2.3.26 Problems 2501 to 2600

Table 2.583: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

2501

9308

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=10+42 \,{\mathrm e}^{3 x} \\ \end{align*}

0.186

2502

11153

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

0.186

2503

11238

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

0.186

2504

15809

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

0.186

2505

17376

\begin{align*} t y^{\prime \prime }+2 y^{\prime }+16 t y&=0 \\ \end{align*}

0.186

2506

19633

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=4 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.186

2507

22798

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

0.186

2508

23630

\begin{align*} y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.186

2509

24923

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

0.186

2510

1046

\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}
Series expansion around \(x=0\).

0.187

2511

4379

\begin{align*} 2 x^{3}-y^{4}+x y^{3} y^{\prime }&=0 \\ \end{align*}

0.187

2512

4495

\begin{align*} y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y&=72 \,{\mathrm e}^{3 x}+729 x^{2} \\ \end{align*}

0.187

2513

14637

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=3 \,{\mathrm e}^{x} x^{2}-7 \,{\mathrm e}^{x} \\ \end{align*}

0.187

2514

15207

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+13 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 6 \\ \end{align*}
Using Laplace transform method.

0.187

2515

21984

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

0.187

2516

22335

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

0.187

2517

22821

\begin{align*} y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}
Series expansion around \(x=0\).

0.187

2518

25512

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

0.187

2519

934

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

0.188

2520

3689

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

0.188

2521

3786

\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}+4 x^{2} y&=0 \\ \end{align*}

0.188

2522

3787

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

0.188

2523

6682

\begin{align*} 6 y^{\prime }+6 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}

0.188

2524

6874

\begin{align*} {y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\ \end{align*}

0.188

2525

9111

\begin{align*} y^{\prime }-2 y x&=6 x \,{\mathrm e}^{x^{2}} \\ y \left (1\right ) &= 1 \\ \end{align*}

0.188

2526

9281

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

0.188

2527

9710

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

0.188

2528

10755

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

0.188

2529

10758

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

0.188

2530

10934

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x -12 y&=0 \\ \end{align*}

0.188

2531

13146

\(\left [\begin {array}{cc} 8 & -10 \\ 2 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.188

2532

14811

\begin{align*} -y+y^{\prime }&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

0.188

2533

18177

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

0.188

2534

20593

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

0.188

2535

24611

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

0.188

2536

4377

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

0.189

2537

6942

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

0.189

2538

7990

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

0.189

2539

10818

\begin{align*} u^{\prime \prime }+\frac {u}{x^{2}}&=0 \\ \end{align*}

0.189

2540

13174

\(\left [\begin {array}{cc} 5 & -3 \\ 2 & 0 \end {array}\right ]\)

N/A

N/A

N/A

0.189

2541

15324

\begin{align*} x^{\prime }+y^{\prime }+x&=0 \\ x^{\prime }-x+2 y^{\prime }&={\mathrm e}^{-t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.189

2542

15831

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

0.189

2543

21888

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=x^{3}+{\mathrm e}^{x} \\ \end{align*}

0.189

2544

22903

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

0.189

2545

25320

\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

0.189

2546

3212

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

0.190

2547

8791

\begin{align*} {y^{\prime }}^{2}&=4 x^{2} \\ \end{align*}

0.190

2548

9312

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

0.190

2549

11002

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

0.190

2550

11287

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

0.190

2551

14353

\begin{align*} x^{\prime \prime }-x^{\prime }-6 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

0.190

2552

2185

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+15 y&={\mathrm e}^{2 x} \left (15 x \cos \left (2 x \right )+32 \sin \left (2 x \right )\right ) \\ \end{align*}

0.191

2553

5510

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

0.191

2554

6659

\begin{align*} \operatorname {a3} y+\operatorname {a2} y^{\prime }+\operatorname {a1} y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}

0.191

2555

10972

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

0.191

2556

10977

\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}

0.191

2557

11014

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

0.191

2558

13144

\(\left [\begin {array}{cc} 10 & -8 \\ 6 & -4 \end {array}\right ]\)

N/A

N/A

N/A

0.191

2559

15219

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=t +2 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.191

2560

19593

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

0.191

2561

22248

\begin{align*} y^{\prime \prime }+y&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

0.191

2562

23673

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

0.191

2563

24529

\begin{align*} y^{\prime \prime \prime }+9 y^{\prime \prime }&=11 \\ \end{align*}

0.191

2564

25238

\begin{align*} t y^{\prime \prime }+\left (1+t \right ) y^{\prime }+y&=0 \\ \end{align*}
Using Laplace transform method.

0.191

2565

1079

\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.192

2566

1778

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

0.192

2567

13173

\(\left [\begin {array}{cc} 6 & -6 \\ 4 & -4 \end {array}\right ]\)

N/A

N/A

N/A

0.192

2568

18897

\begin{align*} y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.192

2569

20389

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

0.192

2570

6776

\begin{align*} y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

0.193

2571

6778

\begin{align*} a y+12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

0.193

2572

6945

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

0.193

2573

10574

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

0.193

2574

13175

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

N/A

N/A

N/A

0.193

2575

15223

\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=4 \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}
Using Laplace transform method.

0.193

2576

15827

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

0.193

2577

16581

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y&=0 \\ \end{align*}

0.193

2578

18887

\begin{align*} 6 y^{\prime \prime }+5 y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.193

2579

19408

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

0.193

2580

23394

\begin{align*} x^{6} y^{\left (6\right )}-12 x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

0.193

2581

1044

\begin{align*} 2 y^{\prime }+3 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.194

2582

1080

\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.194

2583

1097

\begin{align*} y^{\prime \prime }&=y x \\ \end{align*}
Series expansion around \(x=0\).

0.194

2584

2218

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-x} \left (20-12 x \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -4 \\ y^{\prime \prime }\left (0\right ) &= 7 \\ y^{\prime \prime \prime }\left (0\right ) &= -22 \\ \end{align*}

0.194

2585

4063

\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.194

2586

5381

\begin{align*} {y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\ \end{align*}

0.194

2587

5395

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

0.194

2588

7364

\begin{align*} y^{\prime } x&=y \\ \end{align*}
Series expansion around \(x=0\).

0.194

2589

7453

\begin{align*} \theta r^{\prime }+3 r-\theta -1&=0 \\ \end{align*}

0.194

2590

8124

\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.194

2591

10764

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

0.194

2592

10852

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

0.194

2593

11174

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

0.194

2594

13141

\(\left [\begin {array}{cc} 4 & -3 \\ 2 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.194

2595

13147

\(\left [\begin {array}{cc} 9 & -10 \\ 2 & 0 \end {array}\right ]\)

N/A

N/A

N/A

0.194

2596

13192

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

N/A

N/A

N/A

0.194

2597

14435

\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\ y \left (2\right ) &= 0 \\ y^{\prime }\left (2\right ) &= 2 \\ y^{\prime \prime }\left (2\right ) &= 6 \\ \end{align*}

0.194

2598

15186

\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.194

2599

16578

\begin{align*} x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 y^{\prime } x -18 y&=0 \\ \end{align*}

0.194

2600

18886

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

0.194