2.2.164 Problems 16301 to 16400

Table 2.341: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

16301

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

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

1.292

16302

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

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

3.857

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‘]]

49.898

16304

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

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

1.631

16305

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

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

1.211

16306

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

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

1.326

16307

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

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

7.912

16308

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

[[_1st_order, _with_linear_symmetries], _Bernoulli]

2.111

16309

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

[[_homogeneous, ‘class C‘], _Riccati]

2.419

16310

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

2.420

16311

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

[‘y=_G(x,y’)‘]

2.389

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]

2.352

16313

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

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

2.503

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]

0.217

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‘]]

7.015

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]

2.777

16317

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

[_separable]

1.861

16318

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

[_exact, _rational, _Bernoulli]

2.066

16319

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

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

76.194

16320

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

[[_homogeneous, ‘class G‘], _exact]

2.451

16321

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

[_separable]

2.367

16322

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

[[_1st_order, _with_exponential_symmetries], _exact]

1.410

16323

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

[_separable]

2.714

16324

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

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

6.233

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‘]]

5.112

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]‘]]

1.457

16327

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

[_separable]

4.245

16328

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

[_separable]

1.602

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‘]]

0.667

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‘]]

2.833

16331

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

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

3.451

16332

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

[_linear]

1.056

16333

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

[_separable]

3.467

16334

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

[_separable]

2.095

16335

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

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

1.924

16336

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

[_quadrature]

0.260

16337

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

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

16.956

16338

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

[[_homogeneous, ‘class C‘], _Riccati]

1.224

16339

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

[_linear]

2.076

16340

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

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

1.586

16341

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

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

7.957

16342

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

[_linear]

1.896

16343

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

[_exact, _rational, _Bernoulli]

1.993

16344

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

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

3.375

16345

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

[_linear]

2.074

16346

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

[_quadrature]

0.424

16347

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

[_quadrature]

0.268

16348

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

[_separable]

1.964

16349

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

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

2.465

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]‘]]

4.548

16351

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

[_separable]

4.796

16352

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

[_quadrature]

0.313

16353

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

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

5.694

16354

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

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

6.412

16355

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

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

4.199

16356

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

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

4.143

16357

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

[_separable]

2.694

16358

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

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

1.647

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]‘]]

1.842

16360

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

[_quadrature]

1.729

16361

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

[[_linear, ‘class A‘]]

1.111

16362

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

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

7.285

16363

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

[_quadrature]

0.278

16364

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

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

2.956

16365

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

[[_1st_order, _with_linear_symmetries], _Bernoulli]

1.638

16366

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

[_linear]

2.253

16367

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

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

0.244

16368

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

[_Bernoulli]

2.828

16369

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

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

2.046

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)]‘]]

1.877

16371

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

[_separable]

2.795

16372

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

[[_linear, ‘class A‘]]

1.597

16373

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

[_quadrature]

0.230

16374

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

[_separable]

4.967

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)]‘]]

2.520

16376

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

[_separable]

1.516

16377

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

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

2.962

16378

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

[_separable]

1.205

16379

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

[_linear]

1.720

16380

\begin{align*} x \left (1-2 y\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‘]]

1.817

16381

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

[_linear]

1.922

16382

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

[[_2nd_order, _missing_y]]

0.928

16383

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

[[_2nd_order, _missing_y]]

0.687

16384

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

[[_2nd_order, _missing_x]]

0.661

16385

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

[[_2nd_order, _missing_y]]

0.898

16386

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

[[_2nd_order, _missing_y]]

0.537

16387

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

[[_2nd_order, _missing_y]]

0.635

16388

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

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

0.432

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]]

1.466

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]]

7.616

16391

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

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

0.581

16392

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

[[_2nd_order, _missing_y]]

1.873

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]]

0.401

16394

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

[[_2nd_order, _missing_x]]

0.897

16395

\begin{align*} \left (y-3\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]]

0.242

16396

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

[[_2nd_order, _missing_y]]

0.939

16397

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

[[_3rd_order, _missing_x]]

0.040

16398

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

[[_3rd_order, _missing_y]]

0.164

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]]

0.661

16400

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

[[_high_order, _missing_x]]

0.049