2.3.104 Problems 10301 to 10400

Table 2.781: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10301

1751

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

0.775

10302

9470

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

0.775

10303

14098

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

0.775

10304

16900

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+\frac {y}{1-x}&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.775

10305

19191

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

0.775

10306

22197

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

Series expansion around \(x=0\).

0.775

10307

458

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

Series expansion around \(x=0\).

0.776

10308

2016

\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*}

Series expansion around \(x=0\).

0.776

10309

2626

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

Series expansion around \(t=0\).

0.776

10310

2729

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

0.776

10311

2737

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

With initial conditions

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

0.776

10312

2754

\begin{align*} x_{1}^{\prime }&=-4 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=10 x_{1}+9 x_{2}+x_{3} \\ x_{3}^{\prime }&=-4 x_{1}-3 x_{2}+x_{3} \\ \end{align*}

With initial conditions

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

0.776

10313

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 \(x=0\).

0.776

10314

5402

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

0.776

10315

9324

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

0.776

10316

9694

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

0.776

10317

10443

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

0.776

10318

12385

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

0.776

10319

12507

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

0.776

10320

15261

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

0.776

10321

18099

\begin{align*} 2 y^{\prime \prime }&=\frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }} \\ y \left (1\right ) &= \frac {\sqrt {2}}{5} \\ y^{\prime }\left (1\right ) &= \frac {\sqrt {2}}{2} \\ \end{align*}

0.776

10322

18200

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

0.776

10323

18890

\begin{align*} y^{\prime \prime }+4 y&=3 \,{\mathrm e}^{-2 t} \sin \left (2 t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

Using Laplace transform method.

0.776

10324

19063

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

0.776

10325

20996

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

0.776

10326

22783

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

0.776

10327

24109

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

Series expansion around \(x=0\).

0.776

10328

26072

\begin{align*} y^{\prime }&=-3 y+z-w \\ z^{\prime }&=5 y-z-7 w \\ w^{\prime }&=-y+z-3 w \\ \end{align*}

0.776

10329

2045

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

Series expansion around \(x=0\).

0.777

10330

3754

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

0.777

10331

4596

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

Series expansion around \(x=0\).

0.777

10332

8024

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

0.777

10333

8306

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

0.777

10334

10421

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

0.777

10335

12924

\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +y^{4} a \right )&=0 \\ \end{align*}

0.777

10336

16688

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

0.777

10337

16920

\begin{align*} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }+\left (1-4 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.777

10338

20851

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

0.777

10339

21268

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

Series expansion around \(t=0\).

0.777

10340

21547

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

0.777

10341

23627

\begin{align*} x^{\prime }&=-10 x+y+7 z \\ y^{\prime }&=-9 x+4 y+5 z \\ z^{\prime }&=-17 x+y+12 z \\ \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) &= 6 \\ y \left (0\right ) &= 1 \\ z \left (0\right ) &= 10 \\ \end{align*}

0.777

10342

25196

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

0.777

10343

26994

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

0.777

10344

8278

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

0.778

10345

17768

\begin{align*} y^{\prime \prime }+9 y&=\sin \left (3 t \right ) \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.778

10346

20595

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

0.778

10347

462

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

Series expansion around \(x=0\).

0.779

10348

2049

\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.779

10349

3767

\begin{align*} y^{\prime \prime }+5 y^{\prime }+4 y&=F \left (x \right ) \\ \end{align*}

0.779

10350

8147

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

Series expansion around \(x=0\).

0.779

10351

10370

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

0.779

10352

14975

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

Series expansion around \(x=0\).

0.779

10353

15654

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

0.779

10354

16908

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

Series expansion around \(x=0\).

0.779

10355

18373

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

Series expansion around \(x=0\).

0.779

10356

21698

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

Series expansion around \(x=0\).

0.779

10357

22139

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

0.779

10358

2804

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

0.780

10359

4475

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

0.780

10360

5436

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

0.780

10361

5564

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

0.780

10362

6773

\begin{align*} 6 x y^{\prime \prime }+6 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

0.780

10363

9778

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

0.780

10364

10262

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

0.780

10365

12544

\begin{align*} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }-\left (4 x^{2}+12 x +3\right ) y&=0 \\ \end{align*}

0.780

10366

14298

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

0.780

10367

18444

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

0.780

10368

24561

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

0.780

10369

25375

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

With initial conditions

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

0.780

10370

25382

\begin{align*} y_{1}^{\prime }&=5 y_{1}+2 y_{2}+t \\ y_{2}^{\prime }&=-8 y_{1}-3 y_{2}-2 t \\ \end{align*}

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}

0.780

10371

3132

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

0.781

10372

3874

\begin{align*} x_{1}^{\prime }&=-x_{1}+2 x_{2}+54 t \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=-2 x_{1}+4 x_{2}+9 \,{\mathrm e}^{3 t} \\ \end{align*}

0.781

10373

12900

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

0.781

10374

12989

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

0.781

10375

15002

\begin{align*} x^{\prime }&=11 x-2 y \\ y^{\prime }&=3 x+4 y \\ \end{align*}

0.781

10376

23400

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

0.781

10377

1188

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

0.782

10378

8009

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

0.782

10379

8602

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

Series expansion around \(x=0\).

0.782

10380

13103

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

0.782

10381

15259

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

0.782

10382

15570

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

0.782

10383

19222

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

0.782

10384

22796

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

0.782

10385

1064

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

Series expansion around \(x=0\).

0.783

10386

2246

\begin{align*} y_{1}^{\prime }&=-6 y_{1}-4 y_{2}-8 y_{3} \\ y_{2}^{\prime }&=-4 y_{1}-4 y_{3} \\ y_{3}^{\prime }&=-8 y_{1}-4 y_{2}-6 y_{3} \\ \end{align*}

0.783

10387

7170

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

Series expansion around \(x=0\).

0.783

10388

10106

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

0.783

10389

10368

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

0.783

10390

13102

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

0.783

10391

14283

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

0.783

10392

14573

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=2-12 x +6 \,{\mathrm e}^{x} \\ \end{align*}

0.783

10393

16388

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

0.783

10394

18820

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

0.783

10395

18823

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

0.783

10396

19613

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

Series expansion around \(x=0\).

0.783

10397

20617

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

0.783

10398

22294

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

0.783

10399

26345

\begin{align*} 4 {y^{\prime }}^{2}-9 x&=0 \\ \end{align*}

0.783

10400

3328

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

0.784