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

21630

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

Series expansion around \(x=1\).

1.697

11302

24594

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

1.697

11303

2604

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

1.698

11304

9376

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

Series expansion around \(x=0\).

1.698

11305

9829

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

1.698

11306

19430

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

1.698

11307

19757

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

1.698

11308

1596

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

1.699

11309

861

\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +25 y&=0 \\ \end{align*}

1.700

11310

16525

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

1.700

11311

23823

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

1.700

11312

24637

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

1.700

11313

104

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

1.701

11314

11908

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

1.701

11315

14670

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

1.701

11316

19501

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=12 x -10 \\ \end{align*}

1.701

11317

12430

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

1.702

11318

15836

\begin{align*} v^{\prime }&=\frac {K -v}{R C} \\ \end{align*}

1.702

11319

16643

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}

1.702

11320

16819

\begin{align*} y^{\prime \prime \prime \prime }-16 y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.702

11321

22883

\begin{align*} u^{\prime }&=2 v-1 \\ v^{\prime }&=1+2 u \\ \end{align*}

1.703

11322

25157

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

1.703

11323

16125

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=3+2 \cos \left (2 t \right ) \\ \end{align*}

1.704

11324

22162

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

1.704

11325

24757

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

1.704

11326

15667

\begin{align*} y^{\prime \prime }+9 y&=27 x +18 \\ y \left (0\right ) &= 23 \\ y^{\prime }\left (0\right ) &= 21 \\ \end{align*}

1.705

11327

22159

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

1.705

11328

26792

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

1.705

11329

808

\begin{align*} y^{\prime \prime }-9 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 15 \\ \end{align*}

1.706

11330

9960

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

Series expansion around \(x=0\).

1.706

11331

16676

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

1.706

11332

18394

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

1.706

11333

23789

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

1.706

11334

27159

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

1.706

11335

2356

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

1.707

11336

12616

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

1.707

11337

14630

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11 \\ \end{align*}

1.707

11338

16770

\begin{align*} y^{\prime \prime \prime }-27 y&={\mathrm e}^{-3 t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= 4 \\ \end{align*}

Using Laplace transform method.

1.707

11339

26653

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

1.707

11340

5820

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

1.708

11341

19064

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

1.708

11342

21679

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

Series expansion around \(x=0\).

1.708

11343

21694

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

Series expansion around \(x=0\).

1.708

11344

22158

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

1.708

11345

716

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

1.709

11346

1792

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

1.709

11347

3982

\begin{align*} y^{\prime \prime }+9 y&=15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.709

11348

9502

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

Series expansion around \(x=0\).

1.709

11349

20616

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

1.709

11350

25132

\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=16 \,{\mathrm e}^{t} \\ \end{align*}

1.709

11351

10076

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

1.710

11352

14741

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

Series expansion around \(x=1\).

1.710

11353

19698

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

1.710

11354

6116

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

1.711

11355

6946

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

1.711

11356

21689

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

Series expansion around \(x=0\).

1.711

11357

8154

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

1.712

11358

15405

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

1.712

11359

25119

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

1.712

11360

7639

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

Series expansion around \(x=1\).

1.713

11361

8031

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

1.713

11362

9843

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

Series expansion around \(x=0\).

1.713

11363

19875

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

1.713

11364

19974

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

1.713

11365

22924

\begin{align*} x^{\prime }-x+2 y^{\prime }+7 y&=3 t -15 \\ 2 x^{\prime }+y^{\prime }+x+5 y&=9 t -7 \\ \end{align*}

With initial conditions

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

1.713

11366

7179

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

Series expansion around \(x=0\).

1.714

11367

9682

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

1.714

11368

14048

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

1.714

11369

18016

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

1.714

11370

6233

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

1.715

11371

165

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

1.716

11372

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*}

1.716

11373

16090

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

1.716

11374

19195

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

1.716

11375

19220

\begin{align*} x^{\prime }+5 x+y&=7 \,{\mathrm e}^{t}-27 \\ -2 x+y^{\prime }+3 y&=-3 \,{\mathrm e}^{t}+12 \\ \end{align*}

1.716

11376

21638

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

Series expansion around \(x=0\).

1.716

11377

7690

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

1.717

11378

18961

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

Using Laplace transform method.

1.717

11379

19504

\begin{align*} y^{\prime \prime }+y^{\prime }&=10 x^{4}+2 \\ \end{align*}

1.717

11380

26641

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

1.717

11381

8584

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

Series expansion around \(x=0\).

1.718

11382

15102

\begin{align*} x^{\prime \prime }+10 x^{\prime }+25 x&=2^{t}+t \,{\mathrm e}^{-5 t} \\ \end{align*}

1.718

11383

21754

\begin{align*} x^{\prime }&=2 x-y-5 t \\ y^{\prime }&=3 x+6 y-4 \\ \end{align*}

1.719

11384

1549

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

1.720

11385

5757

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

1.720

11386

5806

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

1.720

11387

6175

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

1.720

11388

9521

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

Series expansion around \(x=0\).

1.720

11389

9835

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

Series expansion around \(x=0\).

1.720

11390

12371

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

1.720

11391

25181

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

1.720

11392

25221

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

1.720

11393

27673

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

1.720

11394

27696

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

1.720

11395

7174

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

Series expansion around \(x=0\).

1.721

11396

8133

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

Series expansion around \(x=0\).

1.721

11397

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*}

1.721

11398

23608

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

With initial conditions

\begin{align*} x \left (\pi \right ) &= 1 \\ y \left (\pi \right ) &= {\frac {4}{5}} \\ \end{align*}

1.721

11399

23939

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

1.721

11400

23982

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

1.721