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

[[_1st_order, _with_linear_symmetries], _dAlembert]

2.105

5402

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.776

5403

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

[_quadrature]

3.704

5404

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.891

5405

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

[[_homogeneous, ‘class G‘]]

113.961

5406

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.833

5407

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

[_quadrature]

0.493

5408

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

[[_1st_order, _with_linear_symmetries]]

0.958

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]]

0.816

5410

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

[[_1st_order, _with_linear_symmetries]]

1.701

5411

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

[_quadrature]

2.253

5412

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

[_quadrature]

0.569

5413

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

[[_1st_order, _with_linear_symmetries]]

1.781

5414

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

[_quadrature]

1.240

5415

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

[_dAlembert]

23.588

5416

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

[_quadrature]

7.719

5417

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

[_quadrature]

1.279

5418

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

[_quadrature]

12.963

5419

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

[_quadrature]

194.513

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]

32.575

5421

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

[_dAlembert]

9.775

5422

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

[_dAlembert]

23.668

5423

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

[_quadrature]

1.929

5424

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

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

4.307

5425

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

[_quadrature]

0.536

5426

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

[_quadrature]

6.551

5427

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

[_separable]

0.634

5428

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

[[_homogeneous, ‘class G‘]]

11.352

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]]

73.582

5430

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

[_separable]

3.264

5431

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

[[_homogeneous, ‘class G‘]]

6.976

5432

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

[_separable]

4.454

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]]

2.737

5434

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

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

6.946

5435

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

3.231

5436

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.780

5437

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

[[_homogeneous, ‘class G‘]]

5.427

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]

19.569

5439

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

5.159

5440

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

[[_homogeneous, ‘class G‘]]

9.530

5441

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

[_quadrature]

2.525

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]]

1.658

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]

5.409

5444

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

2.076

5445

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

2.139

5446

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

[[_1st_order, _with_linear_symmetries]]

2.011

5447

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

[_quadrature]

9.607

5448

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

[_quadrature]

5.095

5449

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

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

9.909

5450

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

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

10.494

5451

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

[_rational, _dAlembert]

4.824

5452

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

[_rational, _dAlembert]

4.977

5453

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

[_rational, _dAlembert]

5.017

5454

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

[_rational, _dAlembert]

5.323

5455

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

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

10.888

5456

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

[_quadrature]

0.605

5457

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

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

187.598

5458

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

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

5.504

5459

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

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

11.494

5460

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

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

109.273

5461

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

[[_homogeneous, ‘class G‘]]

140.987

5462

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

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

13.836

5463

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

[[_homogeneous, ‘class G‘]]

4.711

5464

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

1.007

5465

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

[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

0.989

5466

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

[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

1.075

5467

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

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

23.473

5468

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

[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

1.082

5469

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

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

9.837

5470

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

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

115.454

5471

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

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

5.905

5472

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

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

5.281

5473

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

[[_homogeneous, ‘class G‘]]

6.879

5474

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

[_quadrature]

0.527

5475

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

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

58.826

5476

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

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

31.047

5477

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

[_quadrature]

0.646

5478

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

[_quadrature]

0.526

5479

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

[_quadrature]

0.718

5480

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

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

6.433

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]

1.006

5482

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

0.887

5483

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

[_rational, _dAlembert]

9.694

5484

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

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

4.881

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]

0.975

5486

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

[_rational, _dAlembert]

5.448

5487

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

[_quadrature]

5.103

5488

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

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

5.506

5489

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

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

47.369

5490

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

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

139.098

5491

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

[[_homogeneous, ‘class G‘]]

4.512

5492

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

[_quadrature]

0.631

5493

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

[[_homogeneous, ‘class G‘]]

3.651

5494

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

[_quadrature]

0.595

5495

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

[_separable]

0.579

5496

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

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

16.737

5497

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

[_linear]

0.612

5498

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

[_separable]

8.852

5499

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

[_separable]

0.595

5500

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

[_rational]

4.419