2.2.195 Problems 19401 to 19500

Table 2.403: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

19401

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

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

7.568

19402

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

[_linear]

25.569

19403

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

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

6.351

19404

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

[[_2nd_order, _missing_y]]

0.801

19405

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

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

2.797

19406

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

[_linear]

3.201

19407

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

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

11.818

19408

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

[_linear]

0.129

19409

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

[_exact]

5.341

19410

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

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

1.428

19411

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

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

23.863

19412

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

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

9.085

19413

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

[_Bernoulli]

12.760

19414

\begin{align*} \frac {\cos \left (y\right )}{x +3}-\left (\sin \left (y\right ) \ln \left (5 x +15\right )-\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}

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

6.928

19415

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

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

1.045

19416

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

[_linear]

2.751

19417

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

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

9.356

19418

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

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

1.164

19419

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

[_linear]

2.958

19420

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

[[_2nd_order, _missing_y]]

1.462

19421

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

[[_2nd_order, _missing_y]]

1.427

19422

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

[[_2nd_order, _with_linear_symmetries]]

0.453

19423

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

[[_2nd_order, _with_linear_symmetries]]

2.979

19424

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

[[_2nd_order, _missing_x]]

2.318

19425

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.616

19426

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

[[_2nd_order, _quadrature]]

1.755

19427

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

[[_2nd_order, _missing_x]]

1.473

19428

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.569

19429

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

[[_2nd_order, _with_linear_symmetries]]

1.790

19430

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

[[_2nd_order, _missing_y]]

1.378

19431

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.539

19432

\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.911

19433

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

[[_2nd_order, _missing_x]]

4.101

19434

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 5 \\ \end{align*}

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

3.432

19435

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

[[_2nd_order, _missing_x]]

0.448

19436

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

[[_2nd_order, _missing_x]]

0.374

19437

\begin{align*} x^{2} y^{\prime \prime }-2 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 8 \\ \end{align*}

[[_2nd_order, _exact, _linear, _homogeneous]]

0.999

19438

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.441

19439

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.459

19440

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

[[_2nd_order, _missing_x]]

2.308

19441

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

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

2.023

19442

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

[[_2nd_order, _with_linear_symmetries]]

0.708

19443

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

[[_2nd_order, _missing_x]]

0.196

19444

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

[[_2nd_order, _missing_x]]

0.187

19445

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

[[_2nd_order, _missing_y]]

0.163

19446

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.176

19447

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

[_Gegenbauer]

0.184

19448

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

[[_2nd_order, _with_linear_symmetries]]

0.169

19449

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

[[_2nd_order, _with_linear_symmetries]]

0.173

19450

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

[[_Emden, _Fowler]]

0.168

19451

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

[[_2nd_order, _with_linear_symmetries]]

0.171

19452

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

[[_2nd_order, _with_linear_symmetries]]

0.800

19453

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

[[_2nd_order, _with_linear_symmetries]]

0.183

19454

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

[_Laguerre]

2.948

19455

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

[_Laguerre]

1.274

19456

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

[_Laguerre]

0.920

19457

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

[_Laguerre]

0.967

19458

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

3.587

19459

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

[[_2nd_order, _missing_x]]

0.271

19460

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

[[_2nd_order, _missing_x]]

0.376

19461

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

[[_2nd_order, _missing_x]]

2.653

19462

\begin{align*} 2 y^{\prime \prime }-4 y^{\prime }+8 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.493

19463

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

[[_2nd_order, _missing_x]]

0.361

19464

\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.265

19465

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

[[_2nd_order, _missing_x]]

0.465

19466

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

[[_2nd_order, _missing_x]]

0.386

19467

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

[[_2nd_order, _missing_x]]

1.735

19468

\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.428

19469

\begin{align*} 4 y^{\prime \prime }+20 y^{\prime }+25 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.377

19470

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

[[_2nd_order, _missing_x]]

0.442

19471

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

[[_2nd_order, _missing_x]]

2.785

19472

\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+7 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.431

19473

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

[[_2nd_order, _missing_x]]

0.267

19474

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

[[_2nd_order, _missing_x]]

0.374

19475

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

[[_2nd_order, _missing_x]]

0.320

19476

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

[[_2nd_order, _missing_x]]

0.275

19477

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (1\right ) &= {\mathrm e}^{2} \\ y^{\prime }\left (1\right ) &= 3 \,{\mathrm e}^{2} \\ \end{align*}

[[_2nd_order, _missing_x]]

0.480

19478

\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.452

19479

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.568

19480

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.437

19481

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

[[_2nd_order, _missing_x]]

0.553

19482

\begin{align*} y^{\prime \prime }+8 y^{\prime }-9 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.458

19483

\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

2.466

19484

\begin{align*} 2 x^{2} y^{\prime \prime }+10 y^{\prime } x +8 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

1.844

19485

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

[[_Emden, _Fowler]]

1.150

19486

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

[[_Emden, _Fowler]]

0.283

19487

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

1.843

19488

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

1.142

19489

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

[[_Emden, _Fowler]]

2.596

19490

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

2.262

19491

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

1.985

19492

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

[[_2nd_order, _with_linear_symmetries]]

3.998

19493

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

[[_2nd_order, _with_linear_symmetries]]

3.961

19494

\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=6 \,{\mathrm e}^{4 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.512

19495

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.641

19496

\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=14 \,{\mathrm e}^{-5 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.649

19497

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=25 x^{2}+12 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.585

19498

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=20 \,{\mathrm e}^{-2 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.505

19499

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.572

19500

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.584