2.3.74 Problems 7301 to 7400

Table 2.721: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

7301

9605

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

Using Laplace transform method.

0.545

7302

12653

\begin{align*} y^{\prime \prime }&=-\frac {3 y}{16 x^{2} \left (x -1\right )^{2}} \\ \end{align*}

0.545

7303

21145

\begin{align*} x^{\prime \prime }-x&={\mathrm e}^{k t} \\ \end{align*}

0.545

7304

21877

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

0.545

7305

22245

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

Using Laplace transform method.

0.545

7306

24597

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

0.545

7307

25135

\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=6 \,{\mathrm e}^{-4 t} \\ \end{align*}

0.545

7308

25138

\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&=10 t \,{\mathrm e}^{4 t} \\ \end{align*}

0.545

7309

506

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

Series expansion around \(x=0\).

0.546

7310

2420

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

Series expansion around \(t=0\).

0.546

7311

2598

\begin{align*} y^{\prime \prime }+5 y^{\prime }+4 y&=t^{2} {\mathrm e}^{7 t} \\ \end{align*}

0.546

7312

8578

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

Series expansion around \(x=0\).

0.546

7313

9036

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

0.546

7314

10504

\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \\ \end{align*}

0.546

7315

10523

\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 y x&=0 \\ \end{align*}

0.546

7316

16078

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.546

7317

16707

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 x y^{\prime }+9 y&=12 x \sin \left (x^{2}\right ) \\ \end{align*}

0.546

7318

16841

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

Series expansion around \(x=1\).

0.546

7319

17441

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=-32 t^{2} \\ \end{align*}

0.546

7320

17442

\begin{align*} 8 y^{\prime \prime }+6 y^{\prime }+y&=5 t^{2} \\ \end{align*}

0.546

7321

19442

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

0.546

7322

20008

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

0.546

7323

20911

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

Series expansion around \(x=0\).

0.546

7324

21648

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

Series expansion around \(x=0\).

0.546

7325

21898

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

0.546

7326

23929

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

0.546

7327

24060

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

0.546

7328

26756

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

With initial conditions

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

0.546

7329

27108

\(\left [\begin {array}{ccc} 0 & 1 & 0 \\ 1 & -2 & 0 \\ 0 & 0 & 3 \end {array}\right ]\)

N/A

N/A

N/A

0.546

7330

27124

\(\left [\begin {array}{ccc} 0 & 1 & 0 \\ 1 & -2 & 0 \\ 0 & 0 & 3 \end {array}\right ]\)

N/A

N/A

N/A

0.546

7331

27608

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }&=\frac {6 y^{2}}{x^{2}}-4 y \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*}

0.546

7332

1839

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

Series expansion around \(x=0\).

0.547

7333

1882

\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 y x&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.547

7334

3124

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

0.547

7335

3694

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

0.547

7336

6644

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

0.547

7337

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*}

0.547

7338

7796

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

0.547

7339

8150

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

Series expansion around \(x=0\).

0.547

7340

8965

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

Series expansion around \(x=0\).

0.547

7341

13154

\(\left [\begin {array}{ccc} 3 & 5 & -2 \\ 0 & 2 & 0 \\ 0 & 2 & 1 \end {array}\right ]\)

N/A

N/A

N/A

0.547

7342

16083

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

0.547

7343

19503

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

0.547

7344

21102

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

With initial conditions

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

0.547

7345

21735

\begin{align*} x^{\prime }&=8 x-y \\ y^{\prime }&=4 x+12 y \\ \end{align*}

0.547

7346

24756

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

0.547

7347

27550

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

0.547

7348

27614

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

0.547

7349

27773

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

Series expansion around \(x=0\).

0.547

7350

1032

\begin{align*} x_{1}^{\prime }&=-2 x_{1}+17 x_{2}+4 x_{3} \\ x_{2}^{\prime }&=-x_{1}+6 x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{2}+2 x_{3} \\ \end{align*}

0.548

7351

1870

\begin{align*} \left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y&=0 \\ \end{align*}

Series expansion around \(x=2\).

0.548

7352

3136

\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.548

7353

5791

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

0.548

7354

7092

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

0.548

7355

16084

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

0.548

7356

17827

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

0.548

7357

18901

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

Using Laplace transform method.

0.548

7358

21131

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

0.548

7359

21638

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

Series expansion around \(x=0\).

0.548

7360

23479

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

0.548

7361

259

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}

0.549

7362

1337

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

0.549

7363

1432

\begin{align*} x_{1}^{\prime }&=4 x_{1}-2 x_{2}+\frac {1}{t^{3}} \\ x_{2}^{\prime }&=8 x_{1}-4 x_{2}-\frac {1}{t^{2}} \\ \end{align*}

0.549

7364

1893

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

Series expansion around \(x=0\).

0.549

7365

7185

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

Series expansion around \(x=0\).

0.549

7366

7286

\begin{align*} y^{\prime \prime }+4 y^{\prime }+12 y&=80 \sin \left (2 x \right ) \\ \end{align*}

0.549

7367

7290

\begin{align*} y^{\prime \prime }+9 y&=30 \sin \left (3 x \right ) \\ \end{align*}

0.549

7368

11668

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

0.549

7369

18017

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

0.549

7370

18374

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

Series expansion around \(x=0\).

0.549

7371

24599

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

0.549

7372

24696

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

0.549

7373

24724

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

0.549

7374

24747

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

0.549

7375

26117

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

0.549

7376

26506

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&={\mathrm e}^{5 x} \\ \end{align*}

0.549

7377

26631

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

0.549

7378

2390

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

0.550

7379

3088

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

0.550

7380

3166

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

0.550

7381

12372

\begin{align*} x y^{\prime \prime }+a y^{\prime }+b \,x^{\operatorname {a1}} y&=0 \\ \end{align*}

0.550

7382

12435

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

0.550

7383

12786

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

0.550

7384

17751

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

0.550

7385

17897

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

0.550

7386

21135

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

0.550

7387

21483

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

0.550

7388

21591

\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&={\mathrm e}^{x} x^{2} \\ \end{align*}

0.550

7389

21644

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

Series expansion around \(x=2\).

0.550

7390

22254

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

Using Laplace transform method.

0.550

7391

22762

\begin{align*} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x +1 \\ \end{align*}

0.550

7392

23485

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

0.550

7393

23721

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

Series expansion around \(x=0\).

0.550

7394

23793

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

0.550

7395

24694

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

0.550

7396

25634

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

Using Laplace transform method.

0.550

7397

7762

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=8 \,{\mathrm e}^{4 x} \\ \end{align*}

0.551

7398

14384

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

0.551

7399

27142

\begin{align*} x_{1}^{\prime }&=5 x_{1}-4 x_{2}+4 x_{3} \\ x_{2}^{\prime }&=12 x_{1}-11 x_{2}+12 x_{3} \\ x_{3}^{\prime }&=4 x_{1}-4 x_{2}+5 x_{3} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= -3 \\ x_{3} \left (0\right ) &= 5 \\ \end{align*}

0.551

7400

916

\begin{align*} x^{\prime \prime }+3 x^{\prime }+3 x&=8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \\ \end{align*}

0.552