2.2.146 Problems 14501 to 14600

Table 2.293: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

14501

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2}+4 x -2 \\ y_{2}^{\prime }=y_{1}-2 y_{2}+3 x \end {array}\right ] \]

system_of_ODEs

0.456

14502

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x} \\ y_{2}^{\prime }=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x} \end {array}\right ] \]

system_of_ODEs

0.035

14503

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\ y_{2}^{\prime }=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \end {array}\right ] \]

system_of_ODEs

0.035

14504

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}+y_{2}-2 y_{3} \\ y_{2}^{\prime }=3 y_{2}-2 y_{3} \\ y_{3}^{\prime }=3 y_{1}+y_{2}-3 y_{3} \end {array}\right ] \]

system_of_ODEs

0.436

14505

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-5 y_{2}-5 y_{3} \\ y_{2}^{\prime }=-y_{1}+4 y_{2}+2 y_{3} \\ y_{3}^{\prime }=3 y_{1}-5 y_{2}-3 y_{3} \end {array}\right ] \]

system_of_ODEs

0.689

14506

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}+6 y_{2}+6 y_{3} \\ y_{2}^{\prime }=y_{1}+3 y_{2}+2 y_{3} \\ y_{3}^{\prime }=-y_{1}-4 y_{2}-3 y_{3} \end {array}\right ] \]

system_of_ODEs

0.490

14507

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2}-3 y_{3} \\ y_{2}^{\prime }=-3 y_{1}+4 y_{2}-2 y_{3} \\ y_{3}^{\prime }=2 y_{1}+y_{3} \end {array}\right ] \]

system_of_ODEs

0.766

14508

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}-y_{2}+y_{3} \\ y_{2}^{\prime }=-y_{1}-2 y_{2}-y_{3} \\ y_{3}^{\prime }=y_{1}-y_{2}-2 y_{3} \end {array}\right ] \]

system_of_ODEs

0.398

14509

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+y_{2}+2 y_{3} \\ y_{2}^{\prime }=y_{1}+y_{2}+2 y_{3} \\ y_{3}^{\prime }=2 y_{1}+2 y_{2}+4 y_{3} \end {array}\right ] \]

system_of_ODEs

0.372

14510

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}+y_{2} \\ y_{2}^{\prime }=-y_{1}+2 y_{2} \\ y_{3}^{\prime }=3 y_{3}-4 y_{4} \\ y_{4}^{\prime }=4 y_{3}+3 y_{4} \end {array}\right ] \]

system_of_ODEs

0.835

14511

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{2} \\ y_{2}^{\prime }=-3 y_{1}+2 y_{3} \\ y_{3}^{\prime }=y_{4} \\ y_{4}^{\prime }=2 y_{1}-5 y_{3} \end {array}\right ] \]

system_of_ODEs

4.731

14512

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+2 y_{2} \\ y_{2}^{\prime }=3 y_{2}-2 y_{1} \\ y_{3}^{\prime }=y_{3} \\ y_{4}^{\prime }=2 y_{4} \end {array}\right ] \]

system_of_ODEs

0.698

14513

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{2}+y_{4} \\ y_{2}^{\prime }=y_{1}-y_{3} \\ y_{3}^{\prime }=y_{4} \\ y_{4}^{\prime }=y_{3} \end {array}\right ] \]

system_of_ODEs

0.468

14514

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

system_of_ODEs

0.438

14515

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

system_of_ODEs

0.410

14516

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

system_of_ODEs

0.704

14517

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

system_of_ODEs

0.553

14518

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

system_of_ODEs

0.503

14519

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

system_of_ODEs

0.503

14520

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

system_of_ODEs

0.618

14521

\[ {}\left [\begin {array}{c} x^{\prime }=3 x-2 y-6 \\ y^{\prime }=4 x-y+2 \end {array}\right ] \]

system_of_ODEs

0.979

14522

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

[_separable]

1.990

14523

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

[_separable]

2.217

14524

\[ {}y^{\prime } = t^{4} y \]

[_separable]

1.648

14525

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

[_quadrature]

1.486

14526

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

[_quadrature]

1.405

14527

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

[_quadrature]

1.602

14528

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

[_quadrature]

3.373

14529

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

[_separable]

2.001

14530

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

[_separable]

4.408

14531

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

[_separable]

1.942

14532

\[ {}y^{\prime } = t y^{{1}/{3}} \]

[_separable]

6.908

14533

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

[_quadrature]

1.877

14534

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

[_separable]

2.260

14535

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

[_quadrature]

2.281

14536

\[ {}y^{\prime } = \frac {4 t}{1+3 y^{2}} \]

[_separable]

1.240

14537

\[ {}v^{\prime } = t^{2} v-2-2 v+t^{2} \]

[_separable]

1.664

14538

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

[_separable]

1.890

14539

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

[_separable]

1.755

14540

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

[_quadrature]

3.743

14541

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

[_separable]

1.635

14542

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

[_quadrature]

2.011

14543

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

[_separable]

3.052

14544

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

[_separable]

2.918

14545

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

[_quadrature]

4.193

14546

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

[_separable]

3.556

14547

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

[_quadrature]

1.936

14548

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

[_separable]

7.588

14549

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

[_quadrature]

1.911

14550

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

[_separable]

2.322

14551

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

[_separable]

3.057

14552

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

[_quadrature]

7.217

14553

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

[_separable]

2.593

14554

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

[_quadrature]

2.121

14555

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

[_separable]

2.194

14556

\[ {}y^{\prime } = \frac {y^{2}+5}{y} \]
i.c.

[_quadrature]

4.366

14557

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

[_quadrature]

0.455

14558

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

[_quadrature]

0.436

14559

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

[_quadrature]

1.642

14560

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

[_quadrature]

1.982

14561

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

[_quadrature]

2.407

14562

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

[[_linear, ‘class A‘]]

1.260

14563

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

[_quadrature]

2.798

14564

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

[[_linear, ‘class A‘]]

1.527

14565

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

[_Riccati]

1.783

14566

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

[_separable]

3.026

14567

\[ {}S^{\prime } = S^{3}-2 S^{2}+S \]
i.c.

[_quadrature]

17.293

14568

\[ {}S^{\prime } = S^{3}-2 S^{2}+S \]
i.c.

[_quadrature]

16.936

14569

\[ {}S^{\prime } = S^{3}-2 S^{2}+S \]
i.c.

[_quadrature]

18.758

14570

\[ {}S^{\prime } = S^{3}-2 S^{2}+S \]
i.c.

[_quadrature]

18.585

14571

\[ {}S^{\prime } = S^{3}-2 S^{2}+S \]
i.c.

[_quadrature]

17.342

14572

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

[_quadrature]

2.202

14573

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

[_quadrature]

1.977

14574

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

[_quadrature]

17.349

14575

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

[_quadrature]

0.458

14576

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

[_separable]

2.270

14577

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

[_separable]

1.504

14578

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

[_separable]

1.484

14579

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

[_quadrature]

0.514

14580

\[ {}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \]

[_quadrature]

35.954

14581

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

[_quadrature]

0.812

14582

\[ {}\theta ^{\prime } = \frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10} \]

[_quadrature]

35.741

14583

\[ {}v^{\prime } = -\frac {v}{R C} \]

[_quadrature]

1.062

14584

\[ {}v^{\prime } = \frac {K -v}{R C} \]

[_quadrature]

0.948

14585

\[ {}v^{\prime } = 2 V \left (t \right )-2 v \]

[[_linear, ‘class A‘]]

1.072

14586

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

[_quadrature]

2.056

14587

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

[[_Riccati, _special]]

2.157

14588

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

[[_Riccati, _special]]

2.262

14589

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

[_quadrature]

32.553

14590

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

[_quadrature]

2.422

14591

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

[_quadrature]

2.436

14592

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

[_quadrature]

1.733

14593

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

[_quadrature]

1.770

14594

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

[_quadrature]

16.481

14595

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

[_Abel]

0.771

14596

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

[_quadrature]

1.732

14597

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

[_quadrature]

1.878

14598

\[ {}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \]
i.c.

[_quadrature]

1647.895

14599

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

[_quadrature]

38.355

14600

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

[_quadrature]

5.095