2.2.39 Problems 3801 to 3900

Table 2.79: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

3801

\[ {}y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y = 8 \,{\mathrm e}^{-x}+1 \]

[[_3rd_order, _with_linear_symmetries]]

0.126

3802

\[ {}y^{\prime \prime }-4 y = 5 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

1.234

3803

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.239

3804

\[ {}y^{\prime \prime }-y = 4 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

1.183

3805

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.921

3806

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

[[_2nd_order, _linear, _nonhomogeneous]]

6.447

3807

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

[[_2nd_order, _with_linear_symmetries]]

1.185

3808

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.121

3809

\[ {}y^{\prime \prime }+y = 4 \cos \left (2 x \right )+3 \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3.834

3810

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2} \\ x_{2}^{\prime }=2 x_{1}+3 x_{2} \end {array}\right ] \]

system_of_ODEs

0.504

3811

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-3 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ] \]

system_of_ODEs

0.497

3812

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+2 x_{2} \\ x_{2}^{\prime }=x_{2}-x_{1} \end {array}\right ] \]

system_of_ODEs

0.547

3813

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+4 x_{2} \\ x_{2}^{\prime }=-4 x_{1}-6 x_{2} \end {array}\right ] \]

system_of_ODEs

0.461

3814

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{2} \\ x_{2}^{\prime }=-2 x_{1} \end {array}\right ] \]

system_of_ODEs

0.516

3815

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \end {array}\right ] \]

system_of_ODEs

0.520

3816

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1} \\ x_{2}^{\prime }=x_{2}-x_{3} \\ x_{3}^{\prime }=x_{2}+x_{3} \end {array}\right ] \]

system_of_ODEs

0.464

3817

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}-x_{2}+3 x_{3} \\ x_{3}^{\prime }=-x_{2}-3 x_{3} \end {array}\right ] \]

system_of_ODEs

0.618

3818

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{2} \\ x_{2}^{\prime }=x_{1}+x_{2} \end {array}\right ] \]
i.c.

system_of_ODEs

0.582

3819

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+5 x_{2} \\ x_{2}^{\prime }=-x_{1}-2 x_{2} \end {array}\right ] \]
i.c.

system_of_ODEs

0.573

3820

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2} \\ x_{2}^{\prime }=-x_{1}+4 x_{2} \end {array}\right ] \]
i.c.

system_of_ODEs

0.562

3821

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}+5 \,{\mathrm e}^{4 t} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ] \]

system_of_ODEs

0.459

3822

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2}+t \\ x_{2}^{\prime }=-2 x_{1}+x_{2}+1 \end {array}\right ] \]

system_of_ODEs

0.434

3823

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=3 x_{1}-x_{2}+5 \,{\mathrm e}^{2 t} \end {array}\right ] \]

system_of_ODEs

0.509

3824

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\tan \left (t \right ) x_{1}+3 \cos \left (t \right )^{2} \\ x_{2}^{\prime }=x_{1}+\tan \left (t \right ) x_{2}+2 \sin \left (t \right ) \end {array}\right ] \]
i.c.

system_of_ODEs

0.040

3825

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ] \]

system_of_ODEs

0.489

3826

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=-b x_{1}-a x_{2} \end {array}\right ] \]

system_of_ODEs

0.615

3827

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{2} \\ x_{2}^{\prime }=-3 x_{1} \end {array}\right ] \]

system_of_ODEs

0.503

3828

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+3 x_{2} \\ x_{2}^{\prime }=-2 x_{1}+5 x_{2} \end {array}\right ] \]
i.c.

system_of_ODEs

0.593

3829

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ] \]

system_of_ODEs

0.513

3830

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2} \\ x_{2}^{\prime }=x_{2}-x_{1} \end {array}\right ] \]

system_of_ODEs

0.442

3831

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \\ x_{3}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \end {array}\right ] \]

system_of_ODEs

0.466

3832

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{t} \\ x_{2}^{\prime }=x_{2} \end {array}\right ] \]

system_of_ODEs

0.029

3833

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{t}+t x_{2} \\ x_{2}^{\prime }=-\frac {x_{1}}{t} \end {array}\right ] \]

system_of_ODEs

0.032

3834

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+2 x_{2} \end {array}\right ] \]

system_of_ODEs

0.478

3835

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-7 x_{2} \\ x_{2}^{\prime }=-x_{1}+4 x_{2} \end {array}\right ] \]

system_of_ODEs

0.478

3836

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{2} \\ x_{2}^{\prime }=4 x_{1} \end {array}\right ] \]

system_of_ODEs

0.490

3837

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2} \\ x_{2}^{\prime }=5 x_{1}-5 x_{2} \end {array}\right ] \]

system_of_ODEs

0.549

3838

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+2 x_{2} \\ x_{2}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ] \]

system_of_ODEs

0.506

3839

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1} \\ x_{2}^{\prime }=5 x_{2}-7 x_{3} \\ x_{3}^{\prime }=2 x_{2}-4 x_{3} \end {array}\right ] \]

system_of_ODEs

0.449

3840

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1} \\ x_{2}^{\prime }=x_{1}+5 x_{2}-x_{3} \\ x_{3}^{\prime }=x_{1}+6 x_{2}-2 x_{3} \end {array}\right ] \]

system_of_ODEs

0.416

3841

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=-x_{1} \\ x_{3}^{\prime }=5 x_{3} \end {array}\right ] \]

system_of_ODEs

0.458

3842

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+3 x_{3} \\ x_{2}^{\prime }=-4 x_{2} \\ x_{3}^{\prime }=-3 x_{1}+2 x_{3} \end {array}\right ] \]

system_of_ODEs

0.475

3843

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+6 x_{3} \\ x_{2}^{\prime }=-2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=-x_{1}-2 x_{2}-4 x_{3} \end {array}\right ] \]

system_of_ODEs

0.628

3844

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{2}+x_{3} \\ x_{2}^{\prime }=-2 x_{1}-x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{3} \end {array}\right ] \]

system_of_ODEs

0.433

3845

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{3} \\ x_{2}^{\prime }=-3 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{2}-x_{3} \end {array}\right ] \]

system_of_ODEs

0.694

3846

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }=-x_{1}+x_{2}+x_{3} \end {array}\right ] \]

system_of_ODEs

0.395

3847

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \\ x_{2}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \\ x_{3}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \end {array}\right ] \]

system_of_ODEs

0.378

3848

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}+3 x_{3}+4 x_{4} \\ x_{2}^{\prime }=4 x_{1}+3 x_{2}+2 x_{3}+x_{4} \\ x_{3}^{\prime }=4 x_{1}+5 x_{2}+6 x_{3}+7 x_{4} \\ x_{4}^{\prime }=7 x_{1}+6 x_{2}+5 x_{3}+4 x_{4} \end {array}\right ] \]

system_of_ODEs

0.795

3849

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=-x_{1} \\ x_{3}^{\prime }=-x_{4} \\ x_{4}^{\prime }=x_{3} \end {array}\right ] \]

system_of_ODEs

0.599

3850

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+4 x_{2} \\ x_{2}^{\prime }=2 x_{1}-3 x_{2} \end {array}\right ] \]
i.c.

system_of_ODEs

0.629

3851

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-6 x_{2} \\ x_{2}^{\prime }=3 x_{1}+5 x_{2} \end {array}\right ] \]
i.c.

system_of_ODEs

0.601

3852

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \\ x_{3}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \end {array}\right ] \]
i.c.

system_of_ODEs

0.474

3853

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{2} \\ x_{2}^{\prime }=-4 x_{1} \end {array}\right ] \]
i.c.

system_of_ODEs

0.574

3854

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=-b x_{1}-a x_{2} \end {array}\right ] \]

system_of_ODEs

0.603

3855

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2} \\ x_{2}^{\prime }=-x_{1}+3 x_{2} \end {array}\right ] \]

system_of_ODEs

0.429

3856

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+4 x_{2} \end {array}\right ] \]

system_of_ODEs

0.442

3857

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ] \]

system_of_ODEs

0.452

3858

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2}-x_{3} \end {array}\right ] \]

system_of_ODEs

0.419

3859

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+2 x_{2}-x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{1}+3 x_{2}-x_{3} \end {array}\right ] \]

system_of_ODEs

0.434

3860

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1} \\ x_{2}^{\prime }=x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }=-x_{1}+x_{2}-x_{3} \end {array}\right ] \]

system_of_ODEs

0.369

3861

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=15 x_{1}-32 x_{2}+12 x_{3} \\ x_{2}^{\prime }=8 x_{1}-17 x_{2}+6 x_{3} \\ x_{3}^{\prime }=-x_{3} \end {array}\right ] \]

system_of_ODEs

0.413

3862

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1} \\ x_{2}^{\prime }=x_{1}+4 x_{2} \\ x_{3}^{\prime }=x_{2}+4 x_{3} \end {array}\right ] \]

system_of_ODEs

0.342

3863

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=3 x_{2}+2 x_{3} \\ x_{3}^{\prime }=2 x_{1}-2 x_{2}-x_{3} \end {array}\right ] \]

system_of_ODEs

0.368

3864

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2} \\ x_{2}^{\prime }=-x_{1}+5 x_{2} \\ x_{3}^{\prime }=4 x_{3} \end {array}\right ] \]

system_of_ODEs

0.358

3865

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}-x_{1} \\ x_{2}^{\prime }=-2 x_{1}-3 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2}-2 x_{3} \end {array}\right ] \]

system_of_ODEs

0.404

3866

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{2} \\ x_{2}^{\prime }=x_{1} \\ x_{3}^{\prime }=x_{1}+2 x_{3}+x_{4} \\ x_{4}^{\prime }=x_{2}+2 x_{4} \end {array}\right ] \]

system_of_ODEs

0.866

3867

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+3 x_{2} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2} \\ x_{3}^{\prime }=x_{1}+x_{3}+x_{4} \\ x_{4}^{\prime }=x_{2}+x_{4} \end {array}\right ] \]

system_of_ODEs

0.671

3868

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{2} \\ x_{2}^{\prime }=x_{1} \\ x_{3}^{\prime }=x_{1}-x_{4} \\ x_{4}^{\prime }=x_{2}+x_{3} \end {array}\right ] \]

system_of_ODEs

0.565

3869

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}-4 x_{2} \end {array}\right ] \]
i.c.

system_of_ODEs

0.559

3870

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }=-x_{2} \\ x_{3}^{\prime }=-x_{1}-3 x_{2}+2 x_{3} \end {array}\right ] \]
i.c.

system_of_ODEs

0.392

3871

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-3 x_{2}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=2 x_{1}-x_{2}+{\mathrm e}^{t} \end {array}\right ] \]

system_of_ODEs

0.520

3872

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2} \\ x_{2}^{\prime }=-x_{1}+2 x_{2}+4 \,{\mathrm e}^{t} \end {array}\right ] \]

system_of_ODEs

0.460

3873

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2}+t \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }=3 x_{2}+{\mathrm e}^{3 t} \end {array}\right ] \]

system_of_ODEs

0.397

3874

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{2}+20 \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }=3 x_{1}+x_{2}+12 \,{\mathrm e}^{t} \end {array}\right ] \]

system_of_ODEs

0.552

3875

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+2 x_{2}+54 t \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }=-2 x_{1}+4 x_{2}+9 \,{\mathrm e}^{3 t} \end {array}\right ] \]

system_of_ODEs

0.502

3876

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+4 x_{2}+8 \sin \left (2 t \right ) \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2}+8 \cos \left (2 t \right ) \end {array}\right ] \]

system_of_ODEs

1.197

3877

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}-3 \,{\mathrm e}^{t} \\ x_{2}^{\prime }=-2 x_{1}-x_{2}+6 t \,{\mathrm e}^{t} \end {array}\right ] \]

system_of_ODEs

0.474

3878

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-{\mathrm e}^{t} \\ x_{2}^{\prime }=2 x_{1}-3 x_{2}+2 x_{3}+6 \,{\mathrm e}^{-t} \\ x_{3}^{\prime }=x_{1}-2 x_{2}+2 x_{3}+{\mathrm e}^{t} \end {array}\right ] \]

system_of_ODEs

0.711

3879

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-2 x_{2}+2 x_{3}-{\mathrm e}^{3 t} \\ x_{2}^{\prime }=2 x_{1}+4 x_{2}-x_{3}+4 \,{\mathrm e}^{3 t} \\ x_{3}^{\prime }=3 x_{3}+3 \,{\mathrm e}^{3 t} \end {array}\right ] \]

system_of_ODEs

0.681

3880

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-3 x_{2}+34 \sin \left (t \right ) \\ x_{2}^{\prime }=-4 x_{1}-2 x_{2}+17 \cos \left (t \right ) \end {array}\right ] \]

system_of_ODEs

0.696

3881

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2} \\ x_{2}^{\prime }=2 x_{2} \end {array}\right ] \]

system_of_ODEs

0.412

3882

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2} \\ x_{2}^{\prime }=-x_{2} \end {array}\right ] \]

system_of_ODEs

0.435

3883

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1} \\ x_{2}^{\prime }=3 x_{2}-x_{3} \\ x_{3}^{\prime }=x_{2}+x_{3} \end {array}\right ] \]

system_of_ODEs

0.356

3884

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ] \]

system_of_ODEs

0.441

3885

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=4 x_{1}-x_{2} \end {array}\right ] \]

system_of_ODEs

0.450

3886

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1} \\ x_{2}^{\prime }=x_{2}-8 x_{3} \\ x_{3}^{\prime }=2 x_{2}-7 x_{3} \end {array}\right ] \]

system_of_ODEs

0.408

3887

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+3 x_{3} \\ x_{2}^{\prime }=2 x_{1}+3 x_{2}-2 x_{3} \\ x_{3}^{\prime }=2 x_{2}+2 x_{3} \end {array}\right ] \]

system_of_ODEs

10.441

3888

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-8 x_{1}+6 x_{2}-3 x_{3} \\ x_{2}^{\prime }=-12 x_{1}+10 x_{2}-3 x_{3} \\ x_{3}^{\prime }=-2 x_{3} \end {array}\right ] \]

system_of_ODEs

0.400

3889

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=6 x_{2}-7 x_{3}+3 x_{4} \\ x_{3}^{\prime }=3 x_{3}-x_{4} \\ x_{4}^{\prime }=-4 x_{2}+9 x_{3}-3 x_{4} \end {array}\right ] \]

system_of_ODEs

0.667

3890

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{2} \\ x_{2}^{\prime }=x_{1} \\ x_{3}^{\prime }=x_{2}-x_{4} \\ x_{4}^{\prime }=x_{2}+x_{3} \end {array}\right ] \]

system_of_ODEs

0.694

3891

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=\left (-1+2 t \right ) x_{1} \\ x_{2}^{\prime }={\mathrm e}^{-t^{2}+t} x_{1}+x_{2} \end {array}\right ] \]

system_of_ODEs

0.034

3892

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=t \cot \left (t^{2}\right ) x_{1}+\frac {t \cos \left (t^{2}\right ) x_{3}}{2} \\ x_{2}^{\prime }=\frac {x_{2}}{t}-x_{3}+2-t \sin \left (t \right ) \\ x_{3}^{\prime }=\csc \left (t^{2}\right ) x_{1}+x_{2}-x_{3}+1-t \cos \left (t \right ) \end {array}\right ] \]

system_of_ODEs

0.053

3893

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-6 x_{1}+x_{2} \\ x_{2}^{\prime }=6 x_{1}-5 x_{2} \end {array}\right ] \]

system_of_ODEs

0.490

3894

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}-2 x_{2} \\ x_{2}^{\prime }=5 x_{1}-2 x_{2} \end {array}\right ] \]

system_of_ODEs

0.481

3895

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=10 x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}+2 x_{2} \end {array}\right ] \]

system_of_ODEs

0.440

3896

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-8 x_{1}+5 x_{2} \\ x_{2}^{\prime }=-5 x_{1}+2 x_{2} \end {array}\right ] \]

system_of_ODEs

0.449

3897

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+4 x_{3} \\ x_{2}^{\prime }=2 x_{2} \\ x_{3}^{\prime }=-4 x_{1}-5 x_{3} \end {array}\right ] \]

system_of_ODEs

0.396

3898

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-x_{2} \\ x_{2}^{\prime }=4 x_{1}-7 x_{2} \\ x_{3}^{\prime }=6 x_{1}+6 x_{2}+4 x_{3} \end {array}\right ] \]

system_of_ODEs

0.477

3899

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+13 x_{2} \\ x_{2}^{\prime }=-x_{1}-3 x_{2} \end {array}\right ] \]

system_of_ODEs

0.549

3900

\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-10 x_{2} \\ x_{2}^{\prime }=5 x_{1}+11 x_{2} \end {array}\right ] \]

system_of_ODEs

0.570