2.2.55 Problems 5401 to 5500

Table 2.127: 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]

1.799

5402

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.681

5403

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

[_quadrature]

3.218

5404

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.818

5405

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

[[_homogeneous, ‘class G‘]]

116.119

5406

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.745

5407

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

[_quadrature]

0.303

5408

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

[[_1st_order, _with_linear_symmetries]]

0.806

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]]

0.719

5410

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

[[_1st_order, _with_linear_symmetries]]

1.457

5411

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

[_quadrature]

1.856

5412

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

[_quadrature]

0.352

5413

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

[[_1st_order, _with_linear_symmetries]]

1.463

5414

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

[_quadrature]

0.921

5415

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

[_dAlembert]

22.129

5416

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

[_quadrature]

6.715

5417

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

[_quadrature]

0.954

5418

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

[_quadrature]

10.290

5419

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

[_quadrature]

216.343

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]

33.763

5421

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

[_dAlembert]

8.352

5422

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

[_dAlembert]

22.911

5423

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

[_quadrature]

1.556

5424

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

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

3.963

5425

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

[_quadrature]

0.355

5426

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

[_quadrature]

5.626

5427

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

[_separable]

0.391

5428

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

[[_homogeneous, ‘class G‘]]

9.817

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]]

64.583

5430

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

[_separable]

2.582

5431

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

[[_homogeneous, ‘class G‘]]

5.743

5432

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

[_separable]

3.812

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]]

172.206

5434

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

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

5.909

5435

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

2.703

5436

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.711

5437

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

[[_homogeneous, ‘class G‘]]

4.576

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]

14.551

5439

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

4.529

5440

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

[[_homogeneous, ‘class G‘]]

8.164

5441

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

[_quadrature]

2.148

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]]

1.378

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]

4.525

5444

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

1.758

5445

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

1.776

5446

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

[[_1st_order, _with_linear_symmetries]]

1.804

5447

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

[_quadrature]

8.327

5448

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

[_quadrature]

4.460

5449

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

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

8.379

5450

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

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

8.902

5451

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

[_rational, _dAlembert]

4.050

5452

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

[_rational, _dAlembert]

4.085

5453

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

[_rational, _dAlembert]

4.100

5454

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

[_rational, _dAlembert]

4.266

5455

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

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

9.239

5456

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

[_quadrature]

0.442

5457

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

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

210.494

5458

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

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

4.650

5459

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

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

9.816

5460

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

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

104.318

5461

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

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

153.273

5462

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

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

11.931

5463

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

[[_homogeneous, ‘class G‘]]

3.843

5464

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

0.898

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]

0.799

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]

0.809

5467

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

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

19.224

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]

0.842

5469

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

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

7.311

5470

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

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

127.869

5471

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

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

5.035

5472

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

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

4.289

5473

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

[[_homogeneous, ‘class G‘]]

5.756

5474

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

[_quadrature]

0.359

5475

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

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

58.270

5476

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

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

26.855

5477

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

[_quadrature]

0.401

5478

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

[_quadrature]

0.299

5479

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

[_quadrature]

0.517

5480

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

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

5.535

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]

0.842

5482

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.813

5483

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

[_rational, _dAlembert]

7.510

5484

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

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

4.001

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]

0.832

5486

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

[_dAlembert]

4.217

5487

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

[_quadrature]

4.440

5488

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

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

4.648

5489

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

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

52.707

5490

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

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

144.444

5491

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

[[_homogeneous, ‘class G‘]]

3.773

5492

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

[_quadrature]

0.590

5493

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

[[_homogeneous, ‘class G‘]]

3.129

5494

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

[_quadrature]

0.531

5495

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

[_separable]

0.349

5496

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

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

14.258

5497

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

[_linear]

0.367

5498

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

[_separable]

7.477

5499

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

[_separable]

0.350

5500

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

[_rational]

3.668