2.3.114 Problems 11301 to 11400

Table 2.801: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11301

826

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

0.888

11302

3057

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

0.888

11303

3357

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

Series expansion around \(x=0\).

0.888

11304

4545

\begin{align*} x^{\prime }-2 x+2 y^{\prime }&=-4 \,{\mathrm e}^{2 t} \\ 2 x^{\prime }-3 x+3 y^{\prime }-y&=0 \\ \end{align*}

0.888

11305

6970

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

0.888

11306

9471

\begin{align*} x^{\prime }&=x+y-5 t +2 \\ y^{\prime }&=4 x-2 y-8 t -8 \\ \end{align*}

0.888

11307

9853

\begin{align*} \left (9 x^{2}+1\right ) y^{\prime \prime }-18 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.888

11308

16992

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

0.888

11309

18005

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

0.888

11310

20528

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

0.888

11311

20622

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

0.888

11312

27074

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

Series expansion around \(x=0\).

0.888

11313

16891

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

Series expansion around \(x=3\).

0.889

11314

23548

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

0.889

11315

24103

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

Series expansion around \(x=0\).

0.889

11316

10098

\begin{align*} y^{\prime \prime }-y^{\prime }-y x -x^{3}+1&=0 \\ \end{align*}

0.890

11317

14801

\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ 2 & 3 & -4 \\ 4 & 1 & -4 \end {array}\right ]\)

N/A

N/A

N/A

0.890

11318

14811

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

Using Laplace transform method.

0.890

11319

14878

\begin{align*} x^{\prime }&=2 \sin \left (t \right )^{2} \\ x \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\ \end{align*}

0.890

11320

15431

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

0.890

11321

24813

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

0.890

11322

5404

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

0.891

11323

8551

\begin{align*} 9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.891

11324

9337

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

0.891

11325

14315

\begin{align*} x^{\prime \prime }-3 x^{\prime }-40 x&=2 \,{\mathrm e}^{-t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.891

11326

19592

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

Series expansion around \(x=0\).

0.891

11327

22740

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

0.891

11328

23047

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

0.891

11329

23565

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

0.891

11330

488

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

Series expansion around \(x=0\).

0.892

11331

4049

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

Series expansion around \(x=0\).

0.892

11332

7093

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

0.892

11333

14976

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

Series expansion around \(x=0\).

0.892

11334

15435

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

0.892

11335

18443

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

0.892

11336

18918

\begin{align*} y_{1}^{\prime }&=-y_{1}-5 y_{2}+3 \\ y_{2}^{\prime }&=y_{1}+3 y_{2}+5 \cos \left (t \right ) \\ \end{align*}

With initial conditions

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

0.892

11337

19044

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

0.892

11338

19603

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

Series expansion around \(x=0\).

0.892

11339

19871

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

0.892

11340

23722

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

Series expansion around \(x=0\).

0.892

11341

26983

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

0.892

11342

27715

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

0.892

11343

501

\begin{align*} 5 x y^{\prime \prime }+\left (30+3 x \right ) y^{\prime }+3 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.893

11344

14822

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=36 t \,{\mathrm e}^{4 t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -6 \\ \end{align*}

Using Laplace transform method.

0.893

11345

18835

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=4 \,{\mathrm e}^{-t} \cos \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.893

11346

18852

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

0.893

11347

21955

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

0.893

11348

23750

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

Series expansion around \(x=0\).

0.893

11349

5727

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

0.894

11350

9509

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

Series expansion around \(x=0\).

0.894

11351

9844

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

Series expansion around \(x=0\).

0.894

11352

19454

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

0.894

11353

19602

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

Series expansion around \(x=0\).

0.894

11354

21151

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

0.894

11355

21169

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

0.894

11356

21753

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

0.894

11357

23736

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

Series expansion around \(x=0\).

0.894

11358

24891

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

0.894

11359

25139

\begin{align*} y^{\prime \prime }-8 y^{\prime }+25 y&=36 t \,{\mathrm e}^{4 t} \sin \left (3 t \right ) \\ \end{align*}

0.894

11360

26585

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

0.894

11361

2247

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

0.895

11362

2456

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

Series expansion around \(t=0\).

0.895

11363

3867

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

0.895

11364

4105

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

0.895

11365

4750

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

0.895

11366

6927

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

0.895

11367

7192

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

Series expansion around \(x=0\).

0.895

11368

9526

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

Series expansion around \(x=0\).

0.895

11369

12866

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

0.895

11370

14392

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

0.895

11371

20905

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

Series expansion around \(x=0\).

0.895

11372

4504

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=15 \,{\mathrm e}^{-x} \sqrt {x +1} \\ \end{align*}

0.896

11373

8947

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

0.896

11374

16903

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

Series expansion around \(x=0\).

0.896

11375

511

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

Series expansion around \(x=0\).

0.897

11376

3769

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

0.897

11377

9856

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

Series expansion around \(x=-3\).

0.897

11378

2249

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

0.898

11379

3298

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

0.898

11380

3842

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

0.898

11381

4000

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

Series expansion around \(x=0\).

0.898

11382

6569

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

0.898

11383

8528

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

Series expansion around \(x=0\).

0.898

11384

9787

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

0.898

11385

12151

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

0.898

11386

12912

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

0.898

11387

18445

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

With initial conditions

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

0.898

11388

19518

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

0.898

11389

21752

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

0.898

11390

25355

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

Series expansion around \(t=0\).

0.898

11391

27130

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

N/A

N/A

N/A

0.898

11392

27570

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

0.898

11393

3761

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=15 \,{\mathrm e}^{-2 x} \ln \left (x \right )+25 \cos \left (x \right ) \\ \end{align*}

0.899

11394

6770

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

0.899

11395

8523

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

Series expansion around \(x=0\).

0.899

11396

18447

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

0.899

11397

24762

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

0.899

11398

3501

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

Series expansion around \(z=0\).

0.900

11399

5607

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

0.900

11400

18987

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

0.900