2.2.35 Problems 3401 to 3500

Table 2.71: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

3401

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.939

3402

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.009

3403

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

[_quadrature]

0.815

3404

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

[_quadrature]

0.470

3405

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

[_quadrature]

0.483

3406

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

[_quadrature]

0.563

3407

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

[_quadrature]

0.559

3408

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

[_quadrature]

0.416

3409

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

[_separable]

1.642

3410

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

[_separable]

2.196

3411

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

[_separable]

2.165

3412

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

[_separable]

1.578

3413

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

[_separable]

6.532

3414

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

[_quadrature]

0.765

3415

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

[_quadrature]

0.332

3416

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

[_quadrature]

0.602

3417

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

[_quadrature]

0.679

3418

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

[_quadrature]

0.460

3419

\[ {}y^{\prime } = t \,{\mathrm e}^{2 t} \]

[_quadrature]

0.497

3420

\[ {}y^{\prime } = \sin \left (3 t \right ) \]

[_quadrature]

0.524

3421

\[ {}y^{\prime } = \sin \left (t \right )^{2} \]

[_quadrature]

0.600

3422

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

[_quadrature]

0.472

3423

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

[_quadrature]

0.394

3424

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

[_quadrature]

0.308

3425

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

[_quadrature]

2.016

3426

\[ {}y^{\prime } = -y^{3} \]
i.c.

[_quadrature]

3.470

3427

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

[_separable]

2.303

3428

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

[_quadrature]

0.774

3429

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

[_quadrature]

0.900

3430

\[ {}y^{\prime } = 8 \,{\mathrm e}^{4 t}+t \]
i.c.

[_quadrature]

0.712

3431

\[ {}y^{\prime } = \frac {y}{t} \]

[_separable]

1.615

3432

\[ {}y^{\prime } = -\frac {t}{y} \]

[_separable]

4.046

3433

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

[_quadrature]

1.882

3434

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

[_quadrature]

1.323

3435

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

[_quadrature]

1.386

3436

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

[_quadrature]

18.510

3437

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

[_quadrature]

2.541

3438

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

[_separable]

1.726

3439

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

[_quadrature]

1.566

3440

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

[[_linear, ‘class A‘]]

1.356

3441

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

[[_linear, ‘class A‘]]

1.273

3442

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

[[_linear, ‘class A‘]]

1.236

3443

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

[_linear]

1.497

3444

\[ {}y^{\prime } = y \tan \left (t \right )+\sec \left (t \right ) \]

[_linear]

1.720

3445

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

[_linear]

2.027

3446

\[ {}y^{\prime } = y \tan \left (t \right )+\sec \left (t \right )^{3} \]

[_linear]

1.908

3447

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

[_quadrature]

2.852

3448

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

[_quadrature]

2.171

3449

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

[_linear]

1.990

3450

\[ {}y^{\prime } = -y \tan \left (t \right )+\sec \left (t \right ) \]
i.c.

[_linear]

1.958

3451

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

[_separable]

2.370

3452

\[ {}t y^{\prime } = -y+t^{3} \]
i.c.

[_linear]

1.951

3453

\[ {}y^{\prime }+4 \tan \left (2 t \right ) y = \tan \left (2 t \right ) \]
i.c.

[_separable]

2.775

3454

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

[_linear]

1.353

3455

\[ {}y^{\prime } = \frac {2 y}{-t^{2}+1}+3 \]
i.c.

[_linear]

1.728

3456

\[ {}y^{\prime } = -\cot \left (t \right ) y+6 \cos \left (t \right )^{2} \]
i.c.

[_linear]

2.492

3457

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

[_separable]

3.495

3458

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

[_separable]

2.302

3459

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

[_separable]

1.839

3460

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

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

2.329

3461

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

[_linear]

5.242

3462

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

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

4.246

3463

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

[_linear]

5.040

3464

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

[_linear]

3.237

3465

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

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

1.595

3466

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

[_rational, _Bernoulli]

1.643

3467

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

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

40.443

3468

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

[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

1.911

3469

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

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

1.848

3470

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

[_separable]

4.120

3471

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

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

2.713

3472

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

[_linear]

3.540

3473

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

[_separable]

1.810

3474

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

[_linear]

1.981

3475

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

[_linear]

1.725

3476

\[ {}y^{\prime }-\frac {y^{2}}{x^{2}} = {\frac {1}{4}} \]
i.c.

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

2.938

3477

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

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

2.284

3478

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

[_linear]

2.409

3479

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

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

4.372

3480

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

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

5.755

3481

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

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

7.762

3482

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

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

54.032

3483

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

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

1.341

3484

\[ {}x^{\prime \prime }+\omega _{0}^{2} x = a \cos \left (\omega t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2.499

3485

\[ {}f^{\prime \prime }+2 f^{\prime }+5 f = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.909

3486

\[ {}f^{\prime \prime }+2 f^{\prime }+5 f = {\mathrm e}^{-t} \cos \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4.641

3487

\[ {}f^{\prime \prime }+6 f^{\prime }+9 f = {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.293

3488

\[ {}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.271

3489

\[ {}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.622

3490

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

[[_2nd_order, _with_linear_symmetries]]

1.198

3491

\[ {}y^{\prime \prime \prime }-12 y^{\prime }+16 y = 32 x -8 \]

[[_3rd_order, _with_linear_symmetries]]

0.098

3492

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

1.514

3493

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

[[_2nd_order, _with_linear_symmetries]]

1.586

3494

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.677

3495

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

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

0.842

3496

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.616

3497

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.206

3498

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

[[_3rd_order, _exact, _nonlinear]]

0.051

3499

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

[[_3rd_order, _missing_y]]

0.129

3500

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

[[_2nd_order, _linear, _nonhomogeneous]]

5.825