\[ {}y {y^{\prime }}^{2}+2 y^{\prime }+1 = 0 \]

[_quadrature]

3.004

3306

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

3.398

3307

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

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

3.790

3308

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

2.174

3309

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

[_quadrature]

0.190

3310

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

[[_homogeneous, ‘class C‘], _dAlembert]

0.497

3311

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

0.967

3312

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

1.448

3313

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

[_dAlembert]

0.316

3314

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

1.918

3315

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

1.439

3316

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

[_dAlembert]

1.538

3317

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

12.705

3318

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

1.871

3319

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.607

3320

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

[[_1st_order, _with_linear_symmetries]]

8.911

3321

\[ {}3 {y^{\prime }}^{4} x = {y^{\prime }}^{3} y+1 \]

[[_1st_order, _with_linear_symmetries], _dAlembert]

3.502

3322

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

[_dAlembert]

1.131

3323

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

24.663

3324

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

35.917

3325

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.412

3326

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

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

0.489

3327

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

[[_homogeneous, ‘class G‘], _Clairaut]

0.892

3328

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

1.923

3329

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.582

3330

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

1.531

3331

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

1.878

3332

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

0.634

3333

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

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

0.437

3334

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

[_separable]

0.783

3335

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

[_quadrature]

0.257

3336

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

[_linear]

0.480

3337

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

[_separable]

0.323

3338

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

[_linear]

0.449

3339

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

[‘y=_G(x,y’)‘]

0.412

3340

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

[_quadrature]

0.304

3341

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

[[_Riccati, _special]]

0.427

3342

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

[‘y=_G(x,y’)‘]

0.178

3343

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

[‘y=_G(x,y’)‘]

0.424

3344

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.531

3345

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

[[_2nd_order, _with_linear_symmetries]]

0.436

3346

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

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.170

3347

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

0.476

3348

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

[[_2nd_order, _missing_x]]

0.207

3349

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

[NONE]

0.840

3350

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

[NONE]

0.823

3351

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

[[_2nd_order, _with_linear_symmetries]]

0.560

3352

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

[[_2nd_order, _with_linear_symmetries]]

0.781

3353

\[ {}x^{2} \left (x +4\right ) y^{\prime \prime }+7 x y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.738

3354

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

[[_2nd_order, _with_linear_symmetries]]

0.685

3355

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

[[_2nd_order, _with_linear_symmetries]]

0.735

3356

\[ {}9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.719

3357

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

[[_2nd_order, _with_linear_symmetries]]

0.787

3358

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

[[_2nd_order, _with_linear_symmetries]]

0.742

3359

\[ {}3 x^{2} y^{\prime \prime }+\left (-x^{2}+5 x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.763

3360

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

[[_2nd_order, _with_linear_symmetries]]

0.691

3361

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

[[_2nd_order, _with_linear_symmetries]]

1.058

3362

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

[[_2nd_order, _with_linear_symmetries]]

0.782

3363

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

[[_2nd_order, _with_linear_symmetries]]

0.763

3364

\[ {}2 x^{2} \left (1-3 x \right ) y^{\prime \prime }+5 x y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.779

3365

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

[[_2nd_order, _with_linear_symmetries]]

0.752

3366

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

[[_2nd_order, _with_linear_symmetries]]

0.743

3367

\[ {}\left (8-x \right ) x^{2} y^{\prime \prime }+6 x y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.775

3368

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

[[_2nd_order, _with_linear_symmetries]]

0.760

3369

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

[[_2nd_order, _with_linear_symmetries]]

0.646

3370

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

[[_2nd_order, _with_linear_symmetries]]

0.624

3371

\[ {}x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 x y^{\prime }-\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.124

3372

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

[[_2nd_order, _with_linear_symmetries]]

0.708

3373

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

[[_Emden, _Fowler]]

0.572

3374

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

[[_2nd_order, _with_linear_symmetries]]

0.423

3375

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

[[_2nd_order, _with_linear_symmetries]]

0.653

3376

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

[[_2nd_order, _with_linear_symmetries]]

0.621

3377

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

[[_2nd_order, _with_linear_symmetries]]

0.674

3378

\[ {}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.527

3379

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

[[_2nd_order, _with_linear_symmetries]]

0.546

3380

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

[[_2nd_order, _with_linear_symmetries]]

0.687

3381

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

[[_2nd_order, _with_linear_symmetries]]

0.743

3382

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

[[_2nd_order, _with_linear_symmetries]]

0.755

3383

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

[[_2nd_order, _with_linear_symmetries]]

0.816

3384

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.659

3385

\[ {}x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.424

3386

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

[[_2nd_order, _with_linear_symmetries]]

1.444

3387

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

[[_2nd_order, _with_linear_symmetries]]

1.329

3388

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

[[_2nd_order, _with_linear_symmetries]]

1.287

3389

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

[[_2nd_order, _with_linear_symmetries]]

1.324

3390

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.524

3391

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

[[_2nd_order, _with_linear_symmetries]]

1.326

3392

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

[[_2nd_order, _with_linear_symmetries]]

0.411

3393

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x +12\right ) y = x^{2}+x \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.921

3394

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.875

3395

\[ {}3 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y = -x^{3}+x \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.072

3396

\[ {}9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y = x^{4}+x^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.840

3397

\[ {}9 x^{2} y^{\prime \prime }+10 x y^{\prime }+y = -1+x \]

[[_2nd_order, _with_linear_symmetries]]

0.644

3398

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.837

3399

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 6 \left (-x^{2}+1\right )^{2} \]

[[_2nd_order, _with_linear_symmetries]]

0.335

3400

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

[[_2nd_order, _with_linear_symmetries]]

0.913