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

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

4.440

11402

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

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

3.740

11403

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

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

5.132

11404

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

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

2.503

11405

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

[_rational, _Riccati]

30.008

11406

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

[_rational, _Riccati]

3.418

11407

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

[_rational, _Riccati]

1.217

11408

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

[_Bernoulli]

4.119

11409

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

[_Bernoulli]

4.271

11410

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

[[_homogeneous, ‘class D‘], _Riccati]

3.430

11411

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

[_rational, _Abel]

11.253

11412

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

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

7.347

11413

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

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

20.624

11414

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

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

3.066

11415

\begin{align*} y^{\prime } x -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)]‘]]

62.366

11416

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

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

7.139

11417

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

[_separable]

4.115

11418

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

[[_homogeneous, ‘class G‘]]

4.457

11419

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

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

2.080

11420

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

[‘y=_G(x,y’)‘]

265.181

11421

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

[‘y=_G(x,y’)‘]

3.794

11422

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

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

6.585

11423

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

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

5.819

11424

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

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

9.891

11425

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

[[_homogeneous, ‘class G‘]]

1.988

11426

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

[[_homogeneous, ‘class G‘]]

3.492

11427

\begin{align*} y^{\prime } x +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)]‘]]

6.262

11428

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

[_rational, _Bernoulli]

2.125

11429

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

[_linear]

4.572

11430

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

[_separable]

4.123

11431

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

[_Bernoulli]

5.247

11432

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

[_linear]

1.892

11433

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

[_linear]

2.401

11434

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

[_separable]

3.275

11435

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

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

4.568

11436

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

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

4.456

11437

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

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

4.786

11438

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

[_rational, _Riccati]

0.469

11439

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

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

4.776

11440

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

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

4.112

11441

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

[_rational, _Riccati]

2.731

11442

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

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

3.955

11443

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

[_rational, _Riccati]

71.132

11444

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

[_rational, _Abel]

5.470

11445

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

[_rational, _Abel]

9.884

11446

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

[_rational, _Abel]

8.028

11447

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

[_linear]

1.662

11448

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

[_linear]

6.804

11449

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

[_linear]

1.777

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]

58.483

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’)‘]

17.802

11452

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

[_linear]

4.394

11453

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

[_linear]

3.748

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]

3.760

11455

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

[_rational, _Bernoulli]

4.782

11456

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

[_rational, _Riccati]

5.705

11457

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

[_separable]

5.560

11458

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

[_separable]

5.120

11459

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

[_rational, _Bernoulli]

2.546

11460

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

[_linear]

2.543

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]

8.791

11462

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

[_rational, _Riccati]

2.493

11463

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

[_rational, _Riccati]

3.835

11464

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

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

5.471

11465

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

[_rational, _Riccati]

6.684

11466

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

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

5.411

11467

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

[_rational, _Riccati]

151.417

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]

11.745

11469

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

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

3.184

11470

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

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

4.612

11471

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

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

6.300

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]

2.121

11473

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

[_separable]

2.714

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]

2.747

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]

117.076

11476

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

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

4.541

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]

4.299

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]

69.518

11479

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

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

4.346

11480

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

[_rational, [_Riccati, _special]]

4.307

11481

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

[_rational, _Riccati]

3.566

11482

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

[_separable]

3.536

11483

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

[_rational, _Riccati]

5.642

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]

26.684

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]

4.890

11486

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

[[_homogeneous, ‘class G‘], _Riccati]

8.113

11487

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

[[_homogeneous, ‘class G‘], _Abel]

9.146

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‘]]

6.086

11489

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

[_separable]

10.720

11490

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

[_separable]

18.421

11491

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

[_linear]

3.059

11492

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

[_linear]

3.198

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]

4.719

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]

0.781

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]

4.158

11496

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

[_Bernoulli]

57.837

11497

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

[_linear]

6.451

11498

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

[_separable]

18.050

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]

18.592

11500

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

[_Riccati]

4.504