2.3.84 Problems 8301 to 8400

Table 2.699: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

8301

17447

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=-78 \cos \left (3 t \right ) \\ \end{align*}

0.415

8302

18152

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

0.415

8303

19243

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

0.415

8304

22796

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y&=64 \sin \left (2 x \right ) \\ \end{align*}

0.415

8305

23534

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

0.415

8306

3145

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

0.416

8307

3398

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

0.416

8308

4593

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

0.416

8309

6075

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

0.416

8310

6465

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

0.416

8311

10118

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

0.416

8312

14604

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

0.416

8313

14976

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

0.416

8314

16746

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=10 \,{\mathrm e}^{-3 x} \\ \end{align*}

0.416

8315

21492

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

0.416

8316

21870

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

0.416

8317

21909

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

0.416

8318

23602

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

0.416

8319

24067

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

0.416

8320

24769

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

0.416

8321

1442

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

0.417

8322

4496

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

0.417

8323

4502

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

0.417

8324

6392

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

0.417

8325

7961

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

0.417

8326

8412

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

0.417

8327

9508

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

0.417

8328

9510

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

0.417

8329

9672

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

0.417

8330

12702

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

0.417

8331

14082

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

0.417

8332

17526

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=65 \cos \left (2 t \right ) \\ \end{align*}

0.417

8333

17595

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

0.417

8334

17896

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

0.417

8335

18027

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

0.417

8336

20140

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

0.417

8337

20614

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

0.417

8338

20935

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

0.417

8339

347

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=x \,{\mathrm e}^{3 x} \sin \left (3 x \right ) \\ \end{align*}

0.418

8340

1336

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

0.418

8341

1403

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

0.418

8342

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 \(x=0\).

0.418

8343

3768

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

0.418

8344

4479

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

0.418

8345

7294

\begin{align*} y^{\prime \prime }+4 y^{\prime }+8 y&=30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right ) \\ \end{align*}

0.418

8346

7658

\begin{align*} z^{\prime \prime }+x z^{\prime }+z&=x^{2}+2 x +1 \\ \end{align*}
Series expansion around \(x=0\).

0.418

8347

8577

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= {\frac {15}{8}} \\ \end{align*}
Series expansion around \(x=0\).

0.418

8348

9472

\begin{align*} x^{\prime }&=3 x-4 y \\ y^{\prime }&=4 x-7 y \\ \end{align*}

0.418

8349

9573

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

0.418

8350

10587

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \\ \end{align*}

0.418

8351

14307

\begin{align*} x^{\prime \prime }+7 x&=t \,{\mathrm e}^{3 t} \\ \end{align*}

0.418

8352

16046

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

0.418

8353

16587

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

0.418

8354

21572

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

0.418

8355

21914

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

0.418

8356

22174

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

0.418

8357

22687

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

0.418

8358

25548

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

0.418

8359

25580

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

0.418

8360

25774

\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (8\right ) &= -4 \\ \end{align*}

0.418

8361

158

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

0.419

8362

2297

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

0.419

8363

3863

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

0.419

8364

8287

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

0.419

8365

10142

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

0.419

8366

10234

\begin{align*} y^{\prime \prime }+20 y^{\prime }+500 y&=100000 \cos \left (100 x \right ) \\ \end{align*}

0.419

8367

14732

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

0.419

8368

14735

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

0.419

8369

14936

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

0.419

8370

15527

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

0.419

8371

16008

\begin{align*} x^{\prime }&=2 x+2 y \\ y^{\prime }&=-4 x+6 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.419

8372

18833

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

0.419

8373

22726

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

0.419

8374

23525

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

0.419

8375

24716

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

0.419

8376

24746

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

0.419

8377

25272

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

0.419

8378

25294

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

0.419

8379

453

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

0.420

8380

589

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

0.420

8381

868

\begin{align*} x^{\prime \prime }+10 x^{\prime }+125 x&=0 \\ x \left (0\right ) &= 6 \\ x^{\prime }\left (0\right ) &= 50 \\ \end{align*}

0.420

8382

3112

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

0.420

8383

3343

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

0.420

8384

10791

\begin{align*} 16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y&=0 \\ \end{align*}

0.420

8385

12895

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

0.420

8386

18077

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

0.420

8387

20015

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

0.420

8388

21139

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

0.420

8389

21496

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

0.420

8390

22702

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

0.420

8391

574

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

0.421

8392

652

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

0.421

8393

866

\begin{align*} 4 x^{\prime \prime }+20 x^{\prime }+169 x&=0 \\ x \left (0\right ) &= 4 \\ x^{\prime }\left (0\right ) &= 16 \\ \end{align*}

0.421

8394

1356

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

0.421

8395

1881

\begin{align*} \left (-2 x^{3}+1\right ) y^{\prime \prime }-10 x^{2} y^{\prime }-8 y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.421

8396

1933

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

0.421

8397

2826

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

0.421

8398

2829

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

0.421

8399

3726

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

0.421

8400

4156

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

0.421