2.3.34 Problems 3301 to 3400

Table 2.599: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

3301

10941

\begin{align*} \left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y&=0 \\ \end{align*}

0.255

3302

11003

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

0.255

3303

11154

\begin{align*} 2 \left (1-x \right ) x y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \\ \end{align*}

0.255

3304

11236

\begin{align*} 2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y&=0 \\ \end{align*}

0.255

3305

11731

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

0.255

3306

14207

\begin{align*} x^{\prime }&=\frac {1}{t \ln \left (t \right )} \\ \end{align*}

0.255

3307

15081

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

0.255

3308

16166

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

0.255

3309

21707

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

0.255

3310

22827

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

0.255

3311

23587

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

0.255

3312

1063

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

0.256

3313

6938

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

0.256

3314

7943

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

0.256

3315

8116

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

0.256

3316

8329

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

0.256

3317

10593

\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}

0.256

3318

10806

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

0.256

3319

11074

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

0.256

3320

14116

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

0.256

3321

21637

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

0.256

3322

1011

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

0.257

3323

2258

\begin{align*} y_{1}^{\prime }&=-10 y_{1}+9 y_{2} \\ y_{2}^{\prime }&=-4 y_{1}+2 y_{2} \\ \end{align*}

0.257

3324

7362

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

0.257

3325

15741

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

N/A

N/A

N/A

0.257

3326

23830

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

0.257

3327

24634

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

0.257

3328

1068

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

0.258

3329

1760

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

0.258

3330

1766

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

0.258

3331

2228

\begin{align*} x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 y^{\prime } x -18 y&=x^{3} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 7 \\ \end{align*}

0.258

3332

5412

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

0.258

3333

11017

\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \\ \end{align*}

0.258

3334

16463

\begin{align*} y^{\prime \prime } x +\left (2 x +2\right ) y^{\prime }+2 y&=8 \,{\mathrm e}^{2 x} \\ \end{align*}

0.258

3335

16803

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

0.258

3336

20392

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

0.258

3337

20553

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

0.258

3338

24618

\begin{align*} y^{\prime \prime \prime }+12 y^{\prime \prime }+48 y^{\prime }+64 y&=8 x \,{\mathrm e}^{-4 x} \\ \end{align*}

0.258

3339

1077

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

0.259

3340

1466

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

0.259

3341

6936

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

0.259

3342

14632

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=4 \,{\mathrm e}^{x}-18 \,{\mathrm e}^{-x} \\ \end{align*}

0.259

3343

14738

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

0.259

3344

18963

\begin{align*} \frac {8 y^{\prime \prime }}{5}+y&=\operatorname {Heaviside}\left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.259

3345

22249

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

0.259

3346

23806

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

0.259

3347

1525

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

0.260

3348

2253

\begin{align*} y_{1}^{\prime }&=3 y_{1}+4 y_{2} \\ y_{2}^{\prime }&=-y_{1}+7 y_{2} \\ \end{align*}

0.260

3349

4669

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

0.260

3350

6690

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

0.260

3351

8174

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=12 x^{2} \\ \end{align*}

0.260

3352

9026

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

0.260

3353

10511

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

0.260

3354

18318

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

0.260

3355

20763

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

0.260

3356

4517

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

0.261

3357

5563

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

0.261

3358

8099

\begin{align*} y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Series expansion around \(x=0\).

0.261

3359

9175

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

0.261

3360

16056

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

0.261

3361

19732

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

0.261

3362

20112

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

0.261

3363

20161

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

0.261

3364

20881

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

0.261

3365

560

\begin{align*} t x^{\prime \prime }+\left (4 t -2\right ) x^{\prime }+\left (13 t -4\right ) x&=0 \\ x \left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.262

3366

1398

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

0.262

3367

7900

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

0.262

3368

9172

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

0.262

3369

10049

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

0.262

3370

10927

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

0.262

3371

11056

\begin{align*} 3 \left (x +3\right ) x^{2} y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \\ \end{align*}

0.262

3372

11107

\begin{align*} \left (-4 x^{2}+1\right ) y^{\prime \prime }-20 y^{\prime } x -16 y&=0 \\ \end{align*}

0.262

3373

11205

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

0.262

3374

14131

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

0.262

3375

14737

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

0.262

3376

15159

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

0.262

3377

19640

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

0.262

3378

20157

\begin{align*} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 y^{\prime } x +4 y&=\frac {2}{x^{3}} \\ \end{align*}

0.262

3379

491

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

0.263

3380

2259

\begin{align*} y_{1}^{\prime }&=-13 y_{1}+16 y_{2} \\ y_{2}^{\prime }&=-9 y_{1}+11 y_{2} \\ \end{align*}

0.263

3381

2616

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

0.263

3382

4358

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

0.263

3383

8074

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

0.263

3384

8744

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

0.263

3385

10685

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

0.263

3386

10768

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

0.263

3387

11011

\begin{align*} 36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y&=0 \\ \end{align*}

0.263

3388

11201

\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}

0.263

3389

12842

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

0.263

3390

16152

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

0.263

3391

22845

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

0.263

3392

23055

\begin{align*} r^{\prime }&=-a \sin \left (\theta \right ) \\ r \left (0\right ) &= 2 a \\ \end{align*}

0.263

3393

403

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

0.264

3394

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.

0.264

3395

1088

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

0.264

3396

5404

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

0.264

3397

6692

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

0.264

3398

16367

\begin{align*} x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime }&=0 \\ \end{align*}

0.264

3399

18472

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

0.264

3400

25635

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

0.264