2.3.144 Problems 14301 to 14400

Table 2.831: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14301

16249

\begin{align*} y^{\prime }-2 y&=-10 \\ y \left (0\right ) &= 8 \\ \end{align*}

1.515

14302

11314

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

1.516

14303

21435

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

1.516

14304

23231

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

1.516

14305

9244

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=0 \\ \end{align*}

1.518

14306

15561

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

1.518

14307

15586

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

1.518

14308

21416

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

1.518

14309

3482

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

1.519

14310

18268

\begin{align*} 9 y+6 y^{\prime }+y^{\prime \prime }&=10 \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.520

14311

19751

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

1.520

14312

20656

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

1.520

14313

24858

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

1.520

14314

7597

\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=0 \\ y \left (-1\right ) &= 3 \\ y^{\prime }\left (-1\right ) &= 9 \\ \end{align*}

1.521

14315

17537

\begin{align*} 4 t^{2} y^{\prime \prime }+4 y^{\prime } t +\left (16 t^{2}-1\right ) y&=16 t^{{3}/{2}} \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (2 \pi \right ) &= 0 \\ \end{align*}

1.521

14316

20278

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

1.521

14317

25405

\begin{align*} y^{\prime }+9 y&=90 \\ y \left (0\right ) &= 1 \\ \end{align*}

1.521

14318

26144

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

1.522

14319

1297

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

1.523

14320

4522

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=2 \sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.523

14321

22097

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

1.523

14322

7275

\begin{align*} y^{\prime \prime }-4 y^{\prime }&=10 \\ \end{align*}

1.524

14323

13825

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

1.524

14324

32

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

1.526

14325

461

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

1.526

14326

17197

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

1.526

14327

20590

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

1.526

14328

21509

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

1.526

14329

24153

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

1.527

14330

3979

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=\delta \left (t -\frac {\pi }{4}\right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.528

14331

19632

\begin{align*} y^{\prime \prime }+a^{2} y&=f \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.528

14332

20131

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

1.528

14333

16557

\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\ \end{align*}

1.529

14334

754

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

1.530

14335

661

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

1.531

14336

1614

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

1.531

14337

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 \(t=0\).

1.532

14338

16860

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

1.532

14339

23081

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

1.532

14340

3564

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

1.533

14341

5385

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

1.533

14342

13755

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

1.533

14343

20407

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

1.534

14344

23567

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

1.534

14345

769

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

1.535

14346

18947

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

1.536

14347

19636

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

1.536

14348

25179

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

1.536

14349

18945

\begin{align*} y^{\prime \prime }+y&=\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )+3 \delta \left (t -\frac {3 \pi }{2}\right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.537

14350

670

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

1.539

14351

25562

\begin{align*} y^{\prime \prime }+\omega _{n}^{2} y&={\mathrm e}^{i \omega t} \\ \end{align*}

1.539

14352

26146

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

1.539

14353

3959

\begin{align*} 3 y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

1.540

14354

14209

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

1.540

14355

13929

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

1.541

14356

8769

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

1.542

14357

8896

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

1.542

14358

14810

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

1.542

14359

16585

\begin{align*} 4 y+y^{\prime \prime }&=24 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

1.542

14360

26

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

1.543

14361

2436

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

1.543

14362

3246

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

1.543

14363

20600

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

1.543

14364

2361

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

1.544

14365

13724

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

1.545

14366

18799

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

1.545

14367

87

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

1.546

14368

1332

\begin{align*} t^{2} y^{\prime \prime }+5 y^{\prime } t +13 y&=0 \\ \end{align*}

1.546

14369

3306

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

1.546

14370

19230

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

1.546

14371

6133

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

1.547

14372

17895

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

1.547

14373

25402

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

1.547

14374

7209

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

1.548

14375

14944

\begin{align*} x^{\prime \prime }+4 x&=289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \\ \end{align*}

1.548

14376

17709

\begin{align*} 2 y^{\prime \prime } x -5 y^{\prime }-3 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.548

14377

22797

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

1.548

14378

12517

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

1.549

14379

13893

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

1.549

14380

2437

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

1.550

14381

22312

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

1.550

14382

4124

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

1.551

14383

8748

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

1.551

14384

11745

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

1.551

14385

20321

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

1.551

14386

23735

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\ \end{align*}
Series expansion around \(x=1\).

1.551

14387

908

\begin{align*} x^{\prime \prime }+9 x&=10 \cos \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.552

14388

8445

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

1.552

14389

11313

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

1.552

14390

19173

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

1.552

14391

21313

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

1.552

14392

22750

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

1.552

14393

25230

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

1.552

14394

5625

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

1.553

14395

26085

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

1.553

14396

16120

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

1.555

14397

5423

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

1.556

14398

9626

\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

1.556

14399

10307

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

1.556

14400

19150

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

1.556