2.2.149 Problems 14801 to 14900

Table 2.311: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

14801

\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ 2 & 3 & -4 \\ 4 & 1 & -4 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.441

14802

\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & -6 & 6 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.458

14803

\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & 1 & -1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.443

14804

\(\left [\begin {array}{ccc} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.417

14805

\(\left [\begin {array}{ccc} 1 & 3 & -6 \\ 0 & 2 & 2 \\ 0 & -1 & 5 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.424

14806

\(\left [\begin {array}{ccc} -5 & -12 & 6 \\ 1 & 5 & -1 \\ -7 & -10 & 8 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.447

14807

\(\left [\begin {array}{ccc} -2 & 5 & 5 \\ -1 & 4 & 5 \\ 3 & -3 & 2 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.454

14808

\(\left [\begin {array}{ccc} -2 & 6 & -18 \\ 12 & -23 & 66 \\ 5 & -10 & 29 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.448

14809

\begin{align*} x^{\prime }&=x+y-z \\ y^{\prime }&=2 x+3 y-4 z \\ z^{\prime }&=4 x+y-4 z \\ \end{align*}

system_of_ODEs

0.655

14810

\begin{align*} x^{\prime }&=x-y-z \\ y^{\prime }&=x+3 y+z \\ z^{\prime }&=-3 x-6 y+6 z \\ \end{align*}

system_of_ODEs

0.692

14811

\begin{align*} -y+y^{\prime }&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

[[_linear, ‘class A‘]]

0.188

14812

\begin{align*} y+y^{\prime }&=2 \sin \left (t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

[[_linear, ‘class A‘]]

0.151

14813

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.094

14814

\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.124

14815

\begin{align*} y^{\prime \prime }+4 y&=8 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.158

14816

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.147

14817

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=18 \,{\mathrm e}^{-t} \sin \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.218

14818

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=t \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.157

14819

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=4 t \,{\mathrm e}^{-3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.145

14820

\begin{align*} y^{\prime \prime }-8 y^{\prime }+15 y&=9 \,{\mathrm e}^{2 t} t \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.167

14821

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y&=20 \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -2 \\ \end{align*}
Using Laplace transform method.

[[_3rd_order, _linear, _nonhomogeneous]]

0.226

14822

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=36 t \,{\mathrm e}^{4 t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -6 \\ \end{align*}
Using Laplace transform method.

[[_3rd_order, _linear, _nonhomogeneous]]

0.217

14823

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.799

14824

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

1.020

14825

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

1.987

14826

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=\left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

1.266

14827

\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} -4 t +8 \pi & 0<t <2 \pi \\ 0 & 2<t \end {array}\right . \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.745

14828

\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right . \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.501

14829

\begin{align*} t x^{\prime \prime }-2 x^{\prime }+9 t^{5} x&=0 \\ \end{align*}

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

4.577

14830

\begin{align*} t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 t x^{\prime }-6 x&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.123

14831

\begin{align*} \left (t^{3}-2 t^{2}\right ) x^{\prime \prime }-\left (t^{3}+2 t^{2}-6 t \right ) x^{\prime }+\left (3 t^{2}-6\right ) x&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

72.194

14832

\begin{align*} t^{3} x^{\prime \prime \prime }-\left (t +3\right ) t^{2} x^{\prime \prime }+2 t \left (t +3\right ) x^{\prime }-2 \left (t +3\right ) x&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.038

14833

\begin{align*} t^{2} x^{\prime \prime }+3 t x^{\prime }+3 x&=0 \\ \end{align*}

[[_Emden, _Fowler]]

4.059

14834

\begin{align*} \left (2 t +1\right ) x^{\prime \prime }+t^{3} x^{\prime }+x&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

51.918

14835

\begin{align*} t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

7.835

14836

\begin{align*} t^{3} x^{\prime \prime }-\left (t^{3}+2 t^{2}-t \right ) x^{\prime }+\left (t^{2}+t -1\right ) x&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

60.547

14837

\begin{align*} t^{3} x^{\prime \prime }+3 t^{2} x^{\prime }+x&=0 \\ \end{align*}

[[_Emden, _Fowler]]

9.884

14838

\begin{align*} \sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

2.120

14839

\begin{align*} \frac {\left (1+t \right ) x^{\prime \prime }}{t}-\frac {x^{\prime }}{t^{2}}+\frac {x}{t^{3}}&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

8.635

14840

\begin{align*} t^{2} x^{\prime \prime }+t x^{\prime }+x&=0 \\ \end{align*}

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

1.961

14841

\begin{align*} \left (t^{4}+t^{2}\right ) x^{\prime \prime }+2 t^{3} x^{\prime }+3 x&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

38.322

14842

\begin{align*} x^{\prime \prime }-\tan \left (t \right ) x^{\prime }+x&=0 \\ \end{align*}

[_Lienard]

2.102

14843

\begin{align*} f \left (t \right ) x^{\prime \prime }+x g \left (t \right )&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.120

14844

\begin{align*} x^{\prime \prime }+\left (1+t \right ) x&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.655

14845

\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.862

14846

\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.408

14847

\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (L \right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.322

14848

\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (L \right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.648

14849

\begin{align*} y^{\prime \prime } x +y^{\prime }+\frac {\lambda y}{x}&=0 \\ y \left (1\right ) &= 0 \\ y \left ({\mathrm e}^{\pi }\right ) &= 0 \\ \end{align*}

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

29.318

14850

\begin{align*} y^{\prime \prime } x +y^{\prime }+\frac {\lambda y}{x}&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left ({\mathrm e}^{\pi }\right ) &= 0 \\ \end{align*}

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

27.377

14851

\begin{align*} 2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }+\frac {\lambda y}{x^{2}+1}&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}

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

3.993

14852

\begin{align*} -\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}

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

3.550

14853

\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=3 x+y \\ \end{align*}

system_of_ODEs

0.339

14854

\begin{align*} x^{\prime }&=3 x+2 y \\ y^{\prime }&=x+2 y \\ \end{align*}

system_of_ODEs

0.358

14855

\begin{align*} x^{\prime }&=3 x+4 y \\ y^{\prime }&=3 x+2 y \\ \end{align*}

system_of_ODEs

0.370

14856

\begin{align*} x^{\prime }&=2 x+5 y \\ y^{\prime }&=x-2 y \\ \end{align*}

system_of_ODEs

0.360

14857

\begin{align*} x^{\prime }&=2 x-4 y \\ y^{\prime }&=2 x-2 y \\ \end{align*}

system_of_ODEs

0.399

14858

\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=4 x+5 y \\ \end{align*}

system_of_ODEs

0.524

14859

\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+5 y \\ \end{align*}

system_of_ODEs

0.523

14860

\begin{align*} x^{\prime }&=x+7 y \\ y^{\prime }&=3 x+5 y \\ \end{align*}

system_of_ODEs

0.374

14861

\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=3 x-y \\ \end{align*}

system_of_ODEs

0.352

14862

\begin{align*} x^{\prime }&=a x+b y \\ y^{\prime }&=c x+d y \\ \end{align*}

system_of_ODEs

0.856

14863

\begin{align*} x^{\prime }&=4 x-4 y-x \left (x^{2}+y^{2}\right ) \\ y^{\prime }&=4 x+4 y-y \left (x^{2}+y^{2}\right ) \\ \end{align*}

system_of_ODEs

0.028

14864

\begin{align*} x^{\prime }&=y+\frac {x \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \\ y^{\prime }&=-x+\frac {y \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \\ \end{align*}

system_of_ODEs

0.048

14865

\begin{align*} x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

19.426

14866

\begin{align*} x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

14.170

14867

\begin{align*} x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

9.444

14868

\begin{align*} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3}&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

10.487

14869

\begin{align*} x^{\prime \prime }+\left (x^{2}+1\right ) x^{\prime }+x^{3}&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

10.566

14870

\begin{align*} x^{\prime }&=x-x^{2} \\ y^{\prime }&=2 y-y^{2} \\ \end{align*}

system_of_ODEs

0.026

14871

\begin{align*} x^{\prime }&=\sin \left (t \right )+\cos \left (t \right ) \\ \end{align*}

[_quadrature]

0.246

14872

\begin{align*} y^{\prime }&=\frac {1}{x^{2}-1} \\ \end{align*}

[_quadrature]

0.200

14873

\begin{align*} u^{\prime }&=4 t \ln \left (t \right ) \\ \end{align*}

[_quadrature]

0.281

14874

\begin{align*} z^{\prime }&={\mathrm e}^{-2 x} x \\ \end{align*}

[_quadrature]

0.221

14875

\begin{align*} T^{\prime }&={\mathrm e}^{-t} \sin \left (2 t \right ) \\ \end{align*}

[_quadrature]

0.287

14876

\begin{align*} x^{\prime }&=\sec \left (t \right )^{2} \\ x \left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}

[_quadrature]

0.421

14877

\begin{align*} y^{\prime }&=x -\frac {1}{3} x^{3} \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_quadrature]

0.316

14878

\begin{align*} x^{\prime }&=2 \sin \left (t \right )^{2} \\ x \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\ \end{align*}

[_quadrature]

0.350

14879

\begin{align*} x V^{\prime }&=x^{2}+1 \\ V \left (1\right ) &= 1 \\ \end{align*}

[_quadrature]

0.355

14880

\begin{align*} x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t}&={\mathrm e}^{-t} \\ x \left (0\right ) &= 3 \\ \end{align*}

[[_linear, ‘class A‘]]

2.400

14881

\begin{align*} x^{\prime }&=1-x \\ \end{align*}

[_quadrature]

0.437

14882

\begin{align*} x^{\prime }&=x \left (2-x\right ) \\ \end{align*}

[_quadrature]

0.857

14883

\begin{align*} x^{\prime }&=\left (1+x\right ) \left (2-x\right ) \sin \left (x\right ) \\ \end{align*}

[_quadrature]

2.971

14884

\begin{align*} x^{\prime }&=-x \left (1-x\right ) \left (2-x\right ) \\ \end{align*}

[_quadrature]

1.690

14885

\begin{align*} x^{\prime }&=x^{2}-x^{4} \\ \end{align*}

[_quadrature]

0.563

14886

\begin{align*} x^{\prime }&=t^{3} \left (1-x\right ) \\ x \left (0\right ) &= 3 \\ \end{align*}

[_separable]

1.891

14887

\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) \tan \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.305

14888

\begin{align*} x^{\prime }&=t^{2} x \\ \end{align*}

[_separable]

1.800

14889

\begin{align*} x^{\prime }&=-x^{2} \\ \end{align*}

[_quadrature]

1.233

14890

\begin{align*} y^{\prime }&=y^{2} {\mathrm e}^{-t^{2}} \\ \end{align*}

[_separable]

2.490

14891

\begin{align*} x^{\prime }+p x&=q \\ \end{align*}

[_quadrature]

0.608

14892

\begin{align*} y^{\prime } x&=k y \\ \end{align*}

[_separable]

2.137

14893

\begin{align*} i^{\prime }&=p \left (t \right ) i \\ \end{align*}

[_separable]

1.897

14894

\begin{align*} x^{\prime }&=\lambda x \\ \end{align*}

[_quadrature]

0.733

14895

\begin{align*} m v^{\prime }&=-m g +k v^{2} \\ \end{align*}

[_quadrature]

2.728

14896

\begin{align*} x^{\prime }&=k x-x^{2} \\ x \left (0\right ) &= x_{0} \\ \end{align*}

[_quadrature]

9.742

14897

\begin{align*} x^{\prime }&=-x \left (k^{2}+x^{2}\right ) \\ x \left (0\right ) &= x_{0} \\ \end{align*}

[_quadrature]

57.937

14898

\begin{align*} y^{\prime }+\frac {y}{x}&=x^{2} \\ \end{align*}

[_linear]

2.034

14899

\begin{align*} x^{\prime }+t x&=4 t \\ x \left (0\right ) &= 2 \\ \end{align*}

[_separable]

1.974

14900

\begin{align*} z^{\prime }&=z \tan \left (y \right )+\sin \left (y \right ) \\ \end{align*}

[_linear]

1.878