2.3.39 Problems 3801 to 3900

Table 2.661: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

3801

3790

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&=5 \,{\mathrm e}^{x} \end {array} \]

0.348

3802

3793

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+2 y^{\prime }+y^{\prime \prime }&=2 x \,{\mathrm e}^{-x} \end {array} \]

0.348

3803

6603

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=4 \,{\mathrm e}^{x} \end {array} \]

0.348

3804

8923

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y x&=\sin \left (x \right ) \end {array} \]

0.348

3805

10383

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+y^{\prime \prime }&=\ln \left (x \right ) \end {array} \]

0.348

3806

11027

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-3 y&=5 \,{\mathrm e}^{x} \end {array} \]

0.348

3807

13178

\(\left [\begin {array}{cc} 6 & -10 \\ 2 & -3 \end {array}\right ]\)

N/A

N/A

N/A

0.348

3808

23017

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=4 \cos \left (2 x \right )+3 \,{\mathrm e}^{x} \end {array} \]

0.348

3809

445

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{1} \left (t \right )+3 x_{2} \left (t \right )\\ \end {array} \]

0.349

3810

579

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-3 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right )\\ \end {array} \]

0.349

3811

852

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=4 x_{1} \left (t \right )+2 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{2} \left (t \right )-x_{1} \left (t \right )\\ \end {array} \]

0.349

3812

3158

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-4 x_{1} \left (t \right )-6 x_{2} \left (t \right )\\ \end {array} \]

0.349

3813

4068

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-2 x_{1} \left (t \right )\\ \end {array} \]

0.349

3814

9103

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )-3 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \end {array} \]

0.349

3815

9105

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{2} \left (t \right )-x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{2} \left (t \right )+x_{3} \left (t \right )\\ \end {array} \]

0.349

3816

10631

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-2 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-x_{2} \left (t \right )-3 x_{3} \left (t \right )\\ \end {array} \]

0.349

3817

10666

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=2 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )\\ \end {array} \]

0.349

3818

10846

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )+5 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-x_{1} \left (t \right )-2 x_{2} \left (t \right )\\ \end {array} \]

0.349

3819

11166

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ \end {array} \]

0.349

3820

12412

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )+2 x_{2} \left (t \right )+5 \,{\mathrm e}^{4 t}\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \end {array} \]

0.349

3821

17012

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-2 x_{1} \left (t \right )+x_{2} \left (t \right )+t\\ \frac {d}{d t}x_{2} \left (t \right )&=-2 x_{1} \left (t \right )+x_{2} \left (t \right )+1\\ \end {array} \]

0.349

3822

18697

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )+{\mathrm e}^{2 t}\\ x_{2}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )-x_{2} \left (t \right )+5 \,{\mathrm e}^{2 t}\\ \end {array} \]

0.349

3823

25947

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-\tan \left (t \right ) x_{1} \left (t \right )+3 \cos \left (t \right )^{2}\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )+\tan \left (t \right ) x_{2} \left (t \right )+2 \sin \left (t \right )\\ \end {array} \]

0.349

3824

27032

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-4 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-3 x_{2} \left (t \right )\\ \end {array} \]

0.349

3825

27755

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-b x_{1} \left (t \right )-a x_{2} \left (t \right )\\ \end {array} \]

0.349

3826

6533

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-3 x_{1} \left (t \right )\\ \end {array} \]

0.350

3827

10075

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-2 x_{1} \left (t \right )+3 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-2 x_{1} \left (t \right )+5 x_{2} \left (t \right )\\ \end {array} \]

0.350

3828

10756

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \end {array} \]

0.350

3829

11031

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{2} \left (t \right )-x_{1} \left (t \right )\\ \end {array} \]

0.350

3830

11234

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ \end {array} \]

0.350

3831

13072

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=\frac {x_{1} \left (t \right )}{t}\\ x_{2}^{\prime }\left (t \right )&=x_{2} \left (t \right )\\ \end {array} \]

0.350

3832

13138

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

N/A

N/A

N/A

0.350

3833

13145

\(\left [\begin {array}{cc} 7 & -6 \\ 12 & -10 \end {array}\right ]\)

N/A

N/A

N/A

0.350

3834

14798

\(\left [\begin {array}{cc} -2 & 7 \\ 3 & 2 \end {array}\right ]\)

N/A

N/A

N/A

0.350

3835

15309

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=4 x_{1} \left (t \right )\\ \end {array} \]

0.350

3836

21726

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=5 x_{1} \left (t \right )-5 x_{2} \left (t \right )\\ \end {array} \]

0.350

3837

22889

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+2 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-x_{2} \left (t \right )\\ \end {array} \]

0.350

3838

581

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=5 x_{2} \left (t \right )-7 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=2 x_{2} \left (t \right )-4 x_{3} \left (t \right )\\ \end {array} \]

0.351

3839

2441

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+5 x_{2} \left (t \right )-x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )+6 x_{2} \left (t \right )-2 x_{3} \left (t \right )\\ \end {array} \]

0.351

3840

10908

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-x_{1} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=5 x_{3} \left (t \right )\\ \end {array} \]

0.351

3841

22099

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )+3 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-3 x_{1} \left (t \right )+2 x_{3} \left (t \right )\\ \end {array} \]

0.351

3842

28139

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+6 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-x_{1} \left (t \right )-2 x_{2} \left (t \right )-4 x_{3} \left (t \right )\\ \end {array} \]

0.351

3843

443

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-3 x_{2} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-2 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=2 x_{3} \left (t \right )\\ \end {array} \]

0.352

3844

4510

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )-x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-3 x_{2} \left (t \right )-x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=2 x_{2} \left (t \right )-x_{3} \left (t \right )\\ \end {array} \]

0.352

3845

7787

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )\\ \end {array} \]

0.352

3846

10470

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ \end {array} \]

0.352

3847

11157

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )+4 x_{4} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=4 x_{1} \left (t \right )+3 x_{2} \left (t \right )+2 x_{3} \left (t \right )+x_{4} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=4 x_{1} \left (t \right )+5 x_{2} \left (t \right )+6 x_{3} \left (t \right )+7 x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=7 x_{1} \left (t \right )+6 x_{2} \left (t \right )+5 x_{3} \left (t \right )+4 x_{4} \left (t \right )\\ \end {array} \]

0.352

3848

11268

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-x_{1} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=x_{3} \left (t \right )\\ \end {array} \]

0.352

3849

11292

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{1} \left (t \right )-3 x_{2} \left (t \right )\\ \end {array} \]

0.352

3850

13179

\(\left [\begin {array}{cc} 11 & -15 \\ 6 & -8 \end {array}\right ]\)

N/A

N/A

N/A

0.352

3851

17564

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ \end {array} \]

0.352

3852

19544

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-4 x_{1} \left (t \right )\\ \end {array} \]

0.352

3853

23272

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-b x_{1} \left (t \right )-a x_{2} \left (t \right )\\ \end {array} \]

0.352

3854

26626

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-x_{1} \left (t \right )+3 x_{2} \left (t \right )\\ \end {array} \]

0.352

3855

452

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-2 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ \end {array} \]

0.353

3856

853

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-3 x_{1} \left (t \right )-2 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \end {array} \]

0.353

3857

7106

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )\\ \end {array} \]

0.353

3858

7208

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=2 x_{1} \left (t \right )+3 x_{2} \left (t \right )-x_{3} \left (t \right )\\ \end {array} \]

0.353

3859

7298

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-2 x_{1} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )-3 x_{2} \left (t \right )-x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )\\ \end {array} \]

0.353

3860

17626

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=15 x_{1} \left (t \right )-32 x_{2} \left (t \right )+12 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=8 x_{1} \left (t \right )-17 x_{2} \left (t \right )+6 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-x_{3} \left (t \right )\\ \end {array} \]

0.353

3861

17673

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=4 x_{1} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{2} \left (t \right )+4 x_{3} \left (t \right )\\ \end {array} \]

0.353

3862

20604

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=3 x_{2} \left (t \right )+2 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=2 x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right )\\ \end {array} \]

0.353

3863

21636

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-x_{1} \left (t \right )+5 x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=4 x_{3} \left (t \right )\\ \end {array} \]

0.353

3864

22617

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{2} \left (t \right )-x_{1} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-2 x_{1} \left (t \right )-3 x_{2} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right )\\ \end {array} \]

0.353

3865

22737

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{1} \left (t \right )+2 x_{3} \left (t \right )+x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=x_{2} \left (t \right )+2 x_{4} \left (t \right )\\ \end {array} \]

0.353

3866

27088

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

N/A

N/A

N/A

0.353

3867

4136

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{1} \left (t \right )-x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=x_{2} \left (t \right )+x_{3} \left (t \right )\\ \end {array} \]

0.354

3868

14799

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

N/A

N/A

N/A

0.354

3869

19640

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-x_{2} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-x_{1} \left (t \right )-3 x_{2} \left (t \right )+2 x_{3} \left (t \right )\\ \end {array} \]

0.354

3870

20042

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=4 x_{1} \left (t \right )-3 x_{2} \left (t \right )+{\mathrm e}^{2 t}\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )+{\mathrm e}^{t}\\ \end {array} \]

0.354

3871

20850

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 \,{\mathrm e}^{t}\\ \end {array} \]

0.354

3872

21646

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right )+t \,{\mathrm e}^{3 t}\\ \frac {d}{d t}x_{2} \left (t \right )&=3 x_{2} \left (t \right )+{\mathrm e}^{3 t}\\ \end {array} \]

0.354

3873

21909

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+x_{2} \left (t \right )+20 \,{\mathrm e}^{3 t}\\ x_{2}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right )+12 \,{\mathrm e}^{t}\\ \end {array} \]

0.354

3874

22762

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-x_{1} \left (t \right )+2 x_{2} \left (t \right )+54 t \,{\mathrm e}^{3 t}\\ \frac {d}{d t}x_{2} \left (t \right )&=-2 x_{1} \left (t \right )+4 x_{2} \left (t \right )+9 \,{\mathrm e}^{3 t}\\ \end {array} \]

0.354

3875

22849

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )+4 x_{2} \left (t \right )+8 \sin \left (2 t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-2 x_{1} \left (t \right )-2 x_{2} \left (t \right )+8 \cos \left (2 t \right )\\ \end {array} \]

0.354

3876

23994

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 \,{\mathrm e}^{t}\\ \frac {d}{d t}x_{2} \left (t \right )&=-2 x_{1} \left (t \right )-x_{2} \left (t \right )+6 \,{\mathrm e}^{t} t\\ \end {array} \]

0.354

3877

27058

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )-{\mathrm e}^{t}\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-3 x_{2} \left (t \right )+2 x_{3} \left (t \right )+6 \,{\mathrm e}^{-t}\\ x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right )+2 x_{3} \left (t \right )+{\mathrm e}^{t}\\ \end {array} \]

0.354

3878

27939

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-x_{1} \left (t \right )-2 x_{2} \left (t \right )+2 x_{3} \left (t \right )-{\mathrm e}^{3 t}\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{1} \left (t \right )+4 x_{2} \left (t \right )-x_{3} \left (t \right )+4 \,{\mathrm e}^{3 t}\\ \frac {d}{d t}x_{3} \left (t \right )&=3 x_{3} \left (t \right )+3 \,{\mathrm e}^{3 t}\\ \end {array} \]

0.354

3879

334

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )-3 x_{2} \left (t \right )+34 \sin \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-4 x_{1} \left (t \right )-2 x_{2} \left (t \right )+17 \cos \left (t \right )\\ \end {array} \]

0.355

3880

590

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{2} \left (t \right )\\ \end {array} \]

0.355

3881

613

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}\\ x_{2}^{\prime }&=-x_{2}\\ \end {array} \]

0.355

3882

3623

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=3 x_{2} \left (t \right )-x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{2} \left (t \right )+x_{3} \left (t \right )\\ \end {array} \]

0.355

3883

6307

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-3 x_{1} \left (t \right )-2 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \end {array} \]

0.355

3884

6472

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )-x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=4 x_{1} \left (t \right )-x_{2} \left (t \right )\\ \end {array} \]

0.355

3885

6475

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{2} \left (t \right )-8 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=2 x_{2} \left (t \right )-7 x_{3} \left (t \right )\\ \end {array} \]

0.355

3886

7108

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{1} \left (t \right )+3 x_{2} \left (t \right )-2 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=2 x_{2} \left (t \right )+2 x_{3} \left (t \right )\\ \end {array} \]

0.355

3887

7134

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-8 x_{1} \left (t \right )+6 x_{2} \left (t \right )-3 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-12 x_{1} \left (t \right )+10 x_{2} \left (t \right )-3 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-2 x_{3} \left (t \right )\\ \end {array} \]

0.355

3888

7287

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=6 x_{2} \left (t \right )-7 x_{3} \left (t \right )+3 x_{4} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=3 x_{3} \left (t \right )-x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=-4 x_{2} \left (t \right )+9 x_{3} \left (t \right )-3 x_{4} \left (t \right )\\ \end {array} \]

0.355

3889

7288

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{2} \left (t \right )-x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=x_{2} \left (t \right )+x_{3} \left (t \right )\\ \end {array} \]

0.355

3890

8626

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=\left (2 t -1\right ) x_{1} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&={\mathrm e}^{-t^{2}+t} x_{1} \left (t \right )+x_{2} \left (t \right )\\ \end {array} \]

0.355

3891

8892

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=t \cot \left (t^{2}\right ) x_{1} \left (t \right )+\frac {t \cos \left (t^{2}\right ) x_{3} \left (t \right )}{2}\\ \frac {d}{d t}x_{2} \left (t \right )&=\frac {x_{2} \left (t \right )}{t}-x_{3} \left (t \right )+2-t \sin \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=\csc \left (t^{2}\right ) x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )+1-t \cos \left (t \right )\\ \end {array} \]

0.355

3892

10633

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-6 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=6 x_{1} \left (t \right )-5 x_{2} \left (t \right )\\ \end {array} \]

0.355

3893

21686

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=9 x_{1} \left (t \right )-2 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=5 x_{1} \left (t \right )-2 x_{2} \left (t \right )\\ \end {array} \]

0.355

3894

25269

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=10 x_{1} \left (t \right )-4 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+2 x_{2} \left (t \right )\\ \end {array} \]

0.355

3895

467

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-8 x_{1} \left (t \right )+5 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-5 x_{1} \left (t \right )+2 x_{2} \left (t \right )\\ \end {array} \]

0.356

3896

6482

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )+4 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-4 x_{1} \left (t \right )-5 x_{3} \left (t \right )\\ \end {array} \]

0.356

3897

7085

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-3 x_{1} \left (t \right )-x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=4 x_{1} \left (t \right )-7 x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+4 x_{3} \left (t \right )\\ \end {array} \]

0.356

3898

8142

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )+13 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-x_{1} \left (t \right )-3 x_{2} \left (t \right )\\ \end {array} \]

0.356

3899

11033

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-3 x_{1} \left (t \right )-10 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=5 x_{1} \left (t \right )+11 x_{2} \left (t \right )\\ \end {array} \]

0.356

3900

11131

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-x_{1} \left (t \right )-5 x_{2} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=4 x_{1} \left (t \right )-9 x_{2} \left (t \right )-x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=3 x_{3} \left (t \right )\\ \end {array} \]

0.356