2.2.55 Problems 5401 to 5500

Table 2.123: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

5401

\begin{align*} {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.720

5402

\begin{align*} {y^{\prime }}^{2}-4 \left (x +1\right ) y^{\prime }+4 y&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.238

5403

\begin{align*} {y^{\prime }}^{2}+a x y^{\prime }&=b c \,x^{2} \\ \end{align*}

[_quadrature]

0.569

5404

\begin{align*} {y^{\prime }}^{2}-a x y^{\prime }+a y&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.276

5405

\begin{align*} {y^{\prime }}^{2}+a x y^{\prime }+b \,x^{2}+c y&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘]]

4.230

5406

\begin{align*} {y^{\prime }}^{2}+\left (b x +a \right ) y^{\prime }+c&=b y \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.282

5407

\begin{align*} {y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 y^{\prime } x&=0 \\ \end{align*}

[_quadrature]

0.201

5408

\begin{align*} {y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries]]

0.289

5409

\begin{align*} {y^{\prime }}^{2}-2 a \,x^{3} y^{\prime }+4 a \,x^{2} y&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries]]

0.290

5410

\begin{align*} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries]]

0.469

5411

\begin{align*} {y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1&=0 \\ \end{align*}

[_quadrature]

0.973

5412

\begin{align*} y^{\prime } y+{y^{\prime }}^{2}&=x \left (x +y\right ) \\ \end{align*}

[_quadrature]

0.203

5413

\begin{align*} {y^{\prime }}^{2}-y^{\prime } y+{\mathrm e}^{x}&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries]]

0.480

5414

\begin{align*} {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+y x&=0 \\ \end{align*}

[_quadrature]

0.369

5415

\begin{align*} {y^{\prime }}^{2}-2 y^{\prime } y-2 x&=0 \\ \end{align*}

[_dAlembert]

24.875

5416

\begin{align*} {y^{\prime }}^{2}+\left (1+2 y\right ) y^{\prime }+y \left (y-1\right )&=0 \\ \end{align*}

[_quadrature]

1.296

5417

\begin{align*} {y^{\prime }}^{2}-2 \left (x -y\right ) y^{\prime }-4 y x&=0 \\ \end{align*}

[_quadrature]

0.382

5418

\begin{align*} {y^{\prime }}^{2}-\left (4 y+1\right ) y^{\prime }+\left (4 y+1\right ) y&=0 \\ \end{align*}

[_quadrature]

1.239

5419

\begin{align*} {y^{\prime }}^{2}-2 \left (1-3 y\right ) y^{\prime }-\left (4-9 y\right ) y&=0 \\ \end{align*}

[_quadrature]

3.509

5420

\begin{align*} {y^{\prime }}^{2}+\left (a +6 y\right ) y^{\prime }+y \left (3 a +b +9 y\right )&=0 \\ \end{align*}

[_quadrature]

14.354

5421

\begin{align*} {y^{\prime }}^{2}+a y y^{\prime }-a x&=0 \\ \end{align*}

[_dAlembert]

2.991

5422

\begin{align*} {y^{\prime }}^{2}-a y y^{\prime }-a x&=0 \\ \end{align*}

[_dAlembert]

28.836

5423

\begin{align*} {y^{\prime }}^{2}+\left (a x +b y\right ) y^{\prime }+a b x y&=0 \\ \end{align*}

[_quadrature]

0.543

5424

\begin{align*} {y^{\prime }}^{2}-x y^{\prime } y+y^{2} \ln \left (a y\right )&=0 \\ \end{align*}

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

1.121

5425

\begin{align*} {y^{\prime }}^{2}-\left (2 y x +1\right ) y^{\prime }+2 y x&=0 \\ \end{align*}

[_quadrature]

0.200

5426

\begin{align*} {y^{\prime }}^{2}-\left (4+y^{2}\right ) y^{\prime }+4+y^{2}&=0 \\ \end{align*}

[_quadrature]

2.612

5427

\begin{align*} {y^{\prime }}^{2}-\left (x -y\right ) y y^{\prime }-x y^{3}&=0 \\ \end{align*}

[_separable]

0.191

5428

\begin{align*} {y^{\prime }}^{2}+y^{2} y^{\prime } x +y^{3}&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘]]

1.418

5429

\begin{align*} {y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3}&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries]]

13.945

5430

\begin{align*} {y^{\prime }}^{2}-x y \left (y^{2}+x^{2}\right ) y^{\prime }+y^{4} x^{4}&=0 \\ \end{align*}

[_separable]

0.855

5431

\begin{align*} {y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4}&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘]]

1.316

5432

\begin{align*} {y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \\ \end{align*}

[_separable]

1.401

5433

\begin{align*} {y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}}&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries]]

97.200

5434

\begin{align*} {y^{\prime }}^{2}&={\mathrm e}^{4 x -2 y} \left (y^{\prime }-1\right ) \\ \end{align*}

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

2.487

5435

\begin{align*} 2 {y^{\prime }}^{2}+y^{\prime } x -2 y&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _dAlembert]

1.177

5436

\begin{align*} 2 {y^{\prime }}^{2}-\left (1-x \right ) y^{\prime }-y&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.235

5437

\begin{align*} 2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 y x&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘]]

0.764

5438

\begin{align*} 2 {y^{\prime }}^{2}+2 \left (6 y-1\right ) y^{\prime }+3 y \left (6 y-1\right )&=0 \\ \end{align*}

[_quadrature]

7.592

5439

\begin{align*} 3 {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.444

5440

\begin{align*} 3 {y^{\prime }}^{2}+4 y^{\prime } x +x^{2}-y&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘]]

0.781

5441

\begin{align*} 4 {y^{\prime }}^{2}&=9 x \\ \end{align*}

[_quadrature]

0.490

5442

\begin{align*} 4 {y^{\prime }}^{2}+2 x \,{\mathrm e}^{-2 y} y^{\prime }-{\mathrm e}^{-2 y}&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries]]

0.547

5443

\begin{align*} 4 {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x -2 y} y^{\prime }-{\mathrm e}^{2 x -2 y}&=0 \\ \end{align*}

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

1.924

5444

\begin{align*} 5 {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.738

5445

\begin{align*} 5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.719

5446

\begin{align*} 9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5}&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries]]

0.677

5447

\begin{align*} x {y^{\prime }}^{2}&=a \\ \end{align*}

[_quadrature]

0.683

5448

\begin{align*} x {y^{\prime }}^{2}&=\left (a -x \right )^{2} \\ \end{align*}

[_quadrature]

1.300

5449

\begin{align*} x {y^{\prime }}^{2}&=y \\ \end{align*}

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

2.191

5450

\begin{align*} x {y^{\prime }}^{2}+x -2 y&=0 \\ \end{align*}

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

2.008

5451

\begin{align*} x {y^{\prime }}^{2}+y^{\prime }&=y \\ \end{align*}

[_rational, _dAlembert]

1.782

5452

\begin{align*} x {y^{\prime }}^{2}+2 y^{\prime }-y&=0 \\ \end{align*}

[_rational, _dAlembert]

1.767

5453

\begin{align*} x {y^{\prime }}^{2}-2 y^{\prime }-y&=0 \\ \end{align*}

[_rational, _dAlembert]

1.761

5454

\begin{align*} x {y^{\prime }}^{2}+4 y^{\prime }-2 y&=0 \\ \end{align*}

[_rational, _dAlembert]

1.932

5455

\begin{align*} x {y^{\prime }}^{2}+y^{\prime } x -y&=0 \\ \end{align*}

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

2.286

5456

\begin{align*} x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x&=0 \\ \end{align*}

[_quadrature]

0.228

5457

\begin{align*} x {y^{\prime }}^{2}+y^{\prime } y+a&=0 \\ \end{align*}

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

20.323

5458

\begin{align*} x {y^{\prime }}^{2}-y^{\prime } y+a&=0 \\ \end{align*}

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

0.688

5459

\begin{align*} x {y^{\prime }}^{2}-y^{\prime } y+a x&=0 \\ \end{align*}

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

1.979

5460

\begin{align*} x {y^{\prime }}^{2}+y^{\prime } y-x^{2}&=0 \\ \end{align*}

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

9.444

5461

\begin{align*} x {y^{\prime }}^{2}+y^{\prime } y+x^{3}&=0 \\ \end{align*}

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

8.211

5462

\begin{align*} x {y^{\prime }}^{2}-y^{\prime } y+a y&=0 \\ \end{align*}

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

1.779

5463

\begin{align*} x {y^{\prime }}^{2}+y^{\prime } y-y^{4}&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘]]

1.158

5464

\begin{align*} x {y^{\prime }}^{2}+\left (-y+a \right ) y^{\prime }+b&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

0.269

5465

\begin{align*} x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

0.289

5466

\begin{align*} x {y^{\prime }}^{2}+\left (a +x -y\right ) y^{\prime }-y&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

0.315

5467

\begin{align*} x {y^{\prime }}^{2}-\left (3 x -y\right ) y^{\prime }+y&=0 \\ \end{align*}

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

8.266

5468

\begin{align*} x {y^{\prime }}^{2}+\left (a +b x -y\right ) y^{\prime }-b y&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

0.336

5469

\begin{align*} x {y^{\prime }}^{2}-2 y^{\prime } y+a&=0 \\ \end{align*}

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

1.014

5470

\begin{align*} x {y^{\prime }}^{2}+2 y^{\prime } y-x&=0 \\ \end{align*}

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

22.683

5471

\begin{align*} x {y^{\prime }}^{2}-2 y^{\prime } y+a x&=0 \\ \end{align*}

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

0.931

5472

\begin{align*} x {y^{\prime }}^{2}-2 y^{\prime } y+x +2 y&=0 \\ \end{align*}

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

0.981

5473

\begin{align*} x {y^{\prime }}^{2}-3 y^{\prime } y+9 x^{2}&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘]]

0.983

5474

\begin{align*} x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y&=0 \\ \end{align*}

[_quadrature]

0.200

5475

\begin{align*} x {y^{\prime }}^{2}-a y y^{\prime }+b&=0 \\ \end{align*}

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

29.484

5476

\begin{align*} x {y^{\prime }}^{2}+a y y^{\prime }+b x&=0 \\ \end{align*}

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

3.563

5477

\begin{align*} x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\ \end{align*}

[_quadrature]

0.188

5478

\begin{align*} x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\ \end{align*}

[_quadrature]

0.144

5479

\begin{align*} x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\ \end{align*}

[_quadrature]

0.252

5480

\begin{align*} \left (x +1\right ) {y^{\prime }}^{2}&=y \\ \end{align*}

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

1.829

5481

\begin{align*} \left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

0.309

5482

\begin{align*} \left (a -x \right ) {y^{\prime }}^{2}+y^{\prime } y-b&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.298

5483

\begin{align*} 2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}

[_rational, _dAlembert]

2.382

5484

\begin{align*} 3 x {y^{\prime }}^{2}-6 y^{\prime } y+x +2 y&=0 \\ \end{align*}

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

1.046

5485

\begin{align*} \left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.306

5486

\begin{align*} \left (3 x +5\right ) {y^{\prime }}^{2}-\left (3+3 y\right ) y^{\prime }+y&=0 \\ \end{align*}

[_dAlembert]

2.688

5487

\begin{align*} 4 x {y^{\prime }}^{2}&=\left (a -3 x \right )^{2} \\ \end{align*}

[_quadrature]

1.339

5488

\begin{align*} 4 x {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}

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

0.924

5489

\begin{align*} 4 x {y^{\prime }}^{2}-3 y^{\prime } y+3&=0 \\ \end{align*}

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

0.967

5490

\begin{align*} 4 x {y^{\prime }}^{2}+4 y^{\prime } y&=1 \\ \end{align*}

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

5.410

5491

\begin{align*} 4 x {y^{\prime }}^{2}+4 y^{\prime } y-y^{4}&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘]]

1.125

5492

\begin{align*} 4 \left (-x +2\right ) {y^{\prime }}^{2}+1&=0 \\ \end{align*}

[_quadrature]

0.234

5493

\begin{align*} 16 x {y^{\prime }}^{2}+8 y^{\prime } y+y^{6}&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘]]

0.766

5494

\begin{align*} x^{2} {y^{\prime }}^{2}&=a^{2} \\ \end{align*}

[_quadrature]

0.260

5495

\begin{align*} x^{2} {y^{\prime }}^{2}&=y^{2} \\ \end{align*}

[_separable]

0.148

5496

\begin{align*} x^{2} {y^{\prime }}^{2}+x^{2}-y^{2}&=0 \\ \end{align*}

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

3.442

5497

\begin{align*} x^{2} {y^{\prime }}^{2}&=\left (x -y\right )^{2} \\ \end{align*}

[_linear]

0.197

5498

\begin{align*} x^{2} {y^{\prime }}^{2}+y^{2}-y^{4}&=0 \\ \end{align*}

[_separable]

2.100

5499

\begin{align*} x^{2} {y^{\prime }}^{2}-y^{\prime } x +y \left (1-y\right )&=0 \\ \end{align*}

[_separable]

0.170

5500

\begin{align*} x^{2} {y^{\prime }}^{2}+2 a x y^{\prime }+a^{2}+x^{2}-2 a y&=0 \\ \end{align*}

[_rational]

1.523