2.2.274 Problems 27301 to 27400

Table 2.565: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

27301

\begin{align*} x \left (2-9 x y^{2}\right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime }&=0 \\ \end{align*}

[_exact, _rational]

2.178

27302

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

[[_1st_order, _with_exponential_symmetries], _exact]

2.014

27303

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

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

1.549

27304

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

[_exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘]]

2.658

27305

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

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

3.167

27306

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

[_exact, _Bernoulli]

6.323

27307

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

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

2.389

27308

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

[_exact]

4.710

27309

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

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

1.930

27310

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

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

1.342

27311

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

[_linear]

2.177

27312

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

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

2.663

27313

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

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

8.093

27314

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

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

3.025

27315

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

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

3.602

27316

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

[[_homogeneous, ‘class G‘]]

11.689

27317

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

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

3.326

27318

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

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

3.188

27319

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

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

3.072

27320

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

[[_homogeneous, ‘class D‘]]

3.680

27321

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

[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]]

3.191

27322

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

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

2.615

27323

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

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

12.188

27324

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

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

5.500

27325

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

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

13.585

27326

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

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

6.493

27327

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

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

18.607

27328

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

[‘y=_G(x,y’)‘]

3.978

27329

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

[[_homogeneous, ‘class G‘]]

5.312

27330

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

[‘y=_G(x,y’)‘]

4.105

27331

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

[_rational]

2.172

27332

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

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

4.395

27333

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

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

6.477

27334

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

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

19.677

27335

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

[[_Riccati, _special]]

3.043

27336

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

80.907

27337

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

[_quadrature]

2.105

27338

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

[_Bernoulli]

1.627

27339

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

[_quadrature]

2.227

27340

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

[_quadrature]

2.467

27341

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

[_quadrature]

0.933

27342

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

[_quadrature]

1.014

27343

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

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

12.061

27344

\begin{align*} y^{\prime }&=\frac {x +2 y-4}{x -y-1} \\ \end{align*}

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

19.704

27345

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

[_quadrature]

1.683

27346

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

[_quadrature]

3.123

27347

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

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

1.805

27348

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

[[_1st_order, _with_linear_symmetries]]

58.089

27349

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

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

9.701

27350

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

[_quadrature]

0.521

27351

\begin{align*} 8 {y^{\prime }}^{3}&=27 y \\ \end{align*}

[_quadrature]

1.759

27352

\begin{align*} \left (y^{\prime }+1\right )^{3}&=27 \left (x +y\right )^{2} \\ \end{align*}

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

1.250

27353

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

[_quadrature]

0.625

27354

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

[_quadrature]

3.553

27355

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

[_quadrature]

6.802

27356

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

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

1.947

27357

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

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

1.551

27358

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

[_quadrature]

0.444

27359

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

[_quadrature]

0.826

27360

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

[_quadrature]

0.508

27361

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

[_separable]

0.509

27362

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

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

1.524

27363

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

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

1.652

27364

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

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

0.907

27365

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

[[_1st_order, _with_exponential_symmetries]]

229.930

27366

\begin{align*} {y^{\prime }}^{2}-2 x y^{\prime }&=8 x^{2} \\ \end{align*}

[_quadrature]

0.450

27367

\begin{align*} \left (x y^{\prime }+3 y\right )^{2}&=7 x \\ \end{align*}

[_linear]

1.041

27368

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

[_separable]

4.320

27369

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

[_separable]

1.122

27370

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

[_quadrature]

1.043

27371

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

[_separable]

1.017

27372

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

[_separable]

0.799

27373

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

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

2.508

27374

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

[[_linear, ‘class A‘]]

0.681

27375

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

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

1.429

27376

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

[_quadrature]

0.771

27377

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

[_quadrature]

0.667

27378

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

[_quadrature]

1072.464

27379

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

[_quadrature]

1.217

27380

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

[_quadrature]

0.913

27381

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

[_quadrature]

1.664

27382

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

[_quadrature]

10.766

27383

\begin{align*} y&=\left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }} \\ \end{align*}

[_quadrature]

1.145

27384

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

[_quadrature]

597.000

27385

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

[_quadrature]

0.944

27386

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

[_quadrature]

562.776

27387

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

[[_homogeneous, ‘class G‘]]

10.316

27388

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

[[_homogeneous, ‘class G‘]]

6.070

27389

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

[_separable]

3.059

27390

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

[[_1st_order, _with_linear_symmetries]]

238.708

27391

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

[[_1st_order, _with_linear_symmetries]]

31.902

27392

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

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

20.619

27393

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

[[_1st_order, _with_linear_symmetries]]

13.987

27394

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

[[_1st_order, _with_linear_symmetries]]

1.013

27395

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

[[_homogeneous, ‘class G‘]]

3.653

27396

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.566

27397

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

[[_homogeneous, ‘class G‘], _dAlembert]

182.532

27398

\begin{align*} y&=3 x y^{\prime }-7 {y^{\prime }}^{3} \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _dAlembert]

9.090

27399

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

[_separable]

3.902

27400

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

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

3.136