2.2.115 Problems 11401 to 11500

Table 2.247: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

11401

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

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

4.595

11402

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

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

4.166

11403

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

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

5.428

11404

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

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

2.447

11405

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

[_rational, _Riccati]

30.356

11406

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

[_rational, _Riccati]

3.381

11407

\begin{align*} x y^{\prime }+a \,x^{\alpha } y^{2}+b y-c \,x^{\beta }&=0 \\ \end{align*}

[_rational, _Riccati]

1.299

11408

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

[_Bernoulli]

4.471

11409

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

[_Bernoulli]

4.630

11410

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

[[_homogeneous, ‘class D‘], _Riccati]

4.102

11411

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

[_rational, _Abel]

8.128

11412

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

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

7.350

11413

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

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

21.751

11414

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

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

2.349

11415

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

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

9.529

11416

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

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

7.305

11417

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

[_separable]

4.042

11418

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

[[_homogeneous, ‘class G‘]]

4.207

11419

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

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

1.837

11420

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

[‘y=_G(x,y’)‘]

51.100

11421

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

[‘y=_G(x,y’)‘]

4.016

11422

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

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

6.607

11423

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

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

5.966

11424

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

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

10.833

11425

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

[[_homogeneous, ‘class G‘]]

2.160

11426

\begin{align*} x y^{\prime }-y f \left (x^{a} y^{b}\right )&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘]]

3.398

11427

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

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

5.757

11428

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

[_rational, _Bernoulli]

1.869

11429

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

[_linear]

4.679

11430

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

[_separable]

4.273

11431

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

[_Bernoulli]

3.652

11432

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

[_linear]

1.601

11433

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

[_linear]

2.246

11434

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

[_separable]

3.441

11435

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

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

4.857

11436

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

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

4.656

11437

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

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

5.197

11438

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

[_rational, _Riccati]

0.467

11439

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

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

5.134

11440

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

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

4.416

11441

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

[_rational, _Riccati]

2.583

11442

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

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

4.205

11443

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

[_rational, _Riccati]

72.026

11444

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

[_rational, _Abel]

2.976

11445

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

[_rational, _Abel]

9.863

11446

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

[_rational, _Abel]

3.938

11447

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

[_linear]

1.759

11448

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

[_linear]

7.357

11449

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

[_linear]

1.791

11450

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

[_rational, _Abel]

54.425

11451

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

[‘y=_G(x,y’)‘]

28.882

11452

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

[_linear]

5.528

11453

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

[_linear]

4.233

11454

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

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

4.174

11455

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

[_rational, _Bernoulli]

5.287

11456

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

[_rational, _Riccati]

3.056

11457

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

[_separable]

6.523

11458

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

[_separable]

5.537

11459

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

[_rational, _Bernoulli]

2.359

11460

\begin{align*} \left (x^{2}-5 x +6\right ) y^{\prime }+3 y x -8 y+x^{2}&=0 \\ \end{align*}

[_linear]

2.303

11461

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

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

10.246

11462

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

[_rational, _Riccati]

2.300

11463

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

[_rational, _Riccati]

4.555

11464

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

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

5.742

11465

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

[_rational, _Riccati]

7.243

11466

\begin{align*} 3 x^{2} y^{\prime }-7 y^{2}-3 y x -x^{2}&=0 \\ \end{align*}

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

5.877

11467

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

[_rational, _Riccati]

156.880

11468

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

[_rational, _Abel]

17.177

11469

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

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

3.681

11470

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

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

5.707

11471

\begin{align*} x^{3} y^{\prime }-y^{2} x^{4}+x^{2} y+20&=0 \\ \end{align*}

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

7.240

11472

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

[_rational, _Riccati]

2.361

11473

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

[_separable]

3.256

11474

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

[_linear]

3.294

11475

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

[_rational, _Riccati]

163.671

11476

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

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

5.381

11477

\begin{align*} 2 x \left (x^{2}-1\right ) y^{\prime }+2 \left (x^{2}-1\right ) y^{2}-\left (3 x^{2}-5\right ) y+x^{2}-3&=0 \\ \end{align*}

[_rational, _Riccati]

3.869

11478

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

[_rational, _Riccati]

76.540

11479

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

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

5.138

11480

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

[_rational, [_Riccati, _special]]

5.105

11481

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

[_rational, _Riccati]

3.310

11482

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

[_separable]

4.330

11483

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

[_rational, _Riccati]

5.952

11484

\begin{align*} x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\ \end{align*}

[_rational, _Abel]

25.794

11485

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

[[_homogeneous, ‘class G‘], _Riccati]

5.481

11486

\begin{align*} x^{n} y^{\prime }-a y^{2}-b \,x^{2 n -2}&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _Riccati]

8.977

11487

\begin{align*} x^{1+2 n} y^{\prime }-a y^{3}-b \,x^{3 n}&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _Abel]

10.158

11488

\begin{align*} x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (m +1\right )}&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘]]

6.694

11489

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

[_separable]

11.553

11490

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

[_separable]

21.487

11491

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

[_linear]

3.217

11492

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

[_linear]

3.147

11493

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

[_Riccati]

5.390

11494

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

[_Riccati]

0.797

11495

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

[_linear]

3.800

11496

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

[_Bernoulli]

9.279

11497

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

[_linear]

6.269

11498

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

[_separable]

23.190

11499

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

[_linear]

18.373

11500

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

[_Riccati]

4.121