2.2.85 Problems 8401 to 8500

Table 2.171: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

8401

[x=x+yzy=2yz=yz]

system_of_ODEs

0.493

8402

[x=2x7yy=5x+10y+4zz=5y+2z]

system_of_ODEs

0.633

8403

[x=x+yy=x+2y+zz=3yz]

system_of_ODEs

0.555

8404

[x=x+zy=yz=x+z]

system_of_ODEs

0.382

8405

[x=xyy=3x43y2+3zz=x8+y4z2]

system_of_ODEs

0.768

8406

[x=xyy=3x43y2+3zz=x8+y4z2]

system_of_ODEs

0.726

8407

[x=x+4y+2zy=4xy2zz=6z]

system_of_ODEs

0.483

8408

[x=x2y=xy2]
i.c.

system_of_ODEs

0.477

8409

[x=x+y+4zy=2yz=x+y+z]
i.c.

system_of_ODEs

0.490

8410

[x=9x10+21y10+16z5y=7x10+13y2+21z5z=11x10+17y10+17z5]

system_of_ODEs

90.929

8411

[x1=x1+2x39x45x2=51x210x4+3x5x3=x1+2x23x3x4=x231x310+4x4x5=14x15+3x42x5]

system_of_ODEs

100.141

8412

[x=3xyy=9x3y]

system_of_ODEs

0.283

8413

[x=6x+5yy=5x+4y]

system_of_ODEs

0.327

8414

[x=x+3yy=3x+5y]

system_of_ODEs

0.321

8415

[x=12x9yy=4x]

system_of_ODEs

0.382

8416

[x=3xyzy=x+yzz=xy+z]

system_of_ODEs

0.446

8417

[x=3x+2y+4zy=2x+2zz=4x+2y+3z]

system_of_ODEs

0.498

8418

[x=5x4yy=x+2zz=2y+5z]

system_of_ODEs

0.492

8419

[x=xy=3y+zz=y+z]

system_of_ODEs

0.437

8420

[x=xy=2x+2yzz=y]

system_of_ODEs

0.431

8421

[x=4x+yy=4y+zz=4z]

system_of_ODEs

0.324

8422

[x=2x+4yy=x+6y]
i.c.

system_of_ODEs

0.506

8423

[x=zy=yz=x]
i.c.

system_of_ODEs

0.432

8424

[x=6xyy=5x+2y]

system_of_ODEs

0.575

8425

[x=x+yy=2xy]

system_of_ODEs

0.445

8426

[x=5x+yy=2x+3y]

system_of_ODEs

0.571

8427

[x=4x+5yy=2x+6y]

system_of_ODEs

0.580

8428

[x=4x5yy=5x4y]

system_of_ODEs

0.499

8429

[x=x8yy=x3y]

system_of_ODEs

0.540

8430

[x=zy=zz=y]

system_of_ODEs

0.472

8431

[x=2x+y+2zy=3x+6zz=4x3z]

system_of_ODEs

1.021

8432

[x=x12y14zy=x+2y3zz=x+y2z]
i.c.

system_of_ODEs

0.819

8433

[x=2x+3y7y=x2y+5]

system_of_ODEs

0.660

8434

[x=5x+9y+2y=x+11y+6]

system_of_ODEs

0.552

8435

x2y2y2=0

[_separable]

1.375

8436

xy2(2x+3y)y+6y=0

[_quadrature]

0.415

8437

x2y25xyy+6y2=0

[_separable]

0.679

8438

x2y2+yxy2y=0

[_separable]

0.566

8439

xy2+(1x2y)yxy=0

[_quadrature]

0.474

8440

y2(x2y+3)y+3x2y=0

[_quadrature]

0.409

8441

xy2(xy+1)y+y=0

[_quadrature]

0.322

8442

y2x2y2=0

[_separable]

1.195

8443

(x+y)2y2=y2

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

1.685

8444

yy2+(xy2)yxy=0

[_quadrature]

0.383

8445

y2yxy(x+y)+x3y3=0

[_separable]

0.661

8446

(4xy)y2+6(xy)y+2x5y=0

[_quadrature]

0.560

8447

(xy)2y2=y2

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

2.025

8448

xyy2+(xy21)yy=0

[_quadrature]

0.378

8449

(x2+y2)2y2=4x2y2

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

3.246

8450

(x+y)2y2+(2y2+xyx2)y+y(yx)=0

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

1.632

8451

xy(x2+y2)(y21)=y(x4+x2y2+y4)

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

54.591

8452

xy3(x+x2+y)y2+(x2+y+xy)yxy=0

[_quadrature]

0.469

8453

xyy2+(x+y)y+1=0

[_quadrature]

0.409

8454

4x2yy+xy2=0

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

1.564

8455

3x4y2yxy=0

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

1.795

8456

y2yxy=0

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.548

8457

y2yx+y=0

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.494

8458

y2+4x5y12yx4=0

[[_1st_order, _with_linear_symmetries]]

1.879

8459

4y3y24yx+y=0

[[_1st_order, _with_linear_symmetries], _rational]

3.535

8460

4y3y2+4yx+y=0

[[_1st_order, _with_linear_symmetries], _rational]

3.063

8461

y3+xy2y=0

[_dAlembert]

2.843

8462

y4y36yx+2y=0

[[_1st_order, _with_linear_symmetries]]

111.627

8463

y2+x3y2x2y=0

[[_1st_order, _with_linear_symmetries]]

1.967

8464

y2+4x5y12yx4=0

[[_1st_order, _with_linear_symmetries]]

1.940

8465

2xy36yy2+x4=0

[[_1st_order, _with_linear_symmetries]]

129.091

8466

y2yx+y=0

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.470

8467

y=yx+ky2

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.544

8468

x8y2+3yx+9y=0

[[_homogeneous, ‘class G‘]]

2.149

8469

x4y2+2x3yy4=0

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

1.271

8470

4x2yy+xy2=0

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

1.650

8471

3x4y2yxy=0

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

1.824

8472

xy2+(xy)y+1y=0

[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

0.561

8473

y(yxy+k)+a=0

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

0.574

8474

x6y33yx3y=0

[[_1st_order, _with_linear_symmetries]]

10.229

8475

y=x6y3yx

[[_1st_order, _with_linear_symmetries]]

13.443

8476

y4x2yy3+12x3=0

[[_1st_order, _with_linear_symmetries]]

2.163

8477

xy3yy2+1=0

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.616

8478

y2yxy=0

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.531

8479

2y3+yx2y=0

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.546

8480

2y2+yx2y=0

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.698

8481

y3+2yxy=0

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.566

8482

4xy23yy+3=0

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

0.601

8483

y3yx+2y=0

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.518

8484

5y2+6yx2y=0

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.554

8485

2xy2+(2xy)y+1y=0

[_rational, _dAlembert]

1.510

8486

5y2+3yxy=0

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.567

8487

y2+3yxy=0

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.545

8488

y=yx+x3y2

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

1.177

8489

y=xy3

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

0.668

8490

x2y+y22yx=0
i.c.

[[_2nd_order, _missing_y]]

0.714

8491

x2y+y22yx=0
i.c.

[[_2nd_order, _missing_y]]

0.739

8492

yy+y2=0

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

1.207

8493

y2y+y3=0

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

0.552

8494

(1+y)y=y2

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.485

8495

2ay+y3=0

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]]

0.855

8496

xy=y+x5
i.c.

[[_2nd_order, _missing_y]]

1.333

8497

xy+y+x=0
i.c.

[[_2nd_order, _missing_y]]

1.337

8498

y=2yy3

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

0.463

8499

yy+y3y2=0

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

0.802

8500

y+β2y=0

[[_2nd_order, _missing_x]]

1.416