2.2.155 Problems 15401 to 15500

Table 2.327: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

15401

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

[[_2nd_order, _missing_x]]

3.461

15402

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

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

4.041

15403

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

[[_2nd_order, _missing_y]]

1.736

15404

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

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

2.642

15405

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

[[_2nd_order, _missing_y]]

0.790

15406

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

[[_2nd_order, _missing_x]]

38.729

15407

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]]

2.833

15408

\begin{align*} y^{\prime \prime \prime }&={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]]

0.923

15409

\begin{align*} y^{\prime \prime \prime } y^{\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]]

1.815

15410

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

[[_2nd_order, _missing_x]]

3.062

15411

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

[[_2nd_order, _missing_x]]

1.737

15412

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

[[_2nd_order, _missing_x]]

2.151

15413

\begin{align*} y^{\prime \prime }+12 y&=7 y^{\prime } \\ \end{align*}

[[_2nd_order, _missing_x]]

0.346

15414

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

[[_2nd_order, _missing_x]]

0.438

15415

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.436

15416

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

[[_2nd_order, _missing_x]]

0.397

15417

\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.473

15418

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

[[_2nd_order, _missing_x]]

0.431

15419

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

[[_high_order, _missing_x]]

0.086

15420

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

[[_3rd_order, _missing_x]]

0.076

15421

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

[[_3rd_order, _missing_x]]

0.091

15422

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

[[_high_order, _missing_x]]

0.098

15423

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

[[_high_order, _missing_x]]

0.099

15424

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

[[_high_order, _missing_x]]

0.089

15425

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

[[_high_order, _missing_x]]

0.083

15426

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

[[_high_order, _missing_x]]

0.076

15427

\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.509

15428

\begin{align*} s^{\prime \prime }-a^{2} s&=1+t \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.582

15429

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=8 \sin \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.563

15430

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

[[_2nd_order, _with_linear_symmetries]]

0.497

15431

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

[[_2nd_order, _with_linear_symmetries]]

0.660

15432

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

[[_2nd_order, _with_linear_symmetries]]

0.528

15433

\begin{align*} y^{\prime \prime }+9 y&=6 \,{\mathrm e}^{3 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.569

15434

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

[[_2nd_order, _missing_y]]

1.273

15435

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.669

15436

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.634

15437

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

[[_3rd_order, _with_linear_symmetries]]

0.187

15438

\begin{align*} y^{\prime \prime \prime \prime }-a^{4} y&=5 a^{4} {\mathrm e}^{a x} \sin \left (a x \right ) \\ \end{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.213

15439

\begin{align*} a^{4} y+2 a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=8 \cos \left (a x \right ) \\ \end{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.994

15440

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

[[_2nd_order, _missing_x]]

1.263

15441

\begin{align*} y^{\prime \prime }+n^{2} y&=h \sin \left (r x \right ) \\ y \left (0\right ) &= a \\ y^{\prime }\left (0\right ) &= c \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.470

15442

\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=\sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.498

15443

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.498

15444

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.109

15445

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

system_of_ODEs

0.635

15446

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

system_of_ODEs

0.481

15447

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

system_of_ODEs

0.952

15448

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

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

4.988

15449

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

[_separable]

7.329

15450

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

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

1.234

15451

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.581

15452

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

[_linear]

7.267

15453

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

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

21.201

15454

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.788

15455

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

[_Bernoulli]

7.105

15456

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

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

11.019

15457

\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

4.911

15458

\begin{align*} x^{\prime }&=2 x-3 y \\ y^{\prime }&=5 x+6 y \\ \end{align*}

system_of_ODEs

1.369

15459

\begin{align*} x^{\prime }&=-4 x-10 y \\ y^{\prime }&=x-2 y \\ \end{align*}

system_of_ODEs

0.694

15460

\begin{align*} x^{\prime }&=12 x+18 y \\ y^{\prime }&=-8 x-12 y \\ \end{align*}

system_of_ODEs

0.434

15461

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

[[_Riccati, _special]]

5.553

15462

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

[_linear]

2.611

15463

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

system_of_ODEs

0.500

15464

\begin{align*} x^{\prime }&=x-5 y \\ y^{\prime }&=x-y \\ \end{align*}

system_of_ODEs

0.559

15465

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

system_of_ODEs

0.734

15466

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

system_of_ODEs

0.733

15467

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

system_of_ODEs

0.718

15468

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

system_of_ODEs

0.515

15469

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

system_of_ODEs

1.245

15470

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

system_of_ODEs

0.408

15471

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

system_of_ODEs

0.506

15472

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

system_of_ODEs

0.476

15473

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

system_of_ODEs

0.451

15474

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

system_of_ODEs

0.711

15475

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

system_of_ODEs

0.309

15476

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

system_of_ODEs

0.336

15477

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

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

5.625

15478

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

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

3.899

15479

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

[[_2nd_order, _missing_x]]

31.415

15480

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

[[_2nd_order, _missing_x]]

31.896

15481

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

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

3.506

15482

\begin{align*} x^{\prime }&=x-5 y \\ y^{\prime }&=x-y \\ \end{align*}

system_of_ODEs

0.530

15483

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

[[_2nd_order, _exact, _linear, _homogeneous]]

2.405

15484

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

[_separable]

3.617

15485

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.543

15486

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

[[_2nd_order, _missing_x]]

0.338

15487

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.883

15488

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

[_quadrature]

1.658

15489

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

[_linear]

4.082

15490

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

[_quadrature]

6.945

15491

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

[_separable]

5.561

15492

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

[_quadrature]

3.742

15493

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

[[_Emden, _Fowler]]

1.382

15494

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

[_quadrature]

0.673

15495

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

[_quadrature]

1.745

15496

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.361

15497

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

[[_2nd_order, _missing_x]]

0.433

15498

\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+12 y^{\prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.076

15499

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

[_separable]

4.987

15500

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

[[_2nd_order, _missing_y]]

0.656