2.2.109 Problems 10801 to 10900

Table 2.219: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

10801

y=_F1(y22ln(x))y2x

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

3.178

10802

y=sin(2y)xsin(2y)+cos(2y)x4+x42x(x+1)

[‘y=_G(x,y’)‘]

19.459

10803

y=xy+y+x4x2+y2x(x+1)

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

7.165

10804

y=sin(2y)xsin(2y)+xcos(2y)+x2x(x+1)

[‘y=_G(x,y’)‘]

12.894

10805

y=1x_F1(yln(x))yey

[NONE]

3.597

10806

y=(2y+1)(y+1)x(2y2+x+2xy)

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

2.313

10807

y=125+300x240x2+64x380y2+64xy2+64y3(4x5)3

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

75.500

10808

y=x+y+y22yln(x)x+x2ln(x)2x

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

1.780

10809

y=x3ey+x4+eyyeyln(ey+x)+xyln(ey+x)x+xx2

[‘y=_G(x,y’)‘]

39.787

10810

y=x22+x36y+x2x36y+x3x36y

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

46.427

10811

y=(ax3+2ax4+8y+2x2ax4+8y+2x3ax4+8y)a2

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

39.150

10812

y=y(3x3y3+y2x7)x(x3y+1)

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

2.575

10813

y=(3+y)3e9x22xe3x22e3x2243e3x22+81e3x22y+243y

[[_Abel, ‘2nd type‘, ‘class C‘]]

5.086

10814

y=(xy)3(x+y)3x(y2+x21)y

[_rational]

2.729

10815

y=2cos(y)+x3cos(2y)ln(x)+x3ln(x)2sin(y)ln(x)x

[‘y=_G(x,y’)‘]

58.917

10816

y=yx(1+xy+xy3+xy4)

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

2.819

10817

y=2x3+x2+3y+x2x2+3y+x3x2+3y

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

36.797

10818

y=2cos(y)+x2cos(2y)ln(x)+x2ln(x)2sin(y)ln(x)x

[‘y=_G(x,y’)‘]

58.983

10819

y=y(1+xy)x(xy1+y4x3)

[_rational]

2.117

10820

y=(4ex24x2ex2+4y24x2ex2y+x4e2x2)x4

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

2.741

10821

y=y(x+y)x(x+y+y3+y4)

[_rational]

1.531

10822

y=y(x3+x2y+y2)x2(1+x)(x+y)

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

3.935

10823

y=((x2+1)3/2x2+(x2+1)3/2+y2(x2+1)3/2+x2y3+y3)x(x2+1)3

[_Abel]

17.556

10824

y=(3xy2+x+3y2)y(6y2+x)x(x+1)

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

2.622

10825

y=y+x3x2+y2x2x2+y2yx

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

6.904

10826

y=(2y+1)(y+1)x(2y2+xy3+2xy4)

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

3.153

10827

y=1+24x2y+1x3+2x54x2y+1+2x64x2y+12x3

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

42.284

10828

y=y(xy)x(xyy3y4)

[_rational]

1.537

10829

y=2a+y2+4ax+x2y2+4ax+x3y2+4axy

[‘y=_G(x,y’)‘]

55.730

10830

y=(x+y+1)y(y4+y3+y2+x)(x+1)

[_rational]

2.481

10831

y=y+x4x2+y2x3x2+y2yx

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

7.183

10832

y=(x4+3xy2+3y2)y(6y2+x)x(x+1)

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

3.097

10833

y=1(y3)2/3x_F1(y33ln(x))(y3)1/3x

[NONE]

2.574

10834

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

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

1.704

10835

y=30x3+25x+25y220x3y100yx+4x6+40x7/2+100x25x

[_rational, _Riccati]

22.113

10836

y=(eyxy+eyxx+x2)eyxx

[[_1st_order, _with_linear_symmetries]]

2.213

10837

y=(eyxy+eyxx+x3)eyxx

[[_1st_order, _with_linear_symmetries]]

2.003

10838

y=bx3+c2a2cbx2a+2cy2a3/2+b2x4a2y2a3/2bx2+a5/2y4ax2y

[_rational]

5.290

10839

y=y+x2ln(x)3+2x2ln(x)2y+x2ln(x)y2xln(x)

[_Riccati]

6.840

10840

y=y+x3ln(x)3+2x3ln(x)2y+x3ln(x)y2xln(x)

[_Riccati]

2.984

10841

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

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

1.717

10842

y=3x3+9x4+4y3+x29x4+4y3+x39x4+4y3y2

[NONE]

39.198

10843

y=1x+(1y+1)x+_F1((1y+1)x)x2_F1((1y+1)x)x2(1y+1)

[‘y=_G(x,y’)‘]

2.374

10844

y=x2+12+x2+2x+14y+x2x2+2x+14y+x3x2+2x+14y

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

36.358

10845

y=cosh(x)sinh(x)+_F1(yln(sinh(x)))

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

5.129

10846

y=x2+1+x24x+4y+x2x24x+4y+x3x24x+4y

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

37.032

10847

y=1sin(x)+_F1(yln(sin(x))+ln(cos(x)+1))

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

7.891

10848

y=b3+y2b3+2yb2ax+x2ba2+y3b3+3y2b2ax+3yba2x2+a3x3b3

[[_homogeneous, ‘class C‘], _Abel]

10.546

10849

y=α3+y2α3+2yα2βx+αβ2x2+y3α3+3y2α2βx+3yαβ2x2+β3x3α3

[[_homogeneous, ‘class C‘], _Abel]

10.727

10850

y=14xy+12+2x+x3y3+6y2x2x2(xy+2+x)

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

2.421

10851

y=y(ln(x)+ln(y)1+x2ln(x)2+2x2ln(y)ln(x)+x2ln(y)2)x

[NONE]

4.447

10852

y=y(ln(y)1+ln(x)+x3ln(x)2+2x3ln(y)ln(x)+x3ln(y)2)x

[NONE]

4.409

10853

y=(1x_F1(y22x))xy2

[NONE]

2.575

10854

y=x4+14+x22x+1+8y+x2x22x+1+8y+x3x22x+1+8y

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

36.918

10855

y=a3+y2a3+2ya2bx+ab2x2+y3a3+3y2a2bx+3yab2x2+b3x3a3

[[_homogeneous, ‘class C‘], _Abel]

10.569

10856

y=x_F1(y22x)y2x

[NONE]

2.625

10857

y=sin(2y)+xcos(2y)+cos(2y)x3+cos(2y)x4+x+x3+x42x

[‘y=_G(x,y’)‘]

3.848

10858

y=(ye1xx_F1(ye1x))e1xx

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

3.000

10859

y=y+xx2+y2+x3x2+y2+x4x2+y2x

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

7.897

10860

y=y(ex22xy+ex24x+2y2e3x24)ex242yex24+2

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

4.029

10861

y=(ln(y1)y(1y)ln(x)xln(y1)(1y)ln(x)xf(x))(1y)

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

3.919

10862

y=x2a2+x2+2ax+a2+4y+x2x2+2ax+a2+4y+x3x2+2ax+a2+4y

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

38.094

10863

y=2x3+1+y2+2x2y3+x49+y3+y2x2+yx43+x627

[[_1st_order, _with_linear_symmetries], _Abel]

1.347

10864

y=2x+1+y22x2y+x4+y33y2x2+3yx4x6

[[_1st_order, _with_linear_symmetries], _Abel]

1.254

10865

y=x+12y+3x22x2y+2x4+x32x3y+2x5x2y

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

2.447

10866

y=(eyxy+eyxx+x+x3+x4)eyxx

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

4.279

10867

y=2xy2+4yln(2x+1)x+2ln(2x+1)2x+y22+ln(2x+1)2+2yln(2x+1)2x+1

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

2.192

10868

y=30x3y+12x6+70x7/230x325yx+50x25x255(5y+2x3+10x5)x

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

2.689

10869

y=2y+1x(2+x+xy2+3xy3+2xy+2xy4)

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

2.970

10870

y=(256ax2+512+512y2+128yax4+8a2x8+512y3+192x4ay2+24ya2x8+a3x12)x512

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

2.077

10871

y=xyy+x5x2+y2x4x2+y2yx(x+1)

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

34.743

10872

y=y2(x2y2x2xy+y)2(2+xy2y)x

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

3.182

10873

y=2xy+2x32xy3+3y2x23yx4+x6y+x21

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

2.058

10874

y=1+y48axy2+16a2x2+y612y4ax+48y2a2x264a3x3y

[_rational]

3.181

10875

y=xyy+x2+y2x2xx2+y2yx(x+1)

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

9.806

10876

y=2ay2a2ay4+16a2xy232a3x22ay6+24y4a2x96y2a3x2+128a4x3

[[_1st_order, _with_linear_symmetries]]

1.973

10877

y=18xy6x318x+27y3+27y2x2+9yx4+x627y+9x2+27

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

2.183

10878

y=(108x3/2216216y2+72x3y6x6216y3+108x3y218yx6+x9)x216

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

7.836

10879

y=(a3+y4a3+2y2a2bx2+ax4b2+y6a3+3y4a2bx2+3y2ab2x4+b3x6)xa7/2y

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

5.056

10880

y=(1y4+2y2x2x4y6+3x2y43x4y2+x6)xy

[_rational]

2.648

10881

y=i(32ix+64+64y4+32y2x2+4x4+64y6+48x2y4+12x4y2+x6)128y

[_rational]

3.640

10882

y=2x24x3y+1+x4y2+x6y33y2x5+3yx4x3x4

[_rational, _Abel]

1.961

10883

y=ya2x+a+a2x+y3a3x3+3y2a2x2+3yax+1a2x2(yax+1+ax)

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

2.587

10884

y=6x2y2x+15x3y22xy+y3x4x2(x2yx+1)

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

3.137

10885

y=(88y3+24y3/2ex18e2x8y9/2+36y3ex54y3/2e2x+27e3x)ex8y

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

42.122

10886

y=xy+1+y4+2y2x2+x4+y6+3x2y4+3x4y2+x6

[_rational]

2.610

10887

y=y2(2y+2x2+2x2y+yx4)x3(x2y+x2y)

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

3.348

10888

y=y2+2xy+x2+e2y2+x21y2+2xy+x2e2y2+x21

[[_1st_order, _with_linear_symmetries]]

3.528

10889

y=6x+x3+x3y2+4x2y+x3y3+6y2x2+12xy+8x3

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

3.111

10890

y=i(ix+1+x4+2y2x2+y4+x6+3x4y2+3x2y4+y6)y

[_rational]

3.566

10891

y=(256ax2y32a2x6256ax2+512y3+192x4ay2+24ya2x8+a3x12)x512y+64ax4+512

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

4.705

10892

y=x+1+y42y2x2+x4+y63x2y4+3x4y2x6y

[_rational]

2.661

10893

y=(108x3/2y+18x9/2108x3/2216y3+108x3y218yx6+x9)x216y+36x3216

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

11.089

10894

y=32x5y+8x3+32x5+64x6y3+48x4y2+12x2y+116x6(4x2y+1+4x2)

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

3.479

10895

y=32x5+64x6+64y2x6+32yx4+4x2+64x6y3+48x4y2+12x2y+164x8

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

1.822

10896

y=2a(y2+4ax1)y3+4yaxy2ay6+24y4a2x96y2a3x2+128a4x3

[[_1st_order, _with_linear_symmetries], _rational]

2.141

10897

y=(yaln(y)x+x2)y(yln(y)yln(x)y+ax)x

[NONE]

2.039

10898

y=xy2+x3xy6+3x2y43x4y2+x6(y2+x21)y

[_rational]

3.075

10899

y=sin(yx)(y+2x2sin(y2x)cos(y2x))2sin(y2x)xcos(y2x)

[[_homogeneous, ‘class D‘]]

8.978

10900

y=sin(yx)(y+2x3cos(y2x)sin(y2x))2sin(y2x)xcos(y2x)

[[_homogeneous, ‘class D‘]]

12.934