2.3.64 Problems 6301 to 6400

Table 2.671: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

6301

1402

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

0.408

6302

2585

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

0.408

6303

3986

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

0.408

6304

4587

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

0.408

6305

4591

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

0.408

6306

9270

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

0.408

6307

9340

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

0.408

6308

12918

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

0.408

6309

13668

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

0.408

6310

14113

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

0.408

6311

15074

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

0.408

6312

15306

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

0.408

6313

15707

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

0.408

6314

17648

\begin{align*} x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+54 y^{\prime } x +42 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}

0.408

6315

18647

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

0.408

6316

18654

\begin{align*} x^{\prime }&=-\frac {3 x}{4}-\frac {7 y}{4} \\ y^{\prime }&=\frac {x}{4}+\frac {5 y}{4} \\ \end{align*}

0.408

6317

19418

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

0.408

6318

21628

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

0.408

6319

24655

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

0.408

6320

24659

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=15 \,{\mathrm e}^{x} \\ \end{align*}

0.408

6321

25637

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

0.408

6322

25815

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

0.408

6323

1084

\begin{align*} \left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}
Series expansion around \(x=1\).

0.409

6324

6390

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

0.409

6325

9171

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

0.409

6326

12337

\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\ \end{align*}

0.409

6327

12973

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

0.409

6328

16071

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=2 \,{\mathrm e}^{-3 t} \\ \end{align*}

0.409

6329

16506

\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.409

6330

16605

\begin{align*} y^{\prime \prime }+9 y&=52 \,{\mathrm e}^{2 x} \\ \end{align*}

0.409

6331

16762

\begin{align*} y^{\prime \prime }+4 y&=20 \,{\mathrm e}^{4 t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align*}
Using Laplace transform method.

0.409

6332

16773

\begin{align*} y^{\prime \prime }+9 y&=27 t^{3} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.409

6333

17992

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

0.409

6334

18241

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=10 \sin \left (x \right )+17 \sin \left (2 x \right ) \\ \end{align*}

0.409

6335

20059

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

0.409

6336

21025

\begin{align*} x^{\prime }-k^{2} x&=1 \\ \end{align*}

0.409

6337

25546

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

0.409

6338

2267

\begin{align*} y_{1}^{\prime }&=-3 y_{1}-4 y_{2} \\ y_{2}^{\prime }&=y_{1}-7 y_{2} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= 2 \\ y_{2} \left (0\right ) &= 3 \\ \end{align*}

0.410

6339

8126

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

0.410

6340

9234

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

0.410

6341

9381

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

0.410

6342

14697

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

0.410

6343

15984

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

0.410

6344

16163

\begin{align*} y^{\prime }&=20 \,{\mathrm e}^{-4 x} \\ \end{align*}

0.410

6345

16509

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

0.410

6346

18795

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

0.410

6347

18821

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

0.410

6348

19508

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

0.410

6349

19593

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

0.410

6350

21493

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

0.410

6351

354

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

0.411

6352

453

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

0.411

6353

468

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

0.411

6354

605

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

0.411

6355

1890

\begin{align*} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.411

6356

3127

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

0.411

6357

3150

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

0.411

6358

4515

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

0.411

6359

6389

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

0.411

6360

6947

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

0.411

6361

9132

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

0.411

6362

9259

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

0.411

6363

9451

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

0.411

6364

9501

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

0.411

6365

9612

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

0.411

6366

16780

\begin{align*} y^{\prime \prime }-4 y^{\prime }+40 y&=122 \,{\mathrm e}^{-3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}
Using Laplace transform method.

0.411

6367

18665

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

0.411

6368

20712

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

0.411

6369

20739

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

0.411

6370

21735

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

0.411

6371

23006

\begin{align*} y^{\prime \prime }-2 y^{\prime }-63 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

0.411

6372

23980

\begin{align*} y^{\prime \prime }+\frac {327 y^{\prime }}{100}-\frac {21 y}{50}&=0 \\ \end{align*}

0.411

6373

24679

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

0.411

6374

25330

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

0.411

6375

1788

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

0.412

6376

2598

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

0.412

6377

7088

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

0.412

6378

10398

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

0.412

6379

10942

\begin{align*} \left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \\ \end{align*}

0.412

6380

13188

\(\left [\begin {array}{ccc} 7 & -8 & 3 \\ 6 & -7 & 3 \\ 2 & -2 & 2 \end {array}\right ]\)

N/A

N/A

N/A

0.412

6381

15125

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

0.412

6382

15743

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

N/A

N/A

N/A

0.412

6383

18664

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

0.412

6384

20660

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

0.412

6385

24431

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

0.412

6386

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.

0.412

6387

480

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

0.413

6388

1369

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

0.413

6389

2243

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

0.413

6390

3373

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

0.413

6391

5968

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

0.413

6392

6132

\begin{align*} 6 y-4 \left (a +x \right ) y^{\prime }+\left (\operatorname {a0} +x \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

0.413

6393

9442

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

0.413

6394

13161

\(\left [\begin {array}{cccc} 1 & 0 & 4 & 0 \\ 0 & 1 & 4 & 0 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 0 & 3 \end {array}\right ]\)

N/A

N/A

N/A

0.413

6395

13189

\(\left [\begin {array}{ccc} 6 & -5 & 2 \\ 4 & -3 & 2 \\ 2 & -2 & 3 \end {array}\right ]\)

N/A

N/A

N/A

0.413

6396

16062

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

0.413

6397

16648

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x} \\ \end{align*}

0.413

6398

17427

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

0.413

6399

344

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

0.414

6400

3427

\begin{align*} y^{\prime }&={\mathrm e}^{2 t} t \\ y \left (1\right ) &= 5 \\ \end{align*}

0.414