2.3.144 Problems 14301 to 14400

Table 2.861: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14301

316

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

1.506

14302

2662

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

Series expansion around \(t=0\).

1.506

14303

10116

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

1.506

14304

13956

\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a \lambda \,{\mathrm e}^{\lambda x}+b \mu \,{\mathrm e}^{\mu x}\right ) y&=0 \\ \end{align*}

1.506

14305

24

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

1.507

14306

2410

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

1.507

14307

9278

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

1.507

14308

13873

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

1.508

14309

18739

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

1.508

14310

5848

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

1.509

14311

18782

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

1.509

14312

20384

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

1.510

14313

9185

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

1.511

14314

19160

\begin{align*} 5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

1.511

14315

24863

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

1.511

14316

26735

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

1.511

14317

665

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

1.512

14318

14336

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

1.512

14319

17454

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=-24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \\ \end{align*}

1.512

14320

18206

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

1.512

14321

20373

\begin{align*} y^{\left (6\right )}-2 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+3 y^{\prime \prime }-2 y^{\prime }+y&=\sin \left (\frac {x}{2}\right )^{2}+{\mathrm e}^{x} \\ \end{align*}

1.512

14322

26751

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

1.512

14323

13001

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

1.513

14324

14225

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

1.513

14325

15892

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

1.513

14326

24989

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

1.513

14327

3918

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

1.516

14328

8421

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

1.516

14329

16710

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

1.516

14330

20546

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

1.516

14331

23136

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

1.516

14332

23385

\begin{align*} x^{2} y^{\prime \prime }+\frac {7 x y^{\prime }}{2}-\frac {3 y}{2}&=0 \\ y \left (-4\right ) &= 1 \\ y^{\prime }\left (-4\right ) &= 0 \\ \end{align*}

1.516

14333

26887

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

1.516

14334

17299

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

1.517

14335

25199

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

1.517

14336

26650

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

1.517

14337

1297

\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\ \end{align*}

1.519

14338

8033

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

1.519

14339

14750

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

Series expansion around \(x=0\).

1.519

14340

5631

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

1.520

14341

5644

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

1.520

14342

5913

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

1.520

14343

13700

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

1.520

14344

14160

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

1.520

14345

16268

\begin{align*} y^{\prime }&=4 y+16 x \\ \end{align*}

1.520

14346

25308

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

Using Laplace transform method.

1.520

14347

6162

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

1.522

14348

23087

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

1.523

14349

1114

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

1.524

14350

23503

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

1.524

14351

27362

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

1.524

14352

229

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

1.525

14353

13688

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

1.525

14354

18094

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

1.525

14355

4098

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

1.526

14356

14654

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

1.527

14357

21776

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

1.527

14358

244

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

1.528

14359

8326

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

1.529

14360

16729

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

1.529

14361

20371

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

1.529

14362

22101

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

1.529

14363

23905

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

1.529

14364

26977

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=8+34 \cos \left (x \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

1.529

14365

27217

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

1.529

14366

27299

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

1.529

14367

7606

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

1.530

14368

16243

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

1.530

14369

19205

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

1.530

14370

24875

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

1.530

14371

9898

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

Series expansion around \(x=2\).

1.531

14372

9964

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

Series expansion around \(x=0\).

1.531

14373

3140

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

1.532

14374

1347

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

1.533

14375

9907

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

Series expansion around \(x=0\).

1.533

14376

20159

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

1.533

14377

21964

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

1.533

14378

22896

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

With initial conditions

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

1.533

14379

25976

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

1.533

14380

15303

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

1.534

14381

17533

\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y&=t^{3}+2 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

1.534

14382

20949

\begin{align*} y^{\prime }&=y^{2}-6 y-16 \\ \end{align*}

1.534

14383

3392

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

Series expansion around \(x=0\).

1.536

14384

5737

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

1.536

14385

9894

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

Series expansion around \(x=0\).

1.536

14386

12861

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

1.536

14387

25446

\begin{align*} z^{\prime }+4 i z&={\mathrm e}^{8 i t} \\ \end{align*}

1.536

14388

18224

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

1.537

14389

22147

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

1.537

14390

23907

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

1.537

14391

6205

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

1.539

14392

9810

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

1.539

14393

15816

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

1.539

14394

18388

\begin{align*} 9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.539

14395

18842

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

1.539

14396

20133

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

1.539

14397

842

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

1.540

14398

5872

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

1.540

14399

9539

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

Series expansion around \(x=0\).

1.540

14400

16276

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

1.540