2.2.143 Problems 14201 to 14300

Table 2.287: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

14201

\[ {}x \cos \left (\frac {y}{x}\right ) y^{\prime } = y \cos \left (\frac {y}{x}\right )-x \]

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

5.373

14202

\[ {}y^{\prime \prime }-4 y = {\mathrm e}^{2 x} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.879

14203

\[ {}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0 \]

[_Bernoulli]

2.470

14204

\[ {}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0 \]

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

1.869

14205

\[ {}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0 \]

[_separable]

3.513

14206

\[ {}\left [\begin {array}{c} x^{\prime }=2 x-3 y \\ y^{\prime }=5 x+6 y \end {array}\right ] \]

system_of_ODEs

0.804

14207

\[ {}\left [\begin {array}{c} x^{\prime }=-4 x-10 y \\ y^{\prime }=x-2 y \end {array}\right ] \]

system_of_ODEs

0.571

14208

\[ {}\left [\begin {array}{c} x^{\prime }=12 x+18 y \\ y^{\prime }=-8 x-12 y \end {array}\right ] \]

system_of_ODEs

0.420

14209

\[ {}y^{\prime } = x +y^{2} \]
i.c.

[[_Riccati, _special]]

2.055

14210

\[ {}y^{\prime }+\frac {y}{x} = {\mathrm e}^{x} \]
i.c.

[_linear]

1.484

14211

\[ {}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=-x-3 y \end {array}\right ] \]
i.c.

system_of_ODEs

0.564

14212

\[ {}\left [\begin {array}{c} x^{\prime }=x-5 y \\ y^{\prime }=x-y \end {array}\right ] \]

system_of_ODEs

0.526

14213

\[ {}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=x-2 y \end {array}\right ] \]

system_of_ODEs

0.588

14214

\[ {}\left [\begin {array}{c} x^{\prime }=-4 x+2 y \\ y^{\prime }=3 x-2 y \end {array}\right ] \]

system_of_ODEs

0.684

14215

\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=2 x+2 y \end {array}\right ] \]

system_of_ODEs

0.598

14216

\[ {}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=3 x-y \end {array}\right ] \]

system_of_ODEs

0.457

14217

\[ {}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=y-x \end {array}\right ] \]

system_of_ODEs

0.775

14218

\[ {}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=x+y \end {array}\right ] \]

system_of_ODEs

0.439

14219

\[ {}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=2 x-2 y \end {array}\right ] \]

system_of_ODEs

0.456

14220

\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 x-3 y \end {array}\right ] \]

system_of_ODEs

0.444

14221

\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=x+3 y \end {array}\right ] \]

system_of_ODEs

0.440

14222

\[ {}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=2 x-4 y \end {array}\right ] \]

system_of_ODEs

0.594

14223

\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=y \end {array}\right ] \]

system_of_ODEs

0.297

14224

\[ {}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=x \end {array}\right ] \]

system_of_ODEs

0.302

14225

\[ {}x^{\prime \prime }+x-x^{3} = 0 \]

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

4.732

14226

\[ {}x^{\prime \prime }+x+x^{3} = 0 \]

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

5.082

14227

\[ {}x^{\prime \prime }+x^{\prime }+x-x^{3} = 0 \]

[[_2nd_order, _missing_x]]

1.933

14228

\[ {}x^{\prime \prime }+x^{\prime }+x+x^{3} = 0 \]

[[_2nd_order, _missing_x]]

1.914

14229

\[ {}x^{\prime \prime } = \left (2 \cos \left (x\right )-1\right ) \sin \left (x\right ) \]

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

4.000

14230

\[ {}\left [\begin {array}{c} x^{\prime }=x-5 y \\ y^{\prime }=x-y \end {array}\right ] \]

system_of_ODEs

0.538

14231

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

1.233

14232

\[ {}-y+x y^{\prime } = 0 \]

[_separable]

1.667

14233

\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.994

14234

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

0.846

14235

\[ {}x^{2} y^{\prime \prime }-2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.669

14236

\[ {}y^{\prime }+\frac {1}{2 y} = 0 \]

[_quadrature]

1.857

14237

\[ {}y^{\prime }-\frac {y}{x} = 1 \]

[_linear]

1.557

14238

\[ {}y^{\prime }-2 \sqrt {{| y|}} = 0 \]

[_quadrature]

2.973

14239

\[ {}x^{2} y^{\prime }+2 x y = 0 \]

[_separable]

2.262

14240

\[ {}y^{\prime }-y^{2} = 1 \]

[_quadrature]

3.381

14241

\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_Emden, _Fowler]]

0.934

14242

\[ {}x y^{\prime }-\sin \left (x \right ) = 0 \]

[_quadrature]

0.584

14243

\[ {}y^{\prime }+3 y = 0 \]

[_quadrature]

1.753

14244

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 0 \]

[[_2nd_order, _missing_x]]

0.880

14245

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

0.970

14246

\[ {}y^{\prime \prime \prime }-7 y^{\prime \prime }+12 y^{\prime } = 0 \]

[[_3rd_order, _missing_x]]

0.050

14247

\[ {}2 x y^{\prime }-y = 0 \]

[_separable]

2.242

14248

\[ {}x^{2} y^{\prime \prime }-x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

0.514

14249

\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

1.189

14250

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

[[_Emden, _Fowler]]

0.879

14251

\[ {}{y^{\prime }}^{2}-4 y = 0 \]

[_quadrature]

0.378

14252

\[ {}{y^{\prime }}^{2}-9 x y = 0 \]

[[_homogeneous, ‘class G‘]]

0.654

14253

\[ {}{y^{\prime }}^{2} = x^{6} \]

[_quadrature]

0.558

14254

\[ {}y^{\prime }-2 x y = 0 \]

[_separable]

1.652

14255

\[ {}y^{\prime }+y = x^{2}+2 x -1 \]

[[_linear, ‘class A‘]]

1.354

14256

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \]

[[_2nd_order, _missing_x]]

0.838

14257

\[ {}y^{\prime } = x \sqrt {y} \]

[_separable]

4.438

14258

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

2.050

14259

\[ {}y^{\prime } = 3 y^{{2}/{3}} \]

[_quadrature]

2.115

14260

\[ {}x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y = 0 \]

[_separable]

1.821

14261

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.370

14262

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.450

14263

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.967

14264

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.961

14265

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

0.109

14266

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]
i.c.

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

1.752

14267

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]
i.c.

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

1.833

14268

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]
i.c.

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

1.733

14269

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]
i.c.

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

1.760

14270

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]
i.c.

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

1.272

14271

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]
i.c.

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

0.989

14272

\[ {}y^{\prime } = 1-x \]

[_quadrature]

0.449

14273

\[ {}y^{\prime } = -1+x \]

[_quadrature]

0.444

14274

\[ {}y^{\prime } = 1-y \]

[_quadrature]

1.427

14275

\[ {}y^{\prime } = y+1 \]

[_quadrature]

1.386

14276

\[ {}y^{\prime } = y^{2}-4 \]

[_quadrature]

3.904

14277

\[ {}y^{\prime } = 4-y^{2} \]

[_quadrature]

3.749

14278

\[ {}y^{\prime } = x y \]

[_separable]

1.645

14279

\[ {}y^{\prime } = -x y \]

[_separable]

1.687

14280

\[ {}y^{\prime } = x^{2}-y^{2} \]

[_Riccati]

1.173

14281

\[ {}y^{\prime } = y^{2}-x^{2} \]

[_Riccati]

1.165

14282

\[ {}y^{\prime } = x +y \]

[[_linear, ‘class A‘]]

1.287

14283

\[ {}y^{\prime } = x y \]

[_separable]

1.661

14284

\[ {}y^{\prime } = \frac {x}{y} \]

[_separable]

4.490

14285

\[ {}y^{\prime } = \frac {y}{x} \]

[_separable]

1.683

14286

\[ {}y^{\prime } = 1+y^{2} \]

[_quadrature]

3.300

14287

\[ {}y^{\prime } = y^{2}-3 y \]

[_quadrature]

2.017

14288

\[ {}y^{\prime } = x^{3}+y^{3} \]

[_Abel]

0.757

14289

\[ {}y^{\prime } = {| y|} \]

[_quadrature]

1.481

14290

\[ {}y^{\prime } = {\mathrm e}^{x -y} \]

[_separable]

2.422

14291

\[ {}y^{\prime } = \ln \left (x +y\right ) \]

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

1.178

14292

\[ {}y^{\prime } = \frac {2 x -y}{x +3 y} \]

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

4.386

14293

\[ {}y^{\prime } = \frac {1}{\sqrt {15-x^{2}-y^{2}}} \]

[‘y=_G(x,y’)‘]

1.530

14294

\[ {}y^{\prime } = \frac {3 y}{\left (x -5\right ) \left (x +3\right )}+{\mathrm e}^{-x} \]

[_linear]

2.224

14295

\[ {}y^{\prime } = \frac {x y}{x^{2}+y^{2}} \]

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

15.597

14296

\[ {}y^{\prime } = \frac {1}{x y} \]

[_separable]

2.480

14297

\[ {}y^{\prime } = \ln \left (y-1\right ) \]

[_quadrature]

1.332

14298

\[ {}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )} \]

[_quadrature]

54.013

14299

\[ {}y^{\prime } = \frac {y}{y-x} \]

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

4.275

14300

\[ {}y^{\prime } = \frac {x}{y^{2}} \]

[_separable]

2.495