2.2.54 Problems 5301 to 5400

Table 2.109: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

5301

(ax3+(ax+by)3)yy+x((ax+by)3+by3)=0

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

19.604

5302

(x+2y+2x2y3+xy4)y+(1+y4)y=0

[_rational]

100.476

5303

2x(x3+y4)y=(x3+2y4)y

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

7.046

5304

x(1x2y4)y+y=0

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

15.757

5305

(x2y5)y=2xy

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

2.184

5306

x(x3+y5)y=(x3y5)y

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

2.289

5307

x3(1+5x3y7)y+(3x5y51)y3=0

[_rational]

1.833

5308

(1+a(x+y))ny+a(x+y)n=0

[[_homogeneous, ‘class C‘], _dAlembert]

4.855

5309

x(a+xyn)y+by=0

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

1.615

5310

f(x)ymy+g(x)ym+1+h(x)yn=0

[_Bernoulli]

4.944

5311

yb2+y2=a2+x2

[_separable]

2.034

5312

yb2y2=a2x2

[_separable]

2.270

5313

yy=x

[_separable]

66.038

5314

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

[[_homogeneous, ‘class C‘], _dAlembert]

1.569

5315

yxy+xy=xy

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

33.194

5316

(x2xy)y=y

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

24.385

5317

(y+1+y2)(x2+1)3/2y=1+y2

[_separable]

2.950

5318

(y+1+y2)(x2+1)3/2y=1+y2

[_separable]

2.902

5319

(xx2+y2)y=y

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

18.819

5320

x(1x2y2)y=y

[‘y=_G(x,y’)‘]

3.949

5321

x(x+x2+y2)y+yx2+y2=0

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

193.199

5322

xy(x+x2y2)y=xy2(x2y2)3/2

[[_1st_order, _with_linear_symmetries], _dAlembert]

42.096

5323

(x1+x2+y2y(x2+y2))y=x(x2+y2)+y1+x2+y2

[[_1st_order, _with_linear_symmetries]]

3.125

5324

ycos(y)(cos(y)sin(A)sin(x))+cos(x)(cos(x)sin(A)sin(y))=0

unknown

39.572

5325

(acos(bx+ay)bsin(ax+by))y+bcos(bx+ay)asin(ax+by)=0

[_exact]

37.986

5326

(x+cos(x)sec(y))y+tan(y)ysin(x)sec(y)=0

[NONE]

43.296

5327

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

[[_1st_order, _with_linear_symmetries]]

1.942

5328

x(xytan(yx))y+(x+ytan(yx))y=0

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

7.309

5329

(ex+xey)y+yex+ey=0

[_exact]

1.727

5330

(12xln(y))y+2y=0

[[_1st_order, _with_linear_symmetries]]

1.707

5331

(sinh(x)+xcosh(y))y+ycosh(x)+sinh(y)=0

[_exact]

36.172

5332

y(1+sinh(x))sinh(y)+cosh(x)(cosh(y)1)=0

[_separable]

8.996

5333

y2=axn

[_quadrature]

0.433

5334

y2=y

[_quadrature]

0.358

5335

y2=xy

[[_homogeneous, ‘class C‘], _dAlembert]

0.705

5336

y2=x2+y

[[_homogeneous, ‘class G‘]]

1.507

5337

y2+x2=4y

[[_homogeneous, ‘class G‘]]

1.570

5338

y2+3x2=8y

[[_homogeneous, ‘class G‘]]

1.592

5339

y2+ax2+by=0

[[_homogeneous, ‘class G‘]]

1.710

5340

y2=1+y2

[_quadrature]

0.862

5341

y2=1y2

[_quadrature]

0.685

5342

y2=a2y2

[_quadrature]

0.843

5343

y2=a2y2

[_quadrature]

0.957

5344

y2=a+by2

[_quadrature]

1.176

5345

y2=y2x2

[_separable]

2.446

5346

y2=(y1)y2

[_quadrature]

15.083

5347

y2=(ya)(yb)(yc)

[_quadrature]

70.980

5348

y2=a2yn

[_quadrature]

0.783

5349

y2=a2(1ln(y)2)y2

[_quadrature]

0.868

5350

y2+f(x)(ya)(yb)=0

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

1.104

5351

y2+f(x)(ya)2(yb)=0

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

1.092

5352

y2+f(x)(ya)(yb)(yc)=0

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

4.507

5353

y2+f(x)(ya)2(yb)(yc)=0

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

2.095

5354

y2=f(x)2(ya)(yb)(yc)2

[_separable]

1.577

5355

y2=f(x)2(yu(x))2(ya)(yb)

[‘y=_G(x,y’)‘]

12.788

5356

y2+2y+x=0

[_quadrature]

0.187

5357

y22y+a(xy)=0

[[_homogeneous, ‘class C‘], _dAlembert]

0.444

5358

y22yy2=0

[_quadrature]

11.882

5359

y25y+6=0

[_quadrature]

0.352

5360

y27y+12=0

[_quadrature]

0.332

5361

y2+ay+b=0

[_quadrature]

0.190

5362

y2+ay+bx=0

[_quadrature]

0.201

5363

y2+ay+by=0

[_quadrature]

0.495

5364

y2+xy+1=0

[_quadrature]

0.268

5365

y2+xyy=0

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.414

5366

y2xy+y=0

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.405

5367

y2xyy=0

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.452

5368

y2+xy+xy=0

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.500

5369

y2+(1x)y+y=0

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.428

5370

y2(x+1)y+y=0

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.424

5371

y2(2x)y+1y=0

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.479

5372

y2+(x+a)yy=0

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.462

5373

y22xy+1=0

[_quadrature]

0.299

5374

y2+2xy3x2=0

[_quadrature]

0.406

5375

y2+2xyy=0

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.458

5376

y2+2xyy=0

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.447

5377

y22xy+2y=0

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.405

5378

y2(2x+1)yx(1x)=0

[_quadrature]

0.210

5379

y2+2(1x)y2x+2y=0

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.492

5380

y2+3xyy=0

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.502

5381

y24(x+1)y+4y=0

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.442

5382

y2+axy=bcx2

[_quadrature]

0.214

5383

y2axy+ay=0

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.477

5384

y2+axy+bx2+cy=0

[[_homogeneous, ‘class G‘]]

2.624

5385

y2+(bx+a)y+c=by

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.664

5386

y22x2y+2xy=0

[_quadrature]

0.353

5387

y2+ax3y2ax2y=0

[[_1st_order, _with_linear_symmetries]]

2.580

5388

y22ax3y+4ax2y=0

[[_1st_order, _with_linear_symmetries]]

2.179

5389

y2+4x5y12x4y=0

[[_1st_order, _with_linear_symmetries]]

1.803

5390

y22ycosh(x)+1=0

[_quadrature]

0.388

5391

y2+yy=(x+y)x

[_quadrature]

0.502

5392

y2yy+ex=0

[[_1st_order, _with_linear_symmetries]]

3.914

5393

y2+(x+y)y+xy=0

[_quadrature]

0.518

5394

y22yy2x=0

[_dAlembert]

41.984

5395

y2+(2y+1)y+y(y1)=0

[_quadrature]

0.421

5396

y22(xy)y4xy=0

[_quadrature]

0.626

5397

y2(1+4y)y+(1+4y)y=0

[_quadrature]

1.135

5398

y22(13y)y(49y)y=0

[_quadrature]

38.253

5399

y2+(a+6y)y+y(3a+b+9y)=0

[_quadrature]

39.197

5400

y2+ayyax=0

[_dAlembert]

1.809