2.2.179 Problems 17801 to 17900

Table 2.359: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

17801

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-3 x_{2}-2 x_{3} \\ x_{2}^{\prime }=8 x_{1}-5 x_{2}-4 x_{3} \\ x_{3}^{\prime }=-4 x_{1}+3 x_{2}+3 x_{3} \end {array}\right ] \]

system_of_ODEs

0.454

17802

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-7 x_{1}+9 x_{2}-6 x_{3} \\ x_{2}^{\prime }=-8 x_{1}+11 x_{2}-7 x_{3} \\ x_{3}^{\prime }=-2 x_{1}+3 x_{2}-x_{3} \end {array}\right ] \]

system_of_ODEs

0.516

17803

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}+6 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2}-x_{3} \\ x_{3}^{\prime }=-2 x_{1}-3 x_{2} \end {array}\right ] \]

system_of_ODEs

0.424

17804

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-8 x_{1}-16 x_{2}-16 x_{3}-17 x_{4} \\ x_{2}^{\prime }=-2 x_{1}-10 x_{2}-8 x_{3}-7 x_{4} \\ x_{3}^{\prime }=-2 x_{1}-2 x_{3}-3 x_{4} \\ x_{4}^{\prime }=6 x_{1}+14 x_{2}+14 x_{3}+14 x_{4} \end {array}\right ] \]

system_of_ODEs

1.350

17805

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}-2 x_{3}+3 x_{4} \\ x_{2}^{\prime }=2 x_{1}-\frac {3 x_{2}}{2}-x_{3}+\frac {7 x_{4}}{2} \\ x_{3}^{\prime }=-x_{1}+\frac {x_{2}}{2}-\frac {3 x_{4}}{2} \\ x_{4}^{\prime }=-2 x_{1}+\frac {3 x_{2}}{2}+3 x_{3}-\frac {7 x_{4}}{2} \end {array}\right ] \]

system_of_ODEs

0.646

17806

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}-7 x_{2} \end {array}\right ] \]
i.c.

system_of_ODEs

0.569

17807

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ] \]
i.c.

system_of_ODEs

0.561

17808

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }=6 x_{1}+4 x_{2}+6 x_{3} \\ x_{3}^{\prime }=-5 x_{1}-2 x_{2}-4 x_{3} \end {array}\right ] \]
i.c.

system_of_ODEs

0.486

17809

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2} \\ x_{2}^{\prime }=-14 x_{1}-5 x_{2}+x_{3} \\ x_{3}^{\prime }=15 x_{1}+5 x_{2}-2 x_{3} \end {array}\right ] \]
i.c.

system_of_ODEs

0.487

17810

\[ {}\left [\begin {array}{c} x^{\prime }=-2 y+x y \\ y^{\prime }=x+4 x y \end {array}\right ] \]

system_of_ODEs

0.031

17811

\[ {}\left [\begin {array}{c} x^{\prime }=1+5 y \\ y^{\prime }=1-6 x^{2} \end {array}\right ] \]

system_of_ODEs

0.031

17812

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

[_quadrature]

0.801

17813

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

[_quadrature]

0.453

17814

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

[[_2nd_order, _quadrature]]

1.892

17815

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

[_separable]

38.145

17816

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

[_separable]

37.098

17817

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

[_separable]

40.595

17818

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

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

5.888

17819

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

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

4.868

17820

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

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

40.454

17821

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

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

38.960

17822

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

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

5.399

17823

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

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

3.648

17824

\[ {}\left (x +2 y+1\right ) y^{\prime } = 2 x +4 y+3 \]

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

1.937

17825

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

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

1.840

17826

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

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

4.213

17827

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

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

2.931

17828

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

[_linear]

2.537

17829

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

[_linear]

1.667

17830

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

[_linear]

1.389

17831

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

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

2.106

17832

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

[_Bernoulli]

2.371

17833

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

[_rational, _Bernoulli]

2.224

17834

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

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

1.643

17835

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

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

2.419

17836

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

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

1.887

17837

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

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

2.258

17838

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

[_rational, _Riccati]

1.779

17839

\[ {}y^{\prime } = y^{2}+\frac {1}{x^{4}} \]

[_rational, [_Riccati, _special]]

1.589

17840

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

[‘y=_G(x,y’)‘]

221.525

17841

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

[_rational]

2.917

17842

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

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

2.411

17843

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

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

1.587

17844

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

[[_linear, ‘class A‘]]

1.049

17845

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

[_Riccati]

1.136

17846

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

[[_1st_order, _with_linear_symmetries], _exact]

2.936

17847

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

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

34.625

17848

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

[_exact]

39.342

17849

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

[_exact, _rational]

1.946

17850

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

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

2.016

17851

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

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

7.622

17852

\[ {}a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right ) = 0 \]

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

2.892

17853

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

[_rational]

1.502

17854

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

[_linear]

1.664

17855

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

[_Bernoulli]

2.367

17856

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

[_rational]

2.671

17857

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

[_quadrature]

0.474

17858

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

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

9.706

17859

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

[_quadrature]

1.109

17860

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

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

12.278

17861

\[ {}x {y^{\prime }}^{3} = 1+y^{\prime } \]

[_quadrature]

0.543

17862

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

[_quadrature]

0.587

17863

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

[_quadrature]

177.885

17864

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

[_quadrature]

0.724

17865

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

[_quadrature]

1.591

17866

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

[_quadrature]

0.599

17867

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

[[_homogeneous, ‘class G‘]]

0.722

17868

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

[[_homogeneous, ‘class G‘]]

1.849

17869

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

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

9.878

17870

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

[_dAlembert]

73.238

17871

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

[_dAlembert]

3.024

17872

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.420

17873

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

[[_1st_order, _with_linear_symmetries]]

107.730

17874

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

0.597

17875

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.482

17876

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

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

2.165

17877

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

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

1.326

17878

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

[_quadrature]

1.806

17879

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

[_quadrature]

1.555

17880

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

[_quadrature]

1.347

17881

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

2.502

17882

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

2.414

17883

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

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

1.451

17884

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

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

13.428

17885

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

[_quadrature]

1.667

17886

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

[[_homogeneous, ‘class G‘]]

0.740

17887

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

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

1.733

17888

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

[‘y=_G(x,y’)‘]

5.742

17889

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

[[_homogeneous, ‘class G‘]]

1.975

17890

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

[[_1st_order, _with_linear_symmetries]]

4.035

17891

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

[[_3rd_order, _quadrature]]

0.686

17892

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

12.609

17893

\[ {}a^{3} y^{\prime \prime \prime } y^{\prime \prime } = \sqrt {1+c^{2} {y^{\prime \prime }}^{2}} \]

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

1.427

17894

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

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

3.898

17895

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

1.597

17896

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

[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]]

0.582

17897

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

[[_2nd_order, _missing_x]]

1.316

17898

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

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.320

17899

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

[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

1.148

17900

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

0.148