2.2.139 Problems 13801 to 13900

Table 2.279: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

13801

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

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

1.873

13802

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

[_quadrature]

0.505

13803

\[ {}y = 5 y^{\prime } x -{y^{\prime }}^{2} \]

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.592

13804

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

[[_Riccati, _special]]

19.311

13805

\[ {}y^{\prime } = \left (x -5 y\right )^{{1}/{3}}+2 \]

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

1.825

13806

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

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

1.741

13807

\[ {}x^{\prime }+5 x = 10 t +2 \]
i.c.

[[_linear, ‘class A‘]]

2.845

13808

\[ {}x^{\prime } = \frac {x}{t}+\frac {x^{2}}{t^{3}} \]
i.c.

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

2.842

13809

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.536

13810

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.562

13811

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

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

2.030

13812

\[ {}x^{\prime }-x \cot \left (t \right ) = 4 \sin \left (t \right ) \]

[_linear]

1.850

13813

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

[[_homogeneous, ‘class G‘]]

1.710

13814

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

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

1.930

13815

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

[_quadrature]

0.555

13816

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

[_rational]

1.279

13817

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

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

4.699

13818

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

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

1.691

13819

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

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

3.090

13820

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

[_Bernoulli]

2.164

13821

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

[_linear]

2.565

13822

\[ {}\left (3+2 x +4 y\right ) y^{\prime }-2 y-x -1 = 0 \]

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

1.958

13823

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

[_exact, _rational]

1.129

13824

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

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

4.753

13825

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

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

2.444

13826

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.580

13827

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.519

13828

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

[_separable]

1.355

13829

\[ {}y^{\prime \prime }-6 y^{\prime }+10 y = 100 \]
i.c.

[[_2nd_order, _missing_x]]

0.747

13830

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.051

13831

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

[[_3rd_order, _missing_x]]

0.082

13832

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.825

13833

\[ {}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 2 \]

[[_2nd_order, _with_linear_symmetries]]

1.251

13834

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.764

13835

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

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

0.407

13836

\[ {}x^{\prime \prime }-4 x^{\prime }+4 x = {\mathrm e}^{t}+{\mathrm e}^{2 t}+1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.647

13837

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

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

0.879

13838

\[ {}x^{3} x^{\prime \prime }+1 = 0 \]

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

2.089

13839

\[ {}y^{\prime \prime \prime \prime }-16 y = x^{2}-{\mathrm e}^{x} \]

[[_high_order, _linear, _nonhomogeneous]]

0.183

13840

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

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

2.964

13841

\[ {}x^{\left (6\right )}-x^{\prime \prime \prime \prime } = 1 \]

[[_high_order, _missing_x]]

0.141

13842

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

[[_high_order, _with_linear_symmetries]]

0.143

13843

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

[[_Emden, _Fowler]]

0.290

13844

\[ {}x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-\frac {1}{25}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.517

13845

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

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

0.618

13846

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

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

4.458

13847

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.769

13848

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{r} = 0 \]

[[_2nd_order, _missing_y]]

0.520

13849

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

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

0.584

13850

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

[[_2nd_order, _missing_x]]

1.799

13851

\[ {}x^{\prime \prime }+9 x = t \sin \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.862

13852

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.757

13853

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

[[_3rd_order, _with_linear_symmetries]]

0.145

13854

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.698

13855

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

[[_2nd_order, _with_linear_symmetries]]

0.521

13856

\[ {}m x^{\prime \prime } = f \left (x\right ) \]

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

1.127

13857

\[ {}m x^{\prime \prime } = f \left (x^{\prime }\right ) \]

[[_2nd_order, _missing_x]]

0.762

13858

\[ {}y^{\left (6\right )}-3 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-y^{\prime \prime \prime } = x \]

[[_high_order, _missing_y]]

0.157

13859

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

[[_high_order, _linear, _nonhomogeneous]]

0.853

13860

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.733

13861

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.159

13862

\[ {}x^{\prime \prime \prime \prime }+x = t^{3} \]

[[_high_order, _linear, _nonhomogeneous]]

0.151

13863

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

[[_2nd_order, _quadrature]]

1.408

13864

\[ {}x^{\prime \prime }+10 x^{\prime }+25 x = 2^{t}+t \,{\mathrm e}^{-5 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.851

13865

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

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

0.390

13866

\[ {}y^{\left (6\right )}-y = {\mathrm e}^{2 x} \]

[[_high_order, _with_linear_symmetries]]

0.203

13867

\[ {}y^{\left (6\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime } = x +{\mathrm e}^{x} \]

[[_high_order, _missing_y]]

0.188

13868

\[ {}6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0 \]

[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]

0.804

13869

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

[[_2nd_order, _missing_y]]

0.721

13870

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.200

13871

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

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

3.839

13872

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

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

0.506

13873

\[ {}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x \end {array}\right ] \]
i.c.

system_of_ODEs

0.392

13874

\[ {}\left [\begin {array}{c} x^{\prime }+5 x+y={\mathrm e}^{t} \\ y^{\prime }-x-3 y={\mathrm e}^{2 t} \end {array}\right ] \]

system_of_ODEs

1.688

13875

\[ {}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=z \\ z^{\prime }=x \end {array}\right ] \]

system_of_ODEs

1.059

13876

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

system_of_ODEs

0.057

13877

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

[_separable]

1.641

13878

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

[_separable]

1.979

13879

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

[‘y=_G(x,y’)‘]

1.463

13880

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

[_separable]

2.453

13881

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

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

1.979

13882

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

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

1.197

13883

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

[‘y=_G(x,y’)‘]

1.900

13884

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

[_separable]

1.409

13885

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

[‘y=_G(x,y’)‘]

0.816

13886

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

[_separable]

2.352

13887

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

[[_Emden, _Fowler]]

0.440

13888

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

[[_3rd_order, _linear, _nonhomogeneous]]

0.102

13889

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

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

5.984

13890

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

[[_high_order, _missing_y]]

0.177

13891

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

[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]]

0.070

13892

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

[[_3rd_order, _linear, _nonhomogeneous]]

0.089

13893

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

[_linear]

39.522

13894

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

[[_3rd_order, _linear, _nonhomogeneous]]

0.079

13895

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

[_quadrature]

1.009

13896

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

[‘y=_G(x,y’)‘]

1.598

13897

\[ {}5 y^{\prime }-x y = 0 \]

[_separable]

1.118

13898

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

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

2.564

13899

\[ {}2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y = 1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.843

13900

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

[[_3rd_order, _quadrature]]

0.112