2.2.164 Problems 16301 to 16400

Table 2.345: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

16301

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

[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

3.941

16302

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

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

13.358

16303

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

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

59.980

16304

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

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

4.374

16305

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

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

2.582

16306

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

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

5.368

16307

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

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

15.310

16308

\begin{align*} y^{\prime }+3 y&=\frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Bernoulli]

4.667

16309

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

[[_homogeneous, ‘class C‘], _Riccati]

4.896

16310

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

7.375

16311

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

[‘y=_G(x,y’)‘]

2.865

16312

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

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

4.122

16313

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

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

7.864

16314

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

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

0.409

16315

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

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

23.250

16316

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

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

5.744

16317

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

[_separable]

3.331

16318

\begin{align*} 1+3 x^{2} y^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime }&=0 \\ \end{align*}

[_exact, _rational, _Bernoulli]

3.517

16319

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

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

130.420

16320

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

[[_homogeneous, ‘class G‘], _exact]

6.089

16321

\begin{align*} 1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }&=0 \\ \end{align*}

[_separable]

4.569

16322

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

[[_1st_order, _with_exponential_symmetries], _exact]

2.365

16323

\begin{align*} 1+y^{4}+x y^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.201

16324

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

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

30.619

16325

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

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

79.165

16326

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

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

2.498

16327

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

[_separable]

20.189

16328

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

[_separable]

3.019

16329

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

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

76.178

16330

\begin{align*} 4 y x +\left (3 x^{2}+5 y\right ) y^{\prime }&=0 \\ \end{align*}

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

30.193

16331

\begin{align*} 6+12 x^{2} y^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime }&=0 \\ \end{align*}

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

6.815

16332

\begin{align*} x y^{\prime }&=2 y-6 x^{3} \\ \end{align*}

[_linear]

2.139

16333

\begin{align*} x y^{\prime }&=2 y^{2}-6 y \\ \end{align*}

[_separable]

9.275

16334

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

[_separable]

3.467

16335

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

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

6.053

16336

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

[_quadrature]

0.435

16337

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

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

34.374

16338

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

[[_homogeneous, ‘class C‘], _Riccati]

2.584

16339

\begin{align*} 4 y x -6+x^{2} y^{\prime }&=0 \\ \end{align*}

[_linear]

4.256

16340

\begin{align*} x y^{2}-6+x^{2} y y^{\prime }&=0 \\ \end{align*}

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

5.139

16341

\begin{align*} x^{3}+y^{3}+x y^{2} y^{\prime }&=0 \\ \end{align*}

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

13.812

16342

\begin{align*} 3 y-x^{3}+x y^{\prime }&=0 \\ \end{align*}

[_linear]

3.718

16343

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

[_exact, _rational, _Bernoulli]

3.341

16344

\begin{align*} 3 x y^{3}-y+x y^{\prime }&=0 \\ \end{align*}

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

10.349

16345

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

[_linear]

2.788

16346

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

[_quadrature]

1.132

16347

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

[_quadrature]

0.593

16348

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

[_separable]

11.770

16349

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

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

4.390

16350

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

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

10.295

16351

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

[_separable]

12.413

16352

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

[_quadrature]

0.755

16353

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

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

15.858

16354

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

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

10.744

16355

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

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

13.201

16356

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

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

11.954

16357

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

[_separable]

4.528

16358

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

[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

5.242

16359

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

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

3.329

16360

\begin{align*} y^{2}+1-y^{\prime }&=0 \\ \end{align*}

[_quadrature]

3.247

16361

\begin{align*} y^{\prime }-3 y&=12 \,{\mathrm e}^{2 x} \\ \end{align*}

[[_linear, ‘class A‘]]

2.062

16362

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

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

28.738

16363

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

[_quadrature]

0.536

16364

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

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

6.107

16365

\begin{align*} y^{\prime }&=4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Bernoulli]

3.115

16366

\begin{align*} 2 y-6 x +\left (x +1\right ) y^{\prime }&=0 \\ \end{align*}

[_linear]

4.208

16367

\begin{align*} x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime }&=0 \\ \end{align*}

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

0.519

16368

\begin{align*} y y^{\prime }-x y^{2}&=6 x \,{\mathrm e}^{4 x^{2}} \\ \end{align*}

[_Bernoulli]

4.711

16369

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

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

4.420

16370

\begin{align*} x +y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }&=0 \\ \end{align*}

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

2.701

16371

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

[_separable]

3.927

16372

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

[[_linear, ‘class A‘]]

2.273

16373

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

[_quadrature]

0.398

16374

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

[_separable]

5.627

16375

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

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

3.966

16376

\begin{align*} y^{\prime }&={\mathrm e}^{4 x +3 y} \\ \end{align*}

[_separable]

2.904

16377

\begin{align*} y^{\prime }&=\tan \left (6 x +3 y+1\right )-2 \\ \end{align*}

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

7.948

16378

\begin{align*} y^{\prime }&={\mathrm e}^{4 x +3 y} \\ \end{align*}

[_separable]

2.385

16379

\begin{align*} y^{\prime }&=x \left (6 y+{\mathrm e}^{x^{2}}\right ) \\ \end{align*}

[_linear]

2.295

16380

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

[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]]

4.731

16381

\begin{align*} x^{2} y^{\prime }+3 y x&=6 \,{\mathrm e}^{-x^{2}} \\ \end{align*}

[_linear]

2.579

16382

\begin{align*} x y^{\prime \prime }+4 y^{\prime }&=18 x^{2} \\ \end{align*}

[[_2nd_order, _missing_y]]

1.272

16383

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

[[_2nd_order, _missing_y]]

0.902

16384

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

[[_2nd_order, _missing_x]]

1.054

16385

\begin{align*} y^{\prime \prime }+2 y^{\prime }&=8 \,{\mathrm e}^{2 x} \\ \end{align*}

[[_2nd_order, _missing_y]]

1.055

16386

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

[[_2nd_order, _missing_y]]

0.926

16387

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

[[_2nd_order, _missing_y]]

0.793

16388

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

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

0.783

16389

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

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]]

2.799

16390

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

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

0.770

16391

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

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

1.112

16392

\begin{align*} x y^{\prime \prime }-{y^{\prime }}^{2}&=6 x^{5} \\ \end{align*}

[[_2nd_order, _missing_y]]

1.560

16393

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

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

0.901

16394

\begin{align*} y^{\prime \prime }&=2 y^{\prime }-6 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.259

16395

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

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.377

16396

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=9 \,{\mathrm e}^{-3 x} \\ \end{align*}

[[_2nd_order, _missing_y]]

1.071

16397

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

[[_3rd_order, _missing_x]]

0.058

16398

\begin{align*} x y^{\prime \prime \prime }+2 y^{\prime \prime }&=6 x \\ \end{align*}

[[_3rd_order, _missing_y]]

0.277

16399

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

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

1.621

16400

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

[[_high_order, _missing_x]]

0.072