2.3.25 Problems 2401 to 2500

Table 2.581: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

2401

567

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

0.148

2402

1627

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

0.148

2403

2154

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=-{\mathrm e}^{x} \left (7+6 x \right ) \\ \end{align*}

0.148

2404

3931

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

0.148

2405

3942

\begin{align*} y^{\prime \prime }+4 y&=10 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.148

2406

3952

\begin{align*} y^{\prime \prime }+y&=6 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

0.148

2407

4519

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t} \sin \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

0.148

2408

5495

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

0.148

2409

6534

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

0.148

2410

6650

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

0.148

2411

6762

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

0.148

2412

8716

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

0.148

2413

9029

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

0.148

2414

9603

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

0.148

2415

10970

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

0.148

2416

11171

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

0.148

2417

11228

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

0.148

2418

12904

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

0.148

2419

13180

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

N/A

N/A

N/A

0.148

2420

14359

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

0.148

2421

15191

\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+37 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}
Using Laplace transform method.

0.148

2422

15195

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*}
Using Laplace transform method.

0.148

2423

15438

\begin{align*} y^{\prime \prime \prime \prime }-a^{4} y&=5 a^{4} {\mathrm e}^{a x} \sin \left (a x \right ) \\ \end{align*}

0.148

2424

16136

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

0.148

2425

16667

\begin{align*} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}

0.148

2426

16673

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

0.148

2427

17569

\begin{align*} 8 y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+66 y^{\prime \prime \prime }-41 y^{\prime \prime }-37 y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -14 \\ y^{\prime \prime }\left (0\right ) &= -14 \\ y^{\prime \prime \prime }\left (0\right ) &= 139 \\ y^{\prime \prime \prime \prime }\left (0\right ) &= -{\frac {29}{4}} \\ \end{align*}

0.148

2428

17600

\begin{align*} y^{\prime \prime \prime }-13 y^{\prime }+12 y&=\cos \left (t \right ) \\ \end{align*}

0.148

2429

3784

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

0.149

2430

9716

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

0.149

2431

10550

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

0.149

2432

11042

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

0.149

2433

12790

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y-32 \sin \left (2 x \right )+24 \cos \left (2 x \right )&=0 \\ \end{align*}

0.149

2434

14112

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

0.149

2435

14366

\begin{align*} x^{\prime \prime }+3 x^{\prime }+2 x&={\mathrm e}^{-4 t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.149

2436

17660

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

0.149

2437

22230

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

0.149

2438

24057

\begin{align*} 2 y^{\prime }+y&={\mathrm e}^{x} \\ y \left (2\right ) &= \frac {4 \,{\mathrm e}^{2}}{3} \\ \end{align*}
Using Laplace transform method.

0.149

2439

542

\begin{align*} x^{\prime \prime }-6 x^{\prime }+8 x&=2 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.150

2440

1510

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

0.150

2441

2111

\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= k_{0} \\ y^{\prime }\left (1\right ) &= k_{1} \\ y^{\prime \prime }\left (1\right ) &= k_{2} \\ \end{align*}

0.150

2442

3192

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

0.150

2443

3694

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

0.150

2444

3722

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

0.150

2445

11040

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

0.150

2446

11238

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

0.150

2447

11254

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

0.150

2448

15187

\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

0.150

2449

17572

\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 16 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime \prime }\left (0\right ) &= 0 \\ y^{\left (5\right )}\left (0\right ) &= 0 \\ \end{align*}

0.150

2450

17630

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

0.150

2451

21197

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

0.150

2452

22904

\begin{align*} x^{\prime }+3 y^{\prime }+y&={\mathrm e}^{t} \\ -x+y^{\prime }&=y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.150

2453

25078

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

0.150

2454

25321

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

0.150

2455

25628

\begin{align*} y^{\prime \prime }+2 y^{\prime }+16 y&=0 \\ \end{align*}
Using Laplace transform method.

0.150

2456

357

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

0.151

2457

532

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

0.151

2458

553

\begin{align*} x^{\prime \prime }+9 x&=6 \cos \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.151

2459

2578

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

0.151

2460

3208

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

0.151

2461

4379

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

0.151

2462

6659

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

0.151

2463

9719

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

0.151

2464

10759

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

0.151

2465

10811

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

0.151

2466

11257

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

0.151

2467

11262

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

0.151

2468

12901

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

0.151

2469

14994

\(\left [\begin {array}{cc} 7 & 1 \\ -4 & 11 \end {array}\right ]\)

N/A

N/A

N/A

0.151

2470

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.

0.151

2471

15321

\begin{align*} y^{\prime \prime }+9 y&=18 t \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.151

2472

16438

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

0.151

2473

16777

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}
Using Laplace transform method.

0.151

2474

17583

\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=9 \,{\mathrm e}^{3 t} \\ \end{align*}

0.151

2475

17627

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

0.151

2476

18908

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

0.151

2477

23394

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

0.151

2478

23655

\begin{align*} 4 y^{\prime \prime }-3 y^{\prime }-y&=34 \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}
Using Laplace transform method.

0.151

2479

25062

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

0.151

2480

556

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

0.152

2481

559

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

0.152

2482

1511

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

0.152

2483

2155

\begin{align*} 2 y^{\prime \prime \prime }-7 y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{2 x} \left (17+30 x \right ) \\ \end{align*}

0.152

2484

5512

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

0.152

2485

6648

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

0.152

2486

6927

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

0.152

2487

6936

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

0.152

2488

7907

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

0.152

2489

8791

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

0.152

2490

9717

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

0.152

2491

10673

\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\ \end{align*}

0.152

2492

10899

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

0.152

2493

10994

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

0.152

2494

11258

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

0.152

2495

11259

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

0.152

2496

11727

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

0.152

2497

15216

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{-2 t} \\ y \left (0\right ) &= -{\frac {2}{13}} \\ y^{\prime }\left (0\right ) &= {\frac {1}{13}} \\ \end{align*}
Using Laplace transform method.

0.152

2498

15696

\begin{align*} 2 y+y^{\prime }&=4 \\ \end{align*}
Using Laplace transform method.

0.152

2499

16817

\begin{align*} y^{\prime \prime }-12 y^{\prime }+45 y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.152

2500

17629

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

0.152