2.2.193 Problems 19201 to 19300

Table 2.387: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

19201

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

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

7.602

19202

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

[_rational]

122.871

19203

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

[_rational, _Bernoulli]

11.544

19204

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

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

1.370

19205

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

0.532

19206

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.393

19207

\[ {}4 {y^{\prime }}^{2} = 9 x \]

[_quadrature]

0.318

19208

\[ {}4 x \left (-1+x \right ) \left (-2+x \right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2} = 0 \]

[_quadrature]

0.308

19209

\[ {}\left (8 {y^{\prime }}^{3}-27\right ) x = \frac {12 {y^{\prime }}^{2}}{x} \]

[_quadrature]

0.776

19210

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

[[_homogeneous, ‘class G‘]]

2.281

19211

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

[_quadrature]

0.701

19212

\[ {}{y^{\prime }}^{2} \left (2-3 y\right )^{2} = 4-4 y \]

[_quadrature]

0.386

19213

\[ {}4 x {y^{\prime }}^{2} = \left (3 x -1\right )^{2} \]

[_quadrature]

0.348

19214

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

[_quadrature]

0.369

19215

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

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

1.645

19216

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

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

1.864

19217

\[ {}{y^{\prime }}^{2}+2 x^{3} y^{\prime }-4 x^{2} y = 0 \]

[[_1st_order, _with_linear_symmetries]]

1.648

19218

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

[[_homogeneous, ‘class G‘]]

2.839

19219

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

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

31.768

19220

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

[[_homogeneous, ‘class G‘]]

0.705

19221

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

[_quadrature]

30.785

19222

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

[[_homogeneous, ‘class G‘]]

1.434

19223

\[ {}{y^{\prime }}^{3} = y^{4} \left (x y^{\prime }+y\right ) \]

[[_1st_order, _with_linear_symmetries]]

13.510

19224

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

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

17.747

19225

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

[_rational]

116.487

19226

\[ {}{y^{\prime }}^{2} = \left (4 y+1\right ) \left (y^{\prime }-y\right ) \]

[_quadrature]

1.024

19227

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

0.984

19228

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

[_rational]

53.674

19229

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

[‘y=_G(x,y’)‘]

20.364

19230

\[ {}8 {y^{\prime }}^{3} x = y \left (12 {y^{\prime }}^{2}-9\right ) \]

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.778

19231

\[ {}4 {y^{\prime }}^{2} x^{2} \left (-1+x \right )-4 y^{\prime } x y \left (4 x -3\right )+\left (16 x -9\right ) y^{2} = 0 \]

[_separable]

0.596

19232

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

[‘y=_G(x,y’)‘]

54.421

19233

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

[_separable]

1.520

19234

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

[_separable]

1.022

19235

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

[_rational]

151.739

19236

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

[[_Emden, _Fowler]]

0.863

19237

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

[[_2nd_order, _with_linear_symmetries]]

1.657

19238

\[ {}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-2 y = 0 \]

[[_3rd_order, _exact, _linear, _homogeneous]]

0.107

19239

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

[[_3rd_order, _missing_y]]

0.166

19240

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = \ln \left (x \right )^{2} \]

[[_3rd_order, _with_linear_symmetries]]

0.315

19241

\[ {}y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}} = 1 \]

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.444

19242

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

[[_3rd_order, _missing_y]]

0.168

19243

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

0.110

19244

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

[[_Emden, _Fowler]]

4.181

19245

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

[[_3rd_order, _missing_y]]

0.335

19246

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

[[_2nd_order, _with_linear_symmetries]]

1.217

19247

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.580

19248

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = x^{4} \]

[[_2nd_order, _with_linear_symmetries]]

1.369

19249

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

[[_2nd_order, _with_linear_symmetries]]

1.367

19250

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.424

19251

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

2.180

19252

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{m} \]

[[_2nd_order, _with_linear_symmetries]]

1.505

19253

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

[[_2nd_order, _missing_y]]

0.940

19254

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = {\mathrm e}^{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.923

19255

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

[[_2nd_order, _with_linear_symmetries]]

1.400

19256

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

[[_3rd_order, _missing_y]]

0.438

19257

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 4 x \]

[[_high_order, _with_linear_symmetries]]

0.751

19258

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y = x^{2}+3 x -4 \]

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.579

19259

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y = \left (x +1\right )^{2} \]

[[_2nd_order, _with_linear_symmetries]]

1.168

19260

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = x^{2}+\frac {1}{x^{2}} \]

[[_3rd_order, _reducible, _mu_y2]]

0.348

19261

\[ {}x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-x y^{\prime }+y = x +\ln \left (x \right ) \]

[[_high_order, _with_linear_symmetries]]

0.401

19262

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

[[_2nd_order, _with_linear_symmetries]]

126.086

19263

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+5 y = x^{2} \sin \left (\ln \left (x \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

264.578

19264

\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \ln \left (x \right ) x \]

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.297

19265

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (1+\ln \left (x \right )\right )^{2} \]

[[_high_order, _linear, _nonhomogeneous]]

0.828

19266

\[ {}\left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5+2 x \right ) y^{\prime }+8 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.316

19267

\[ {}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime } = \left (2 x +3\right ) \left (2 x +4\right ) \]

[[_2nd_order, _missing_y]]

0.998

19268

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.972

19269

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

0.987

19270

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

1.325

19271

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y = x^{2}+3 x -4 \]

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.490

19272

\[ {}x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

[[_3rd_order, _fully, _exact, _linear]]

0.348

19273

\[ {}y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x} = x^{2} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

0.705

19274

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.309

19275

\[ {}\left (x^{2}-x \right ) y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }-4 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

1.058

19276

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

3.039

19277

\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+\left (3+6 x \right ) y^{\prime }+2 y = \left (x +1\right ) {\mathrm e}^{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.295

19278

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

[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.893

19279

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.277

19280

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.509

19281

\[ {}x^{2} y^{\prime \prime \prime }+4 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }+3 x y = 2 \]

[[_3rd_order, _linear, _nonhomogeneous]]

0.040

19282

\[ {}x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+x y^{\prime }+y = \ln \left (x \right ) \]

[[_high_order, _exact, _linear, _nonhomogeneous]]

0.439

19283

\[ {}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+3 x^{2} y = 2 x \]

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.428

19284

\[ {}x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5 \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.593

19285

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

[[_3rd_order, _quadrature]]

0.154

19286

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

[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]

0.035

19287

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

[[_2nd_order, _quadrature]]

2.049

19288

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

[[_2nd_order, _quadrature]]

1.835

19289

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

[[_2nd_order, _quadrature]]

1.053

19290

\[ {}x^{3} y^{\prime \prime \prime } = 1 \]

[[_3rd_order, _quadrature]]

0.174

19291

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

[[_2nd_order, _quadrature]]

1.756

19292

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

[[_3rd_order, _quadrature]]

0.235

19293

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

[[_2nd_order, _quadrature]]

0.652

19294

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

[[_2nd_order, _quadrature]]

0.494

19295

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

[[_2nd_order, _missing_x]]

1.917

19296

\[ {}y^{3} y^{\prime \prime } = a \]

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

2.050

19297

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

[[_2nd_order, _missing_x]]

1.536

19298

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

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

0.865

19299

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

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

4.412

19300

\[ {}y^{\prime \prime } = {\mathrm e}^{2 y} \]
i.c.

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

1.597