2.2.168 Problems 16701 to 16800

Table 2.337: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

16701

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

[[_linear, ‘class A‘]]

1.483

16702

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

[_linear]

10.569

16703

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

[_linear]

2.564

16704

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

[_linear]

3.767

16705

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

[_linear]

1.908

16706

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

[_linear]

2.315

16707

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

[_linear]

1.843

16708

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

[_linear]

2.730

16709

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

[_separable]

1.945

16710

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

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

11.938

16711

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

[[_1st_order, _with_linear_symmetries]]

1.295

16712

\[ {}y^{\prime }+3 x y = y \,{\mathrm e}^{x^{2}} \]

[_separable]

1.569

16713

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

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

4.114

16714

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

[_Bernoulli]

4.592

16715

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

[_Bernoulli]

8.937

16716

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

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

1.819

16717

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

[_separable]

2.500

16718

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

[‘y=_G(x,y’)‘]

3.501

16719

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

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

2.387

16720

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

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

2.906

16721

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

[‘y=_G(x,y’)‘]

3.200

16722

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

[‘y=_G(x,y’)‘]

6.531

16723

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

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

170.376

16724

\[ {}3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0 \]

[_exact, _rational]

1.955

16725

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

[_exact]

23.955

16726

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

[_exact]

49.066

16727

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

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

3.406

16728

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

[_exact]

34.369

16729

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

[_exact, _rational]

1.360

16730

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

[_separable]

27.418

16731

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

[_exact]

38.384

16732

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

[_exact]

49.885

16733

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

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

5.753

16734

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

[_exact, _rational]

2.186

16735

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

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

6.270

16736

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

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

1.573

16737

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

[_linear]

1.221

16738

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

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

1.937

16739

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

[_linear]

1.296

16740

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

[_Bernoulli]

2.059

16741

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

[‘y=_G(x,y’)‘]

3.787

16742

\[ {}2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime } = 0 \]

[_rational]

3.550

16743

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

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

4.615

16744

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

[_rational, _Bernoulli]

2.050

16745

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

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

2.312

16746

\[ {}4 {y^{\prime }}^{2}-9 x = 0 \]

[_quadrature]

0.425

16747

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

[_separable]

0.536

16748

\[ {}{y^{\prime }}^{2}-2 y^{\prime } x -8 x^{2} = 0 \]

[_quadrature]

0.307

16749

\[ {}x^{2} {y^{\prime }}^{2}+3 x y^{\prime } y+2 y^{2} = 0 \]

[_separable]

0.709

16750

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

[_quadrature]

0.411

16751

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

[[_1st_order, _with_exponential_symmetries]]

1.209

16752

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

[_quadrature]

0.498

16753

\[ {}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0 \]

[[_1st_order, _with_linear_symmetries]]

6.374

16754

\[ {}{y^{\prime }}^{2}-4 y^{\prime } x +2 y+2 x^{2} = 0 \]

[[_homogeneous, ‘class G‘]]

1.708

16755

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

[_quadrature]

0.695

16756

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

[_quadrature]

0.740

16757

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

[_quadrature]

3.166

16758

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

[_quadrature]

0.299

16759

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

[_quadrature]

2.389

16760

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

[_quadrature]

0.839

16761

\[ {}x {y^{\prime }}^{2} = {\mathrm e}^{\frac {1}{y^{\prime }}} \]

[_quadrature]

0.629

16762

\[ {}x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = a \]

[_quadrature]

2.547

16763

\[ {}y^{{2}/{5}}+{y^{\prime }}^{{2}/{5}} = a^{{2}/{5}} \]

[_quadrature]

2.418

16764

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

[_quadrature]

0.695

16765

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

[_quadrature]

1.644

16766

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

[_quadrature]

4.955

16767

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

3.574

16768

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.597

16769

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

[_dAlembert]

1.299

16770

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

[_dAlembert]

2.992

16771

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

[_dAlembert]

1.295

16772

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.820

16773

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.474

16774

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

0.581

16775

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

2.703

16776

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

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

0.504

16777

\[ {}{\mathrm e}^{-x} y^{\prime }+y^{2}-2 y \,{\mathrm e}^{x} = 1-{\mathrm e}^{2 x} \]

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

2.502

16778

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

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

2.821

16779

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

[[_1st_order, _with_linear_symmetries], _rational, _Riccati]

1.665

16780

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

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

1.385

16781

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

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

7.723

16782

\[ {}{y^{\prime }}^{2}-4 y = 0 \]

[_quadrature]

0.461

16783

\[ {}{y^{\prime }}^{3}-4 x y^{\prime } y+8 y^{2} = 0 \]

[[_1st_order, _with_linear_symmetries]]

9.827

16784

\[ {}{y^{\prime }}^{2}-y^{2} = 0 \]

[_quadrature]

0.577

16785

\[ {}y^{\prime } = y^{{2}/{3}}+a \]

[_quadrature]

6.402

16786

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

[[_homogeneous, ‘class G‘]]

8.314

16787

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

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

2.440

16788

\[ {}8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2} = 27 y-27 x \]

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

0.572

16789

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

[_quadrature]

0.529

16790

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.556

16791

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

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

89.006

16792

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

[_quadrature]

0.541

16793

\[ {}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0 \]

[[_1st_order, _with_linear_symmetries]]

6.242

16794

\[ {}3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y = 0 \]

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

2.223

16795

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

4.409

16796

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

[[_homogeneous, ‘class C‘], _Riccati]

1.807

16797

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

[_linear]

7.281

16798

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

[_Bernoulli]

5.327

16799

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

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

30.030

16800

\[ {}5 x y-4 y^{2}-6 x^{2}+\left (y^{2}-8 x y+\frac {5 x^{2}}{2}\right ) y^{\prime } = 0 \]

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

69.872