2.2.149 Problems 14801 to 14900

Table 2.299: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

14801

\(\left [\begin {array}{cc} 0 & 1 \\ 2 & 0 \end {array}\right ]\)

Eigenvectors

0.183

14802

\[ {}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=-2 y \end {array}\right ] \]

system_of_ODEs

0.437

14803

\(\left [\begin {array}{cc} 1 & 0 \\ 2 & 3 \end {array}\right ]\)

Eigenvectors

0.129

14804

\[ {}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=x-y \end {array}\right ] \]

system_of_ODEs

0.450

14805

\[ {}\left [\begin {array}{c} x^{\prime }=\pi ^{2} x+\frac {187 y}{5} \\ y^{\prime }=\sqrt {555}\, x+\frac {400617 y}{5000} \end {array}\right ] \]
i.c.

system_of_ODEs

1.124

14806

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

system_of_ODEs

0.554

14807

\[ {}\left [\begin {array}{c} x^{\prime }=-3 x+y \\ y^{\prime }=y-x \end {array}\right ] \]

system_of_ODEs

0.640

14808

\[ {}\left [\begin {array}{c} x^{\prime }=-3 x+y \\ y^{\prime }=-x \end {array}\right ] \]

system_of_ODEs

0.649

14809

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

system_of_ODEs

0.568

14810

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

system_of_ODEs

0.472

14811

\[ {}\left [\begin {array}{c} x^{\prime }=3 x+y \\ y^{\prime }=-x \end {array}\right ] \]

system_of_ODEs

0.651

14812

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

system_of_ODEs

0.485

14813

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

system_of_ODEs

0.858

14814

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.235

14815

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3.155

14816

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

[[_2nd_order, _missing_x]]

1.422

14817

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

[[_2nd_order, _missing_x]]

19.759

14818

\[ {}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{4 t} \]

[[_2nd_order, _with_linear_symmetries]]

1.198

14819

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \,{\mathrm e}^{-3 t} \]

[[_2nd_order, _with_linear_symmetries]]

1.187

14820

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{3 t} \]

[[_2nd_order, _with_linear_symmetries]]

1.193

14821

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = {\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

14.160

14822

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \]

[[_2nd_order, _with_linear_symmetries]]

8.041

14823

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \]

[[_2nd_order, _with_linear_symmetries]]

1.201

14824

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{4 t} \]

[[_2nd_order, _with_linear_symmetries]]

1.193

14825

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 4 \,{\mathrm e}^{-3 t} \]

[[_2nd_order, _with_linear_symmetries]]

1.174

14826

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.006

14827

\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 3 \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.398

14828

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

3.603

14829

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.490

14830

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-\frac {t}{2}} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.105

14831

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.276

14832

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

[[_2nd_order, _with_linear_symmetries]]

1.332

14833

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-\frac {t}{2}} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

5.174

14834

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

4.188

14835

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-4 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

5.062

14836

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

[[_2nd_order, _with_linear_symmetries]]

1.146

14837

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 5 \]
i.c.

[[_2nd_order, _missing_x]]

1.246

14838

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 2 \]
i.c.

[[_2nd_order, _missing_x]]

0.993

14839

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 10 \]
i.c.

[[_2nd_order, _missing_x]]

4.451

14840

\[ {}y^{\prime \prime }+4 y^{\prime }+6 y = -8 \]
i.c.

[[_2nd_order, _missing_x]]

7.657

14841

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

2.444

14842

\[ {}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

2.366

14843

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

[[_2nd_order, _missing_x]]

2.374

14844

\[ {}y^{\prime \prime }+4 y = {\mathrm e}^{t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

2.309

14845

\[ {}y^{\prime \prime }+9 y = 6 \]
i.c.

[[_2nd_order, _missing_x]]

2.128

14846

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

[[_2nd_order, _with_linear_symmetries]]

3.437

14847

\[ {}y^{\prime \prime }+4 y = -3 t^{2}+2 t +3 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

3.691

14848

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

[[_2nd_order, _missing_y]]

2.066

14849

\[ {}y^{\prime \prime }+4 y^{\prime } = 3 t +2 \]
i.c.

[[_2nd_order, _missing_y]]

2.088

14850

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

[[_2nd_order, _with_linear_symmetries]]

1.206

14851

\[ {}y^{\prime \prime }+4 y = t -\frac {1}{20} t^{2} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

3.682

14852

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 4+{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.187

14853

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-t}-4 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.042

14854

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.137

14855

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.143

14856

\[ {}y^{\prime \prime }+4 y = t +{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

5.112

14857

\[ {}y^{\prime \prime }+4 y = 6+t^{2}+{\mathrm e}^{t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

5.357

14858

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.430

14859

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.400

14860

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.398

14861

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.423

14862

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.430

14863

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = -4 \cos \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.521

14864

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 3 \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

33.909

14865

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = -\cos \left (5 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

53.283

14866

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

28.945

14867

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.686

14868

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.514

14869

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \cos \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.694

14870

\[ {}y^{\prime \prime }+6 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

35.302

14871

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.721

14872

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.396

14873

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 3+2 \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

43.904

14874

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-t} \cos \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

32.462

14875

\[ {}y^{\prime \prime }+9 y = \cos \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3.012

14876

\[ {}y^{\prime \prime }+9 y = 5 \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3.498

14877

\[ {}y^{\prime \prime }+4 y = -\cos \left (\frac {t}{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4.274

14878

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.984

14879

\[ {}y^{\prime \prime }+9 y = 2 \cos \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3.951

14880

\[ {}y^{\prime \prime }+4 y = 8 \]
i.c.

[[_2nd_order, _missing_x]]

0.385

14881

\[ {}y^{\prime \prime }-4 y = {\mathrm e}^{2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.347

14882

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 2 \,{\mathrm e}^{t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.414

14883

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (-4+t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.635

14884

\[ {}y^{\prime \prime }+4 y = \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.408

14885

\[ {}y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (-4+t \right ) \cos \left (-20+5 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.629

14886

\[ {}y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3.603

14887

\[ {}y^{\prime \prime }+3 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.308

14888

\[ {}y^{\prime \prime }+3 y = 5 \delta \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.931

14889

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -3\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.586

14890

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = -2 \delta \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.359

14891

\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (t -1\right )-3 \delta \left (-4+t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4.943

14892

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = {\mathrm e}^{-2 t} \sin \left (4 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.618

14893

\[ {}y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3.289

14894

\[ {}y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (-4+t \right )\right ) \cos \left (-4+t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

6.241

14895

\[ {}y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

5.489

14896

\[ {}y^{\prime \prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.386

14897

\[ {}y^{\prime \prime }+4 y = \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.349

14898

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

[[_2nd_order, _missing_x]]

0.236

14899

\[ {}y^{\prime \prime }+16 y = t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.345

14900

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

[_quadrature]

0.580