2.2.169 Problems 16801 to 16900

Table 2.339: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

16801

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

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

2.844

16802

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

[_separable]

5.881

16803

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

[_separable]

1.692

16804

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

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

2.970

16805

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

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

5.799

16806

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

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

5.174

16807

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

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

1.933

16808

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

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

2.530

16809

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

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

2.615

16810

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

[_separable]

2.611

16811

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

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

2.201

16812

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

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

2.408

16813

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

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

2.638

16814

\[ {}2 x^{5}+4 x^{3} y-2 x y^{2}+\left (y^{2}+2 x^{2} y-x^{4}\right ) y^{\prime } = 0 \]

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

3.719

16815

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

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

1.680

16816

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

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

2.368

16817

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

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

2.513

16818

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

[_Bernoulli]

3.023

16819

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

[_separable]

2.636

16820

\[ {}y^{\prime } = \sqrt {\frac {9 y^{2}-6 y+2}{x^{2}-2 x +5}} \]

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

2.434

16821

\[ {}\left (5 x -7 y+1\right ) y^{\prime }+x +y-1 = 0 \]

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

4.554

16822

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

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

2.511

16823

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

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

2.118

16824

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

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

1.980

16825

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

[[_homogeneous, ‘class G‘]]

2.562

16826

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

[_rational, _dAlembert]

1.049

16827

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.973

16828

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

[[_3rd_order, _quadrature]]

0.170

16829

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

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

0.396

16830

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

[[_2nd_order, _quadrature]]

0.810

16831

\[ {}{y^{\prime }}^{4} = 1 \]

[_quadrature]

1.155

16832

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

[[_2nd_order, _missing_x]]

2.132

16833

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

[[_2nd_order, _missing_x]]

0.997

16834

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

[[_2nd_order, _missing_x]]

2.433

16835

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

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

3.293

16836

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

[[_high_order, _quadrature]]

0.092

16837

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

[[_3rd_order, _quadrature]]

0.140

16838

\[ {}y^{\prime \prime } \left (x +2\right )^{5} = 1 \]
i.c.

[[_2nd_order, _quadrature]]

0.838

16839

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

[[_2nd_order, _quadrature]]

1.899

16840

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

[[_2nd_order, _quadrature]]

1.994

16841

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

[[_2nd_order, _missing_y]]

0.833

16842

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

[[_2nd_order, _missing_y]]

0.765

16843

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

[[_2nd_order, _missing_y]]

0.823

16844

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

[[_2nd_order, _missing_y]]

1.008

16845

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

[[_2nd_order, _missing_y]]

0.677

16846

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

[_separable]

2.286

16847

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

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_poly_yn]]

672.473

16848

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

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

4.692

16849

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

[[_3rd_order, _missing_y]]

0.152

16850

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

[[_2nd_order, _missing_x]]

4.010

16851

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

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

0.364

16852

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

[[_2nd_order, _missing_x]]

4.925

16853

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

1.394

16854

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

[[_2nd_order, _missing_x]]

1.148

16855

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

[[_2nd_order, _missing_x]]

0.613

16856

\[ {}y^{\prime \prime }+y^{\prime }+2 = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.121

16857

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

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

0.971

16858

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

[[_2nd_order, _missing_x]]

1.598

16859

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

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

0.349

16860

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

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

0.259

16861

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

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

15.994

16862

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

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

4.785

16863

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

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

3.713

16864

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

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

1.144

16865

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

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

0.355

16866

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

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

1.424

16867

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

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

1.027

16868

\[ {}y^{3} y^{\prime \prime } = -1 \]
i.c.

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

1.447

16869

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

[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]]

0.595

16870

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

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

1.405

16871

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

2.738

16872

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

[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

0.039

16873

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

[[_2nd_order, _missing_x]]

2.084

16874

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

[[_2nd_order, _missing_x]]

0.877

16875

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

[[_3rd_order, _missing_x]]

0.127

16876

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

[[_2nd_order, _missing_x]]

0.975

16877

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.445

16878

\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 0 \]

[[_3rd_order, _missing_x]]

0.055

16879

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

[[_2nd_order, _missing_x]]

1.117

16880

\[ {}y^{\left (6\right )}+2 y^{\left (5\right )}+y^{\prime \prime \prime \prime } = 0 \]

[[_high_order, _missing_x]]

0.064

16881

\[ {}4 y^{\prime \prime }-8 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

1.711

16882

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

[[_3rd_order, _missing_x]]

0.060

16883

\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+10 y^{\prime \prime }+12 y^{\prime }+5 y = 0 \]

[[_high_order, _missing_x]]

0.069

16884

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

[[_2nd_order, _missing_x]]

2.148

16885

\[ {}y^{\prime \prime }-2 y^{\prime }+3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3.040

16886

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }-5 y = 0 \]

[[_high_order, _missing_x]]

0.069

16887

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

[[_high_order, _missing_x]]

0.069

16888

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

[[_3rd_order, _missing_x]]

0.054

16889

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

[[_3rd_order, _missing_x]]

0.057

16890

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

[[_high_order, _missing_x]]

0.059

16891

\[ {}y^{\left (5\right )} = 0 \]

[[_high_order, _quadrature]]

0.050

16892

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

[[_3rd_order, _missing_x]]

0.052

16893

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

[[_3rd_order, _missing_x]]

0.050

16894

\[ {}y^{\prime \prime \prime }+y^{\prime \prime } = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.118

16895

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

[[_2nd_order, _missing_x]]

2.022

16896

\[ {}y^{\prime \prime }-7 y^{\prime } = \left (-1+x \right )^{2} \]

[[_2nd_order, _missing_y]]

2.276

16897

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

[[_2nd_order, _missing_y]]

1.902

16898

\[ {}y^{\prime \prime }+7 y^{\prime } = {\mathrm e}^{-7 x} \]

[[_2nd_order, _missing_y]]

1.978

16899

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \left (1-x \right ) {\mathrm e}^{4 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.267

16900

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 x} \]

[[_2nd_order, _with_linear_symmetries]]

1.213