2.2.167 Problems 16601 to 16700

Table 2.335: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

16601

\[ {}y^{\prime } = y-x \]

[[_linear, ‘class A‘]]

1.537

16602

\[ {}y^{\prime } = \frac {x}{2}-y+\frac {3}{2} \]

[[_linear, ‘class A‘]]

1.653

16603

\[ {}y^{\prime } = \left (y-1\right )^{2} \]

[_quadrature]

1.131

16604

\[ {}y^{\prime } = \left (y-1\right ) x \]

[_separable]

1.528

16605

\[ {}y^{\prime } = x^{2}-y^{2} \]

[_Riccati]

1.217

16606

\[ {}y^{\prime } = \cos \left (x -y\right ) \]

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

2.460

16607

\[ {}y^{\prime } = y-x^{2} \]

[[_linear, ‘class A‘]]

1.342

16608

\[ {}y^{\prime } = x^{2}+2 x -y \]

[[_linear, ‘class A‘]]

1.317

16609

\[ {}y^{\prime } = \frac {y+1}{-1+x} \]

[_separable]

1.843

16610

\[ {}y^{\prime } = \frac {x +y}{x -y} \]

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

39.825

16611

\[ {}y^{\prime } = 1-x \]

[_quadrature]

0.464

16612

\[ {}y^{\prime } = 2 x -y \]

[[_linear, ‘class A‘]]

1.258

16613

\[ {}y^{\prime } = y+x^{2} \]

[[_linear, ‘class A‘]]

1.299

16614

\[ {}y^{\prime } = -\frac {y}{x} \]

[_separable]

2.198

16615

\[ {}y^{\prime } = 1 \]

[_quadrature]

0.853

16616

\[ {}y^{\prime } = \frac {1}{x} \]

[_quadrature]

0.430

16617

\[ {}y^{\prime } = y \]

[_quadrature]

1.574

16618

\[ {}y^{\prime } = y^{2} \]

[_quadrature]

1.954

16619

\[ {}y^{\prime } = x^{2}-y^{2} \]
i.c.

[_Riccati]

1.540

16620

\[ {}y^{\prime } = x +y^{2} \]
i.c.

[[_Riccati, _special]]

15.151

16621

\[ {}y^{\prime } = x +y \]
i.c.

[[_linear, ‘class A‘]]

1.554

16622

\[ {}y^{\prime } = 2 y-2 x^{2}-3 \]
i.c.

[[_linear, ‘class A‘]]

1.541

16623

\[ {}x y^{\prime } = 2 x -y \]
i.c.

[_linear]

3.442

16624

\[ {}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \]

[_separable]

2.799

16625

\[ {}1+y^{2}+x y y^{\prime } = 0 \]

[_separable]

3.755

16626

\[ {}\sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = 0 \]
i.c.

[_separable]

2.714

16627

\[ {}1+y^{2} = x y^{\prime } \]

[_separable]

2.038

16628

\[ {}x \sqrt {1+y^{2}}+y y^{\prime } \sqrt {x^{2}+1} = 0 \]

[_separable]

5.135

16629

\[ {}x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime } = 0 \]
i.c.

[_separable]

13.860

16630

\[ {}{\mathrm e}^{-y} y^{\prime } = 1 \]

[_quadrature]

1.428

16631

\[ {}y \ln \left (y\right )+x y^{\prime } = 1 \]
i.c.

[_separable]

1.766

16632

\[ {}y^{\prime } = a^{x +y} \]

[_separable]

2.476

16633

\[ {}{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right ) = 0 \]

[_separable]

3.415

16634

\[ {}2 x \sqrt {1-y^{2}} = \left (x^{2}+1\right ) y^{\prime } \]

[_separable]

7.696

16635

\[ {}{\mathrm e}^{x} \sin \left (y\right )^{3}+\left (1+{\mathrm e}^{2 x}\right ) \cos \left (y\right ) y^{\prime } = 0 \]

[_separable]

4.732

16636

\[ {}y^{2} \sin \left (x \right )+\cos \left (x \right )^{2} \ln \left (y\right ) y^{\prime } = 0 \]

[_separable]

3.877

16637

\[ {}y^{\prime } = \sin \left (x -y\right ) \]

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

2.631

16638

\[ {}y^{\prime } = a x +b y+c \]

[[_linear, ‘class A‘]]

0.845

16639

\[ {}\left (x +y\right )^{2} y^{\prime } = a^{2} \]

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

5.282

16640

\[ {}x y^{\prime }+y = a \left (1+x y\right ) \]
i.c.

[_linear]

1.138

16641

\[ {}a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime } = 0 \]
i.c.

[_separable]

3.638

16642

\[ {}y^{\prime } = \frac {y}{x} \]
i.c.

[_separable]

1.273

16643

\[ {}\cos \left (y^{\prime }\right ) = 0 \]

[_quadrature]

1.130

16644

\[ {}{\mathrm e}^{y^{\prime }} = 1 \]

[_quadrature]

0.591

16645

\[ {}\sin \left (y^{\prime }\right ) = x \]

[_quadrature]

0.404

16646

\[ {}\ln \left (y^{\prime }\right ) = x \]

[_quadrature]

0.490

16647

\[ {}\tan \left (y^{\prime }\right ) = 0 \]

[_quadrature]

0.598

16648

\[ {}{\mathrm e}^{y^{\prime }} = x \]

[_quadrature]

0.405

16649

\[ {}\tan \left (y^{\prime }\right ) = x \]

[_quadrature]

0.522

16650

\[ {}x^{2} y^{\prime } \cos \left (y\right )+1 = 0 \]
i.c.

[_separable]

3.674

16651

\[ {}x^{2} y^{\prime }+\cos \left (2 y\right ) = 1 \]
i.c.

[_separable]

4.326

16652

\[ {}x^{3} y^{\prime }-\sin \left (y\right ) = 1 \]
i.c.

[_separable]

5.253

16653

\[ {}\left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2} = 0 \]
i.c.

[_separable]

16.628

16654

\[ {}{\mathrm e}^{y} = {\mathrm e}^{4 y} y^{\prime }+1 \]

[_quadrature]

2.669

16655

\[ {}\left (x +1\right ) y^{\prime } = y-1 \]

[_separable]

1.944

16656

\[ {}y^{\prime } = 2 x \left (\pi +y\right ) \]

[_separable]

1.565

16657

\[ {}x^{2} y^{\prime }+\sin \left (2 y\right ) = 1 \]
i.c.

[_separable]

16.709

16658

\[ {}x y^{\prime } = y+x \cos \left (\frac {y}{x}\right )^{2} \]

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

4.271

16659

\[ {}x -y+x y^{\prime } = 0 \]

[_linear]

1.783

16660

\[ {}x y^{\prime } = y \left (\ln \left (y\right )-\ln \left (x \right )\right ) \]

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

4.986

16661

\[ {}x^{2} y^{\prime } = y^{2}-x y+x^{2} \]

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

2.293

16662

\[ {}x y^{\prime } = y+\sqrt {y^{2}-x^{2}} \]

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

6.702

16663

\[ {}2 x^{2} y^{\prime } = x^{2}+y^{2} \]

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

2.277

16664

\[ {}4 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0 \]

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

4.710

16665

\[ {}y-x +\left (x +y\right ) y^{\prime } = 0 \]

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

4.352

16666

\[ {}x +y-2+\left (1-x \right ) y^{\prime } = 0 \]

[_linear]

1.496

16667

\[ {}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0 \]

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

3.567

16668

\[ {}x +y-2+\left (x -y+4\right ) y^{\prime } = 0 \]

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

3.445

16669

\[ {}x +y+\left (x -y-2\right ) y^{\prime } = 0 \]

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

3.572

16670

\[ {}2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime } = 0 \]

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

3.234

16671

\[ {}8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime } = 0 \]

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

2.137

16672

\[ {}x -2 y-1+\left (3 x -6 y+2\right ) y^{\prime } = 0 \]

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

2.191

16673

\[ {}x +y+\left (x +y-1\right ) y^{\prime } = 0 \]

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

1.898

16674

\[ {}2 x y^{\prime } \left (x -y^{2}\right )+y^{3} = 0 \]

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

2.092

16675

\[ {}4 y^{6}+x^{3} = 6 x y^{5} y^{\prime } \]

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

2.439

16676

\[ {}y \left (1+\sqrt {x^{2} y^{4}+1}\right )+2 x y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘]]

2.343

16677

\[ {}x +y^{3}+3 \left (y^{3}-x \right ) y^{2} y^{\prime } = 0 \]

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

1.734

16678

\[ {}y^{\prime }+2 y = {\mathrm e}^{-x} \]

[[_linear, ‘class A‘]]

1.575

16679

\[ {}x^{2}-x y^{\prime } = y \]
i.c.

[_linear]

2.393

16680

\[ {}y^{\prime }-2 x y = 2 x \,{\mathrm e}^{x^{2}} \]

[_linear]

3.275

16681

\[ {}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}} \]

[_linear]

2.091

16682

\[ {}\cos \left (x \right ) y^{\prime }-y \sin \left (x \right ) = 2 x \]
i.c.

[_linear]

2.579

16683

\[ {}x y^{\prime }-2 y = x^{3} \cos \left (x \right ) \]

[_linear]

1.960

16684

\[ {}y^{\prime }-y \tan \left (x \right ) = \frac {1}{\cos \left (x \right )^{3}} \]
i.c.

[_linear]

11.954

16685

\[ {}y^{\prime } x \ln \left (x \right )-y = 3 x^{3} \ln \left (x \right )^{2} \]

[_linear]

1.548

16686

\[ {}\left (2 x -y^{2}\right ) y^{\prime } = 2 y \]

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

2.316

16687

\[ {}y^{\prime }+y \cos \left (x \right ) = \cos \left (x \right ) \]
i.c.

[_separable]

2.062

16688

\[ {}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x} \]

[[_1st_order, _with_linear_symmetries]]

1.731

16689

\[ {}\left (\frac {{\mathrm e}^{-y^{2}}}{2}-x y\right ) y^{\prime }-1 = 0 \]

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

1.636

16690

\[ {}y^{\prime }-y \,{\mathrm e}^{x} = 2 x \,{\mathrm e}^{{\mathrm e}^{x}} \]

[_linear]

1.734

16691

\[ {}y^{\prime }+x y \,{\mathrm e}^{x} = {\mathrm e}^{\left (1-x \right ) {\mathrm e}^{x}} \]

[_linear]

1.654

16692

\[ {}y^{\prime }-y \ln \left (2\right ) = 2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right ) \]

[[_linear, ‘class A‘]]

2.614

16693

\[ {}y^{\prime }-y = -2 \,{\mathrm e}^{-x} \]
i.c.

[[_linear, ‘class A‘]]

1.323

16694

\[ {}\sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = -\frac {\sin \left (x \right )^{2}}{x^{2}} \]
i.c.

[_linear]

4.746

16695

\[ {}x^{2} y^{\prime } \cos \left (\frac {1}{x}\right )-y \sin \left (\frac {1}{x}\right ) = -1 \]
i.c.

[_linear]

3.000

16696

\[ {}2 x y^{\prime }-y = 1-\frac {2}{\sqrt {x}} \]
i.c.

[_linear]

1.901

16697

\[ {}x^{2} y^{\prime }+y = \left (x^{2}+1\right ) {\mathrm e}^{x} \]
i.c.

[_linear]

2.369

16698

\[ {}x y^{\prime }+y = 2 x \]

[_linear]

3.421

16699

\[ {}\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 1 \]

[_linear]

2.411

16700

\[ {}\cos \left (x \right ) y^{\prime }-y \sin \left (x \right ) = -\sin \left (2 x \right ) \]
i.c.

[_linear]

3.372