2.2.174 Problems 17301 to 17400

Table 2.349: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

17301

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

[‘y=_G(x,y’)‘]

2.601

17302

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

[‘y=_G(x,y’)‘]

1.597

17303

\[ {}y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}} \]

[_separable]

1.511

17304

\[ {}y^{\prime } = \frac {\cot \left (t \right ) y}{y+1} \]

[_separable]

1.971

17305

\[ {}y^{\prime } = y^{{1}/{3}} \]
i.c.

[_quadrature]

2.361

17306

\[ {}y^{\prime } = -\frac {t}{2}+\frac {\sqrt {t^{2}+4 y}}{2} \]
i.c.

[[_1st_order, _with_linear_symmetries], _Clairaut]

2.411

17307

\[ {}y^{\prime } = -\frac {4 t}{y} \]
i.c.

[_separable]

13.585

17308

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

[_separable]

2.137

17309

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

[_quadrature]

22.193

17310

\[ {}y^{\prime } = \frac {t^{2}}{y \left (t^{3}+1\right )} \]
i.c.

[_separable]

2.706

17311

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

[_separable]

2.589

17312

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

[_Bernoulli]

1.847

17313

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

[_Bernoulli]

1.830

17314

\[ {}y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \]
i.c.

[[_linear, ‘class A‘]]

0.911

17315

\[ {}y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 1 & 1<t \end {array}\right .\right ) y = 0 \]
i.c.

[_separable]

2.138

17316

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

[_separable]

3.035

17317

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

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

5.851

17318

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

[_exact, _rational]

1.386

17319

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

[_separable]

2.282

17320

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

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

4.305

17321

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

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

11.682

17322

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

[_exact]

7.502

17323

\[ {}{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0 \]

[‘x=_G(y,y’)‘]

9.553

17324

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

[_exact]

38.220

17325

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

[_linear]

1.576

17326

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

[_separable]

1.998

17327

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

[_separable]

4.046

17328

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

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

6.546

17329

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

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

1.986

17330

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

[_separable]

1.655

17331

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

[NONE]

11.207

17332

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

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

1.390

17333

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

[_separable]

2.633

17334

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

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

2.103

17335

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

[[_linear, ‘class A‘]]

1.374

17336

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

[_quadrature]

0.594

17337

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

[[_1st_order, _with_exponential_symmetries]]

1.811

17338

\[ {}{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 y \csc \left (y\right )\right ) y^{\prime } = 0 \]

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

4.187

17339

\[ {}\frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime } = 0 \]

[_rational]

1.307

17340

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

[_rational]

1.423

17341

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

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

63.167

17342

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

[_separable]

3.126

17343

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

[_separable]

1.451

17344

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

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

45.422

17345

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

[_separable]

2.589

17346

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

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

92.378

17347

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

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

79.296

17348

\[ {}y^{\prime } = \frac {4 y-7 x}{5 x -y} \]

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

5.507

17349

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

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

40.295

17350

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

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

7.060

17351

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

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

3.858

17352

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

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

11.645

17353

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

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

1759.074

17354

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

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

2.145

17355

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

[_Bernoulli]

1.345

17356

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

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

1.423

17357

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

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

2.765

17358

\[ {}5 \left (t^{2}+1\right ) y^{\prime } = 4 t y \left (y^{3}-1\right ) \]

[_separable]

39.443

17359

\[ {}3 t y^{\prime }+9 y = 2 t y^{{5}/{3}} \]

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

23.960

17360

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

[_quadrature]

2.916

17361

\[ {}y^{\prime } = r y-k^{2} y^{2} \]

[_quadrature]

3.980

17362

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

[_quadrature]

8.723

17363

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

[_Riccati]

1.894

17364

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

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

6.247

17365

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

[[_1st_order, _with_exponential_symmetries]]

1.395

17366

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

[[_1st_order, _with_linear_symmetries], _Bernoulli]

1.799

17367

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

[_linear]

1.265

17368

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

[_Bernoulli]

36.187

17369

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

[_separable]

1.581

17370

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

[_separable]

2.238

17371

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

[_exact, _Bernoulli]

1.934

17372

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

[_linear]

1.665

17373

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

[_quadrature]

0.533

17374

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

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

75.628

17375

\[ {}4 x y y^{\prime } = 8 x^{2}+5 y^{2} \]

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

7.652

17376

\[ {}y^{\prime }+y-y^{{1}/{4}} = 0 \]

[_quadrature]

6.947

17377

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

system_of_ODEs

0.553

17378

\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y+\sin \left (t \right ) \\ y^{\prime }=-x+y-\cos \left (t \right ) \end {array}\right ] \]

system_of_ODEs

1.366

17379

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

system_of_ODEs

0.031

17380

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

system_of_ODEs

0.793

17381

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

system_of_ODEs

0.798

17382

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

system_of_ODEs

0.030

17383

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

system_of_ODEs

0.033

17384

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

system_of_ODEs

0.525

17385

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

system_of_ODEs

0.462

17386

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

system_of_ODEs

0.497

17387

\[ {}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+2 \sin \left (t \right ) \end {array}\right ] \]
i.c.

system_of_ODEs

0.776

17388

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

system_of_ODEs

0.555

17389

\[ {}\left [\begin {array}{c} x^{\prime }=-x+y+1 \\ y^{\prime }=x+y-3 \end {array}\right ] \]

system_of_ODEs

0.855

17390

\[ {}\left [\begin {array}{c} x^{\prime }=-x-4 y-4 \\ y^{\prime }=x-y-6 \end {array}\right ] \]

system_of_ODEs

0.813

17391

\[ {}\left [\begin {array}{c} x^{\prime }=-\frac {x}{4}-\frac {3 y}{4}+8 \\ y^{\prime }=\frac {x}{2}+y-\frac {23}{2} \end {array}\right ] \]

system_of_ODEs

0.639

17392

\[ {}\left [\begin {array}{c} x^{\prime }=-2 x+y-11 \\ y^{\prime }=-5 x+4 y-35 \end {array}\right ] \]

system_of_ODEs

0.625

17393

\[ {}\left [\begin {array}{c} x^{\prime }=x+y-3 \\ y^{\prime }=-x+y+1 \end {array}\right ] \]

system_of_ODEs

0.692

17394

\[ {}\left [\begin {array}{c} x^{\prime }=-5 x+4 y-35 \\ y^{\prime }=-2 x+y-11 \end {array}\right ] \]

system_of_ODEs

0.601

17395

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

system_of_ODEs

0.471

17396

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

system_of_ODEs

0.470

17397

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

system_of_ODEs

0.466

17398

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

system_of_ODEs

0.474

17399

\[ {}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ] \]

system_of_ODEs

0.451

17400

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

system_of_ODEs

0.458