2.3.236 Problems 23501 to 23600

Table 2.1055: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23501

14545

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=3 \end {array} \]

17.777

23502

23213

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=x^{3} \end {array} \]

17.781

23503

25469

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x -8 y&={\mathrm e}^{x} \left (x^{2}+2\right ) \end {array} \]

17.791

23504

15387

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \sin \left (x \right ) \end {array} \]

17.792

23505

13024

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-7 y^{\prime }-8 y&={\mathrm e}^{x} \left (x^{2}+2\right ) \end {array} \]

17.797

23506

25490

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+4 y&={\mathrm e}^{2 x} \cos \left (x \right )+{\mathrm e}^{2 x} \sin \left (x \right ) \end {array} \]

17.802

23507

12886

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

17.803

23508

20254

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=x +2 \,{\mathrm e}^{-x}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-2\\ \end {array} \]

17.807

23509

19813

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=x \,{\mathrm e}^{x}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]

17.813

23510

13342

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 x}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

17.816

23511

5126

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime }&=x\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]

17.823

23512

22228

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

17.827

23513

12023

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

17.839

23514

12194

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\frac {1}{x} \end {array} \]

17.839

23515

19288

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

17.843

23516

11939

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y&=x \ln \left (x \right ) \end {array} \]

17.848

23517

19235

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+7 y^{\prime }+3 y&=5 \cos \left (t \right )\\ y \left (0\right )&=-3\\ y^{\prime }\left (0\right )&=5\\ \end {array} \]

17.849

23518

23739

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} e i u^{\prime \prime \prime \prime }&=\cos \left (x \right ) \end {array} \]

17.855

23519

26179

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

17.862

23520

5421

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} e i u^{\prime \prime \prime \prime }&=\sinh \left (x \right ) \end {array} \]

17.864

23521

7723

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} e i u^{\prime \prime \prime \prime }&=1 \end {array} \]

17.865

23522

3548

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} e i u^{\prime \prime \prime \prime }&=x^{2} \end {array} \]

17.883

23523

67

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} e i u^{\prime \prime \prime \prime }&=x^{4} \end {array} \]

17.894

23524

6442

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{a x}\\ y \left (0\right )&=y_{0}\\ y^{\prime }\left (0\right )&=y_{1}\\ \end {array} \]

17.912

23525

20284

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (a x \right )\\ y \left (0\right )&=y_{0}\\ y^{\prime }\left (0\right )&=y_{1}\\ \end {array} \]

17.917

23526

8669

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

17.924

23527

15347

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

17.927

23528

8279

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

17.939

23529

19739

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+10 y^{\prime }+25 y&=\frac {{\mathrm e}^{-5 x} \ln \left (x \right )}{x^{2}} \end {array} \]

17.944

23530

28038

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 x}}{x^{3}} \end {array} \]

17.955

23531

5175

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

17.963

23532

26409

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-12 y^{\prime }+36 y&={\mathrm e}^{6 x} \ln \left (x \right ) \end {array} \]

17.966

23533

27250

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \sec \left (x \right ) \end {array} \]

17.966

23534

11461

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sec \left (x \right )^{3} \end {array} \]

17.968

23535

17102

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 x}}{x^{4}} \end {array} \]

17.977

23536

15591

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

17.979

23537

20248

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

17.984

23538

17929

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

17.988

23539

25797

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=x^{{1}/{4}} \ln \left (x \right ) \end {array} \]

17.992

23540

10314

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=\frac {1}{x^{3}} \end {array} \]

17.993

23541

16198

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+7 y^{\prime } x -3 y&=\frac {\ln \left (x \right )}{x^{2}} \end {array} \]

18.012

23542

26864

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=\ln \left (x \right ) \left (\frac {1}{x^{3}}+\frac {1}{x^{5}}\right ) \end {array} \]

18.023

23543

14452

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\csc \left (x \right )\\ y \left (\frac {\pi }{2}\right )&=0\\ y^{\prime }\left (\frac {\pi }{2}\right )&=1\\ \end {array} \]

18.031

23544

1619

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\tan \left (x \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

18.063

23545

11826

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x}\\ y \left (1\right )&={\mathrm e}\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]

18.066

23546

15829

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 x}}{x^{3}}\\ y \left (1\right )&=4 \,{\mathrm e}^{-3}\\ y^{\prime }\left (1\right )&=-2 \,{\mathrm e}^{-3}\\ \end {array} \]

18.084

23547

15541

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sec \left (x \right )^{3}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]

18.091

23548

12463

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 x}}{x^{4}}\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&={\mathrm e}^{2}\\ \end {array} \]

18.096

23549

22426

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}}\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&={\frac {5}{2}}\\ \end {array} \]

18.110

23550

770

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=\frac {1}{x^{3}}\\ y \left (\frac {1}{4}\right )&=0\\ y^{\prime }\left (\frac {1}{4}\right )&={\frac {14}{9}}\\ \end {array} \]

18.119

23551

14450

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=\left (x^{2}+1\right )^{2}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]

18.122

23552

22210

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\left (5\right )}-y^{\prime }-\frac {4 y}{x}&=0 \end {array} \]

18.142

23553

8406

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (1-2 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+4 x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (2+4 x \right ) y&={\mathrm e}^{2 x} \left (1-2 x \ln \left (x \right )\right )^{2}\\ y \left (\frac {1}{2}\right )&=\frac {{\mathrm e}}{2}\\ y^{\prime }\left (\frac {1}{2}\right )&={\mathrm e} \left (2+\ln \left (2\right )\right )\\ \end {array} \]

18.145

23554

18558

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

18.146

23555

13770

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

18.171

23556

20688

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

18.175

23557

8670

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

18.209

23558

15600

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

18.217

23559

8244

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=5 x \left (t \right )-6 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=6 x \left (t \right )-7 y \left (t \right )\\ \end {array} \]

18.229

23560

5162

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

18.237

23561

4351

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

18.240

23562

20680

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

18.245

23563

12146

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

18.260

23564

15929

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

18.270

23565

17099

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

18.270

23566

6461

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

18.279

23567

12039

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

18.281

23568

3030

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

18.287

23569

5951

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-10 x_{1} \left (t \right )+x_{2} \left (t \right )+7 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-9 x_{1} \left (t \right )+4 x_{2} \left (t \right )+5 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-17 x_{1} \left (t \right )+x_{2} \left (t \right )+12 x_{3} \left (t \right )\\ \end {array} \]

18.287

23570

24208

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

18.296

23571

11820

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

18.300

23572

11594

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

18.303

23573

16312

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

18.309

23574

21389

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

18.310

23575

24202

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

18.311

23576

15909

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

18.314

23577

5087

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

18.320

23578

5178

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}N_{1} \left (t \right )&=4 N_{1} \left (t \right )-6 N_{2} \left (t \right )\\ \frac {d}{d t}N_{2} \left (t \right )&=8 N_{1} \left (t \right )-10 N_{2} \left (t \right )\\ \end {array} \]

18.326

23579

1148

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

18.342

23580

11949

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

18.348

23581

6990

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

18.352

23582

12481

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

18.352

23583

4682

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

18.355

23584

17263

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

18.362

23585

24400

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

18.367

23586

15789

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

18.369

23587

19350

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

18.385

23588

1649

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

18.387

23589

20874

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

18.387

23590

5540

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

18.392

23591

23927

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

18.394

23592

16230

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

18.398

23593

5419

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

18.408

23594

1143

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

18.413

23595

15908

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

18.419

23596

25497

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

18.428

23597

27294

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

18.432

23598

18798

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=a \left (b -x \left (t \right )\right )-c f y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=d \left (x \left (t \right )-y \left (t \right )\right )-c f y \left (t \right )-a y \left (t \right )\\ \end {array} \]

18.433

23599

9390

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

18.436

23600

9049

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

18.440