2.2.265 Problems 26401 to 26500

Table 2.547: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

26401

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

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

35.790

26402

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

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

5.335

26403

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

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

4.127

26404

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

[_separable]

5.067

26405

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

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

3.922

26406

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

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

10.767

26407

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

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

2.080

26408

\begin{align*} 2 x^{5}+4 x^{3} y-2 x y^{2}+\left (y^{2}+2 x^{2} y-x^{4}\right ) y^{\prime }&=0 \\ \end{align*}

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

6.375

26409

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

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

7.619

26410

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

[_exact]

27.114

26411

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

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

8.464

26412

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

[_rational]

101.651

26413

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

[[_2nd_order, _missing_x]]

0.319

26414

\begin{align*} y^{\prime \prime }-4 y^{\prime }+8 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.348

26415

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.646

26416

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.350

26417

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

[[_3rd_order, _quadrature]]

0.237

26418

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

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

1.206

26419

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

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

0.641

26420

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

2.052

26421

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

[[_2nd_order, _missing_y]]

0.611

26422

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

[[_2nd_order, _with_linear_symmetries]]

0.703

26423

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

[[_2nd_order, _with_linear_symmetries]]

0.808

26424

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

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear]]

2.919

26425

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

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear]]

3.434

26426

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

2.722

26427

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

[[_2nd_order, _missing_x]]

106.714

26428

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

[[_2nd_order, _missing_x]]

1.259

26429

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

[[_2nd_order, _with_linear_symmetries]]

0.531

26430

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

[[_2nd_order, _with_linear_symmetries]]

0.769

26431

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

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

2.876

26432

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

0.401

26433

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

[[_2nd_order, _missing_x]]

3.715

26434

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

[[_2nd_order, _with_linear_symmetries]]

0.568

26435

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

[[_2nd_order, _missing_x]]

6.124

26436

\begin{align*} y^{3} y^{\prime \prime }&=1 \\ \end{align*}

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

2.663

26437

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

[[_2nd_order, _missing_x]]

3.137

26438

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.728

26439

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

[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

0.749

26440

\begin{align*} y^{\prime \prime \prime }&=x \,{\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}

[[_3rd_order, _quadrature]]

0.158

26441

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

[[_high_order, _quadrature]]

0.121

26442

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

[[_3rd_order, _quadrature]]

0.268

26443

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

[[_3rd_order, _quadrature]]

0.162

26444

\begin{align*} y^{\prime \prime \prime }&=\frac {x}{\left (x +2\right )^{5}} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}

[[_3rd_order, _quadrature]]

0.284

26445

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

[[_2nd_order, _missing_x]]

4.892

26446

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

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

0.555

26447

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

[[_2nd_order, _missing_x]]

104.589

26448

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

[[_2nd_order, _missing_y]]

0.758

26449

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

[[_2nd_order, _missing_x]]

36.618

26450

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

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

1.775

26451

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

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear]]

2.326

26452

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

[[_2nd_order, _quadrature]]

0.569

26453

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

[[_2nd_order, _missing_y]]

0.460

26454

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

[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]]

0.293

26455

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

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear]]

2.967

26456

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

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_poly_yn]]

0.479

26457

\begin{align*} x y^{\prime \prime \prime }+y^{\prime \prime }-x -1&=0 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.084

26458

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

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

1.212

26459

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

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_poly_yn]]

1.415

26460

\begin{align*} x^{4} y^{\prime \prime \prime }+2 x^{3} y^{\prime \prime }&=1 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.374

26461

\begin{align*} \sqrt {-x^{2}+1}\, y^{\prime \prime }+\sqrt {1-{y^{\prime }}^{2}}&=0 \\ \end{align*}

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

0.827

26462

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

[[_3rd_order, _missing_y]]

0.286

26463

\begin{align*} y^{3} y^{\prime \prime }&=1 \\ \end{align*}

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

2.279

26464

\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}-1&=0 \\ \end{align*}

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

3.457

26465

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

2.427

26466

\begin{align*} 2 y^{\prime \prime }&=a \,{\mathrm e}^{y} \\ \end{align*}

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

8.805

26467

\begin{align*} y^{\prime \prime }&=\frac {1}{4 \sqrt {y}} \\ \end{align*}

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

1.259

26468

\begin{align*} 3 y^{\prime \prime }&=\frac {1}{y^{{5}/{3}}} \\ \end{align*}

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

1.698

26469

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

1.954

26470

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

1.083

26471

\begin{align*} y^{4}-y^{3} y^{\prime \prime }&=1 \\ \end{align*}

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

9.175

26472

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

[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]]

0.748

26473

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

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.717

26474

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

0.856

26475

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

2.595

26476

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

[[_2nd_order, _missing_x]]

5.820

26477

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]]

1.356

26478

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

[[_2nd_order, _with_linear_symmetries]]

1.578

26479

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

[[_3rd_order, _with_linear_symmetries]]

0.062

26480

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

[[_2nd_order, _missing_x]]

1.614

26481

\begin{align*} 3 y^{\prime \prime }-2 y^{\prime }-8 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.296

26482

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

[[_3rd_order, _missing_x]]

0.115

26483

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

[[_2nd_order, _missing_x]]

0.356

26484

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.413

26485

\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.054

26486

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

[[_2nd_order, _missing_x]]

0.326

26487

\begin{align*} y^{\left (6\right )}+2 y^{\left (5\right )}+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.068

26488

\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+5 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.336

26489

\begin{align*} y^{\prime \prime \prime }-8 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.050

26490

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+10 y^{\prime \prime }+12 y^{\prime }+5 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.070

26491

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

[[_2nd_order, _missing_x]]

0.440

26492

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

[[_2nd_order, _missing_x]]

0.437

26493

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

[[_high_order, _missing_x]]

0.069

26494

\begin{align*} y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-6 y^{\prime }-4 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.076

26495

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

[[_3rd_order, _missing_x]]

0.054

26496

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

[[_3rd_order, _missing_x]]

0.059

26497

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

[[_high_order, _missing_x]]

0.050

26498

\begin{align*} y^{\left (10\right )}&=0 \\ \end{align*}

[[_high_order, _quadrature]]

0.071

26499

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

[[_3rd_order, _missing_x]]

0.056

26500

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

[[_3rd_order, _missing_x]]

0.056