2.2.144 Problems 14301 to 14400

Table 2.289: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

14301

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

[_separable]

3.310

14302

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

[_separable]

1.406

14303

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

[[_homogeneous, ‘class G‘]]

5.214

14304

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

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

6.358

14305

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

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

16.587

14306

\[ {}y^{\prime } = 4 y-5 \]
i.c.

[_quadrature]

2.080

14307

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

[_quadrature]

2.175

14308

\[ {}y^{\prime } = a y+b \]
i.c.

[_quadrature]

1.047

14309

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

[_quadrature]

0.905

14310

\[ {}y^{\prime } = x y+\frac {1}{x^{2}+1} \]
i.c.

[_linear]

2.220

14311

\[ {}y^{\prime } = \frac {y}{x}+\cos \left (x \right ) \]
i.c.

[_linear]

1.778

14312

\[ {}y^{\prime } = \frac {y}{x}+\tan \left (x \right ) \]
i.c.

[_linear]

2.036

14313

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

[_linear]

2.713

14314

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

[_linear]

2.571

14315

\[ {}y^{\prime } = \cot \left (x \right ) y+\csc \left (x \right ) \]
i.c.

[_linear]

2.009

14316

\[ {}y^{\prime } = -x \sqrt {1-y^{2}} \]
i.c.

[_separable]

6.395

14317

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

2.348

14318

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

[_quadrature]

0.674

14319

\[ {}y^{\prime } = x +\frac {1}{x} \]
i.c.

[_quadrature]

0.743

14320

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

[_quadrature]

0.749

14321

\[ {}y^{\prime } = x \sin \left (x \right ) \]
i.c.

[_quadrature]

0.796

14322

\[ {}y^{\prime } = \frac {1}{-1+x} \]
i.c.

[_quadrature]

0.730

14323

\[ {}y^{\prime } = \frac {1}{-1+x} \]
i.c.

[_quadrature]

0.634

14324

\[ {}y^{\prime } = \frac {1}{x^{2}-1} \]
i.c.

[_quadrature]

0.674

14325

\[ {}y^{\prime } = \frac {1}{x^{2}-1} \]
i.c.

[_quadrature]

0.744

14326

\[ {}y^{\prime } = \tan \left (x \right ) \]
i.c.

[_quadrature]

1.121

14327

\[ {}y^{\prime } = \tan \left (x \right ) \]
i.c.

[_quadrature]

0.710

14328

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

[_quadrature]

3.223

14329

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

[_quadrature]

1.314

14330

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

[_quadrature]

1.795

14331

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

[_separable]

2.316

14332

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

[_separable]

2.039

14333

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

[_separable]

8.974

14334

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

[_quadrature]

2.740

14335

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

[_separable]

1.961

14336

\[ {}x \,{\mathrm e}^{y}+y^{\prime } = 0 \]
i.c.

[_separable]

2.711

14337

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

[_separable]

1.751

14338

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

[_quadrature]

1.887

14339

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

[_separable]

2.777

14340

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

[_linear]

1.252

14341

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

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

62.497

14342

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

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

1.636

14343

\[ {}y^{\prime } = 4 y+1 \]
i.c.

[_quadrature]

2.049

14344

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

[_linear]

1.462

14345

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

[_separable]

2.019

14346

\[ {}y^{\prime } = \frac {y}{-1+x}+x^{2} \]
i.c.

[_linear]

1.425

14347

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

[_linear]

2.204

14348

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

[_linear]

2.205

14349

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

[_linear]

2.153

14350

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

[_separable]

4.461

14351

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

[_separable]

1.659

14352

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

[_linear]

1.601

14353

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

[_separable]

2.507

14354

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

[_separable]

2.506

14355

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

[_separable]

1.705

14356

\[ {}y^{\prime } = \frac {1}{-1+x} \]
i.c.

[_quadrature]

0.615

14357

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

[[_linear, ‘class A‘]]

1.505

14358

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

[_separable]

2.021

14359

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

[_separable]

2.007

14360

\[ {}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x} \]
i.c.

[_linear]

2.208

14361

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

[_linear]

1.783

14362

\[ {}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x} \]
i.c.

[_linear]

2.247

14363

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

[_quadrature]

2.297

14364

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

[_quadrature]

1.937

14365

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

[_quadrature]

2.214

14366

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

[_quadrature]

3.354

14367

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

[_quadrature]

4.831

14368

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

[_quadrature]

10.761

14369

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

[_separable]

3.052

14370

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

[_separable]

2.897

14371

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

[_separable]

2.560

14372

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

[_separable]

3.117

14373

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

[_separable]

3.194

14374

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

[_separable]

3.040

14375

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

[_separable]

3.329

14376

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

[_separable]

2.958

14377

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

[_separable]

40.444

14378

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

[_separable]

8.617

14379

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

[_separable]

114.345

14380

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

[_separable]

11.530

14381

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

[_separable]

14.012

14382

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

[_quadrature]

19.111

14383

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

[_quadrature]

3.829

14384

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

[_quadrature]

61.680

14385

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

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

5.569

14386

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

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

5.072

14387

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

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

5.919

14388

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

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

5.243

14389

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

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

5.011

14390

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

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

5.389

14391

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

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

4.907

14392

\[ {}y^{\prime } = x \sqrt {1-y^{2}} \]
i.c.

[_separable]

4.109

14393

\[ {}y^{\prime } = x \sqrt {1-y^{2}} \]
i.c.

[_separable]

84.826

14394

\[ {}y^{\prime } = x \sqrt {1-y^{2}} \]
i.c.

[_separable]

7.483

14395

\[ {}y^{\prime } = x \sqrt {1-y^{2}} \]
i.c.

[_separable]

3.225

14396

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

2.750

14397

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

2.522

14398

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

2.593

14399

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

3.022

14400

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

2.497