2.3.106 Problems 10501 to 10600

Table 2.785: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10501

1454

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}-2 \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}

0.794

10502

1991

\begin{align*} 6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.794

10503

4497

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

0.794

10504

5796

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{a x} \\ \end{align*}

0.794

10505

7195

\begin{align*} 2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.794

10506

14208

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

0.794

10507

16808

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

Using Laplace transform method.

0.794

10508

17653

\begin{align*} 4 x^{2} y^{\prime \prime }+y&=x^{3} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}

0.794

10509

21575

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=16 x^{3} {\mathrm e}^{3 x} \\ \end{align*}

0.794

10510

21744

\begin{align*} x^{\prime }&=3 x+2 y \\ y^{\prime }&=-5 x+y \\ \end{align*}

0.794

10511

23537

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

0.794

10512

25197

\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y&=2 t \\ y \left (0\right ) &= a \\ y^{\prime }\left (0\right ) &= b \\ \end{align*}

0.794

10513

26760

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

0.794

10514

27141

\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2} \\ x_{2}^{\prime }&=4 x_{1}+2 x_{2} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= -2 \\ x_{2} \left (0\right ) &= 7 \\ \end{align*}

0.794

10515

3770

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=5 x \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.795

10516

4153

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{8}&=\frac {\sin \left (x \right )}{8}-\frac {\cos \left (x \right )}{4} \\ \end{align*}

0.795

10517

6410

\begin{align*} y^{b}+x^{a} y^{\prime \prime }&=0 \\ \end{align*}

0.795

10518

10087

\begin{align*} y^{\prime \prime }-x y^{\prime }-y x -x^{2}&=0 \\ \end{align*}

0.795

10519

10155

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

0.795

10520

15577

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

0.795

10521

15765

\begin{align*} y_{1}^{\prime }&=y_{2}+y_{4} \\ y_{2}^{\prime }&=y_{1}-y_{3} \\ y_{3}^{\prime }&=y_{4} \\ y_{4}^{\prime }&=y_{3} \\ \end{align*}

0.795

10522

19219

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

0.795

10523

19385

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

0.795

10524

21032

\begin{align*} {\mathrm e}^{x^{\prime }}&=x \\ x \left (t_{0} \right ) &= a \\ \end{align*}

0.795

10525

21229

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

With initial conditions

\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ z \left (0\right ) &= 1 \\ \end{align*}

0.795

10526

24095

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

Series expansion around \(x=0\).

0.795

10527

1026

\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2}-2 x_{4} \\ x_{2}^{\prime }&=x_{2} \\ x_{3}^{\prime }&=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\ x_{4}^{\prime }&=-4 x_{2}-x_{4} \\ \end{align*}

0.796

10528

2022

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3+5 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.796

10529

2037

\begin{align*} 4 x^{2} \left (4 x^{2}+1\right ) y^{\prime \prime }+32 x^{3} y^{\prime }+y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.796

10530

2263

\begin{align*} y_{1}^{\prime }&=4 y_{1}-2 y_{2}-2 y_{3} \\ y_{2}^{\prime }&=-2 y_{1}+3 y_{2}-y_{3} \\ y_{3}^{\prime }&=2 y_{1}-y_{2}+3 y_{3} \\ \end{align*}

0.796

10531

3915

\begin{align*} x_{1}^{\prime }&=9 x_{1}-2 x_{2}+9 t \\ x_{2}^{\prime }&=5 x_{1}-2 x_{2} \\ \end{align*}

0.796

10532

8095

\begin{align*} 4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.796

10533

9704

\begin{align*} x^{\prime }&=x-8 y \\ y^{\prime }&=x-3 y \\ \end{align*}

0.796

10534

10189

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

Series expansion around \(x=0\).

0.796

10535

10207

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

Series expansion around \(x=0\).

0.796

10536

17378

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

0.796

10537

17899

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

0.796

10538

18824

\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=16 \,{\mathrm e}^{\frac {t}{2}} \\ \end{align*}

0.796

10539

2023

\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.797

10540

3758

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{-x}}{\sqrt {-x^{2}+4}} \\ \end{align*}

0.797

10541

5811

\begin{align*} \left (c x +b \right ) y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

0.797

10542

10364

\begin{align*} a {y^{\prime \prime }}^{2}&=0 \\ \end{align*}

0.797

10543

11494

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

0.797

10544

13006

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

0.797

10545

16123

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

0.797

10546

22741

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

0.797

10547

13793

\begin{align*} x^{2} y^{\prime \prime }+a x y^{\prime }+\left (b \,x^{n}+c \right ) y&=0 \\ \end{align*}

0.798

10548

24767

\begin{align*} v^{\prime }-2 v+2 w^{\prime }&=2-4 \,{\mathrm e}^{2 x} \\ 2 v^{\prime }-3 v+3 w^{\prime }-w&=0 \\ \end{align*}

0.798

10549

26652

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

0.798

10550

1437

\begin{align*} x_{1}^{\prime }&=-3 x_{1}+\sqrt {2}\, x_{2}+{\mathrm e}^{-t} \\ x_{2}^{\prime }&=\sqrt {2}\, x_{1}-2 x_{2}-{\mathrm e}^{-t} \\ \end{align*}

0.799

10551

2187

\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }-4 y&=-{\mathrm e}^{-x} \left (\cos \left (x \right )-\sin \left (x \right )\right ) \\ \end{align*}

0.799

10552

3297

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

0.799

10553

7961

\begin{align*} \left (3 y-1\right )^{2} {y^{\prime }}^{2}&=4 y \\ \end{align*}

0.799

10554

10193

\begin{align*} x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.799

10555

10467

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

0.799

10556

11819

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

0.799

10557

12442

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

0.799

10558

16441

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

0.799

10559

19734

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

0.799

10560

22686

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

0.799

10561

24547

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=7+75 \sin \left (2 x \right ) \\ \end{align*}

0.799

10562

27372

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

0.799

10563

1428

\begin{align*} x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}+t \\ \end{align*}

0.800

10564

1506

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

Using Laplace transform method.

0.800

10565

1984

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.800

10566

3353

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

Series expansion around \(x=0\).

0.800

10567

8553

\begin{align*} x y^{\prime \prime }+y^{\prime }-7 x^{3} y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.800

10568

9070

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

0.800

10569

14374

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

0.800

10570

17462

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=4 \\ y \left (0\right ) &= {\frac {5}{4}} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.800

10571

17788

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

Series expansion around \(x=0\).

0.800

10572

24038

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

0.800

10573

383

\begin{align*} x^{\prime \prime }+9 x&=10 \cos \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.801

10574

638

\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=2 x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }&=2 x_{1}+x_{2}+7 x_{3} \\ \end{align*}

0.801

10575

3760

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {4 \,{\mathrm e}^{-2 x}}{x^{2}+1}+2 x^{2}-1 \\ \end{align*}

0.801

10576

9764

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

0.801

10577

27078

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

Series expansion around \(x=0\).

0.801

10578

1438

\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\cos \left (t \right ) \\ \end{align*}

0.802

10579

3434

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

0.802

10580

8803

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

0.802

10581

9691

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

0.802

10582

10174

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

Series expansion around \(x=0\).

0.802

10583

14923

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.802

10584

18675

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

0.802

10585

19522

\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \csc \left (x \right ) \\ \end{align*}

0.802

10586

20351

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

0.802

10587

23261

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

0.802

10588

25519

\begin{align*} y^{\prime \prime }+4 y&=F \cos \left (\omega t \right ) \\ \end{align*}

0.802

10589

364

\begin{align*} y^{\prime \prime }+9 y&=\sin \left (x \right )^{4} \\ \end{align*}

0.803

10590

7138

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

0.803

10591

17707

\begin{align*} \left (x^{2}-3 x -4\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.803

10592

21302

\begin{align*} x_{1}^{\prime }&=a x_{1}+5 x_{3} \\ x_{2}^{\prime }&=-x_{2}-2 x_{3} \\ x_{3}^{\prime }&=-3 x_{3} \\ \end{align*}

0.803

10593

22698

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

0.803

10594

23531

\begin{align*} y^{\prime \prime }+y&=\cot \left (x \right ) \csc \left (x \right ) \\ \end{align*}

0.803

10595

3374

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 \left (x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.804

10596

6475

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

0.804

10597

11761

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

0.804

10598

12553

\begin{align*} -\left (5+4 x \right ) y+32 x y^{\prime }+16 x^{2} y^{\prime \prime }&=0 \\ \end{align*}

0.804

10599

14804

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

N/A

N/A

N/A

0.804

10600

16912

\begin{align*} 4 y^{\prime \prime }+\frac {\left (4 x -3\right ) y}{\left (x -1\right )^{2}}&=0 \\ \end{align*}

Series expansion around \(x=1\).

0.804