2.2.108 Problems 10701 to 10800

Table 2.217: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

10701

y=y(1x+yx2ln(x)+x3yln(x)xx2)(1+x)x

[_Bernoulli]

3.711

10702

y=yln(x)xy+2x5b+2x3ay2(ln(x)x1)x

[[_homogeneous, ‘class D‘], _Riccati]

9.037

10703

y=(ln(y)+x+x3+x4)yx

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

2.223

10704

y=(ln(y1)+ln(y+1)+2ln(x))x(y+1)28

[‘y=_G(x,y’)‘]

24.866

10705

y=(ln(y1)+ln(y+1)+2ln(x))2x(y+1)216

[‘y=_G(x,y’)‘]

53.222

10706

y=(y2+4ax)3(y2+4ax1)y

[_rational]

3.481

10707

y=2ax+2a+x3y2+4ax(x+1)y

[‘y=_G(x,y’)‘]

47.092

10708

y=ln(x)+e1x+4x2y+2x+2xy2+2x3ln(x)e1x

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

217.693

10709

y=(ln(y)x+ln(y)1)yx+1

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

3.110

10710

y=x2+2x+1+2x3x2+2x+14y2x+2

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

6.970

10711

y=bya+b2+ab+b2xbaxa2a(ay+b+a+bxax)

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2.652

10712

y=y(ln(1x)+ex+yx2ln(x)+x3yln(x)xx2)(ln(1x)+ex)x

[_Bernoulli]

4.264

10713

y=x2+x+2+2x3x24x+4y2x+2

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

6.349

10714

y=3x4+3x3+9x44y3(x+1)y2

[_rational]

39.999

10715

y=x2+x+ax+a2x2+2ax+a2+4y2(x+1)

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

3.028

10716

y=(1+y2e2x2+y3e3x2)ex2x

[_Abel]

2.198

10717

y=y(ex+ln(2x)x2yln(2x)x)exx

[_Bernoulli]

5.811

10718

y=x3(3x+3+9x44y3)(x+1)y2

[‘y=_G(x,y’)‘]

38.181

10719

y=(18x3/2+36y212x3y+x6)x36

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

4.546

10720

y=y3(1+2yln(x)y)x

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

2.519

10721

y=2ay+2ay416a2xy2+32a3x2

[[_1st_order, _with_linear_symmetries]]

1.573

10722

y=y3(1+yln(x)y)x

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

2.454

10723

y=ln(x)+2ln(2x)xy+ln(2x)+ln(2x)y2+ln(2x)x2ln(x)

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

5.490

10724

y=byacb+b2x+baxa2a(ayc+bx+ax)

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2.414

10725

y=(2x+2+y)y(ln(y)+2x1)(x+1)

[‘x=_G(y,y’)‘]

3.044

10726

y=(x3+3y2)y(6y2+x)x

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

1.768

10727

y=y(xy)x(xy3)

[_rational]

1.419

10728

y=(2y3/23ex)3ex4(2y3/23ex+2)y

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

7.917

10729

y=2y+1x(2+xy2+2xy3)

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

2.853

10730

y=x2xaxa+2x3x2+2ax+a2+4y2x+2

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

7.483

10731

y=2xsin(x)ln(2x)+ln(2x)x42ln(2x)x2y+ln(2x)y2sin(x)

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

148.818

10732

y=(ln(y)xln(y)+x3)yx+1

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

3.165

10733

y=(1+2yln(x))3(1+2yln(x)y)x

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

2.911

10734

y=2x2+2x+x42x2y1+y2x+1

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

3.172

10735

y=x(1+x2xy+2x3)x2y

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]

2.372

10736

y=2ax2y+2ay4x216a2xy2+32a3

[‘y=_G(x,y’)‘]

2.942

10737

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

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

2.489

10738

y=x+y42y2x2+x4y

[_rational]

3.217

10739

y=(ay2+bx2)3xa5/2(ay2+bx2+a)y

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

4.476

10740

y=cos(y)(xcos(y)+1)(xsin(y)1)(x+1)

unknown

56.113

10741

y=i(8ix+16y4+8y2x2+x4)32y

[_rational]

1.327

10742

y=xy+x4+2y2x2+y4

[_rational]

3.166

10743

y=(1+yln(x))3(1+yln(x)y)x

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

2.823

10744

y=i(ix+x4+2y2x2+y4)y

[_rational]

1.184

10745

y=y(tan(x)+ln(2x)xln(2x)x2y)xtan(x)

[_Bernoulli]

38.051

10746

y=y(x+y)x(x+y3)

[_rational]

1.413

10747

y=(xy)2(x+y)2xy

[_rational]

2.667

10748

y=(x2+3y2)y(6y2+x)x

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

1.579

10749

y=(ln(y)x+ln(y)+x4)yx(x+1)

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

2.635

10750

y=cos(y)(cos(y)x3x1)(xsin(y)1)(x+1)

unknown

83.054

10751

y=(x+1+x4ln(y))yln(y)x(x+1)

[‘x=_G(y,y’)‘]

3.315

10752

y=xy+x3+xy2+y3x2

[[_homogeneous, ‘class D‘], _rational, _Abel]

1.486

10753

y=y3/2y3/2+x22xy+y2

[[_1st_order, _with_linear_symmetries], _rational]

2.805

10754

y=2x3y+x6+y2x2+y3x4

[_rational, _Abel]

2.586

10755

y=4xy+x3+2x24x88y+2x2+4x8

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1.370

10756

y=(2x+2+x3y)y(ln(y)+2x1)(x+1)

[‘x=_G(y,y’)‘]

5.696

10757

y=i(54ix2+81y4+18x4y2+x8)x243y

[_rational]

1.438

10758

y=(1+xy2)3x4(xy2+1+x)y

[_rational]

3.497

10759

y=4xyx3+4x24x+88y+2x28x+8

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1.372

10760

y=(ln(y)x+ln(y)x)yx(x+1)

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

3.388

10761

y=(ln(y)x+ln(y)+x)yx(x+1)

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

2.422

10762

y=(ln(y)xln(y)+x4)yx(x+1)

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

3.271

10763

y=y(1ln((1+x)(x+1)x)+ln((1+x)(x+1)x)xy)x

[_Bernoulli]

14.410

10764

y=y(ln(x)xln((1+x)(x+1)x)+ln((1+x)(x+1)x)x2y)xln(x)

[_Bernoulli]

5.464

10765

y=8xyx3+2x28x+3232y+4x28x+32

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1.387

10766

y=y(y+1)x(y1+xy)

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

2.015

10767

y=i(16ix2+16y4+8x4y2+x8)x32y

[_rational]

1.414

10768

y=2y6y3+2+16xy2+32x2y4

[_rational]

3.112

10769

y=4yaxa2x32ax2b4ax+88y+2ax2+4bx+8

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1.738

10770

y=(x+1+ln(y)x)ln(y)yx(x+1)

[‘x=_G(y,y’)‘]

3.571

10771

y=xy+x+y2(1+x)(x+y)

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

3.056

10772

y=4xyx32ax24x+88y+2x2+4ax+8

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1.342

10773

y=xy+yxy+y+1

[[_1st_order, _with_linear_symmetries], _rational]

1.636

10774

y=y(ln(1x)ln(x2+1x)x+ln(x2+1x)x2y)xln(1x)

[_Bernoulli]

9.670

10775

y=y(y+1)x(y1+xy4)

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

3.047

10776

y=3x2y+1+y2x6+y3x9x3

[_rational, _Abel]

2.612

10777

y=x3y+x3+xy2+y3(1+x)x3

[[_homogeneous, ‘class D‘], _rational, _Abel]

2.677

10778

y=xy+y+xx2+y2x(x+1)

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

11.822

10779

y=(x4+x3+x+3y2)y(6y2+x)x

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

1.901

10780

y=y(tanh(1x)ln(x2+1x)x+ln(x2+1x)x2y)xtanh(1x)

[_Bernoulli]

42.867

10781

y=y(tanh(x)+ln(2x)xln(2x)x2y)xtanh(x)

[_Bernoulli]

44.745

10782

y=sinh(x)+x2ln(x)+2yln(x)x+ln(x)+y2ln(x)sinh(x)

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

31.436

10783

y=ln(x)sinh(x)x22sinh(x)xysinh(x)sinh(x)y2ln(x)

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

68.936

10784

y=yln(x)+cosh(x)xay2+cosh(x)x3bxln(x)

[[_homogeneous, ‘class D‘], _Riccati]

47.458

10785

y=x(x1+x22x2y+2x4)(x2y)(x+1)

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

2.293

10786

y=y(ln(1+x)+coth(x+1)xcoth(x+1)x2y)xln(1+x)

[_Bernoulli]

42.121

10787

y=ln(1+x)coth(x+1)x22coth(x+1)xycoth(x+1)coth(x+1)y2ln(1+x)

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

186.936

10788

y=2xln(11+x)coth(x+11+x)+coth(x+11+x)y22coth(x+11+x)x2y+coth(x+11+x)x4ln(11+x)

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

352.082

10789

y=2x2cosh(11+x)2xcosh(11+x)1+y22x2y+x4x+xy22x3y+x5(1+x)cosh(11+x)

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

192.754

10790

y=y(cosh(1x+1)x+cosh(1x+1)x+x2yx2+x3y)x(1+x)cosh(1x+1)

[_Bernoulli]

9.704

10791

y=y(1+xy)x(xy+1y)

[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]

2.097

10792

y=yx(1+y+x2y3+y4x3)

[_rational]

7.414

10793

y=x3+3ax2+3a2x+a3+xy2+ay2+y3(x+a)3

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

74.847

10794

y=y3xe3x2e9x229e3x22+3e3x22y+9y

[[_Abel, ‘2nd type‘, ‘class C‘]]

4.434

10795

y=y(1cosh(x+11+x)x+cosh(x+11+x)x2ycosh(x+11+x)x2+cosh(x+11+x)x3y)x

[_Bernoulli]

13.204

10796

y=(x+y+1)y(2y3+y+x)(x+1)

[_rational]

2.683

10797

y=y(1xex+11+x+x2ex+11+xyx2ex+11+x+x3ex+11+xy)x

[_Bernoulli]

5.106

10798

y=b3+6b2x12bx2+8x34by2+8xy2+8y3(2xb)3

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

76.034

10799

y=(yex24x+2+2y2ex22+2y3e3x24)ex242

[_Abel]

3.511

10800

y=1x_F1(y+1x)x

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

2.659