2.3.74 Problems 7301 to 7400

Table 2.679: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

7301

4184

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

0.643

7302

10015

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

0.643

7303

10698

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

0.643

7304

11115

\begin{align*} 3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \\ \end{align*}

0.643

7305

11180

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

0.643

7306

14360

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

0.643

7307

19883

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

0.643

7308

20144

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

0.643

7309

21667

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

0.643

7310

2448

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

0.644

7311

2803

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

0.644

7312

3375

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

0.644

7313

8534

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

0.644

7314

10293

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

0.644

7315

11116

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

0.644

7316

11128

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

0.644

7317

13298

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

0.644

7318

15938

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

0.644

7319

18434

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

0.644

7320

23743

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

0.644

7321

25284

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

0.644

7322

25317

\begin{align*} y^{\prime }+4 y&=\delta \left (t -3\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.644

7323

642

\begin{align*} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=-5 x_{1}-4 x_{2}-2 x_{3} \\ x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\ \end{align*}

0.645

7324

1040

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

0.645

7325

2760

\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }&=x_{1}-x_{2}+{\mathrm e}^{t} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}

0.645

7326

4018

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

0.645

7327

4577

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

0.645

7328

10672

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

0.645

7329

10957

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

0.645

7330

14072

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

0.645

7331

17827

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

0.645

7332

19063

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

0.645

7333

20212

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

0.645

7334

21727

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

0.645

7335

23353

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

0.645

7336

23732

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{16}\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.645

7337

2371

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= v \\ \end{align*}

0.646

7338

3863

\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{2} \\ x_{2}^{\prime }&=-x_{1}+5 x_{2} \\ x_{3}^{\prime }&=4 x_{3} \\ \end{align*}

0.646

7339

6485

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

0.646

7340

15097

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

0.646

7341

18006

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

0.646

7342

18443

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

0.646

7343

19152

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

0.646

7344

20530

\begin{align*} x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+y^{\prime } x +y&=\ln \left (x \right ) \\ \end{align*}

0.646

7345

8416

\begin{align*} y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\ y \left (-1\right ) &= -3 \\ \end{align*}

0.647

7346

17590

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

0.647

7347

18991

\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*}

0.647

7348

482

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

0.648

7349

1937

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

0.648

7350

1940

\begin{align*} \left (2 x^{2}-11 x +16\right ) y^{\prime \prime }+\left (x^{2}-6 x +10\right ) y^{\prime }-\left (-x +2\right ) y&=0 \\ y \left (3\right ) &= 1 \\ y^{\prime }\left (3\right ) &= -2 \\ \end{align*}
Series expansion around \(x=3\).

0.648

7351

2582

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

0.648

7352

5441

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

0.648

7353

5570

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

0.648

7354

8105

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

0.648

7355

10338

\begin{align*} y^{\prime } t +y&=0 \\ y \left (1\right ) &= 5 \\ \end{align*}
Using Laplace transform method.

0.648

7356

10674

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

0.648

7357

10882

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

0.648

7358

11050

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

0.648

7359

12847

\begin{align*} y^{\prime \prime }-\frac {1}{\left (a y^{2}+b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{{3}/{2}}}&=0 \\ \end{align*}

0.648

7360

14540

\begin{align*} \left (2+x \right ) y^{\prime }+y&=\left \{\begin {array}{cc} 2 x & 0\le x \le 2 \\ 4 & 2<x \end {array}\right . \\ y \left (0\right ) &= 4 \\ \end{align*}

0.648

7361

14673

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

0.648

7362

18633

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

0.648

7363

20892

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

0.648

7364

21907

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

0.648

7365

22276

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=6 x_{1}+4 \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}

0.648

7366

23681

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

0.648

7367

24021

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

0.648

7368

25343

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

0.648

7369

7099

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

0.649

7370

8150

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

0.649

7371

8605

\begin{align*} 9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (36 x^{4}-16\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.649

7372

10307

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

0.649

7373

10559

\begin{align*} 8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}

0.649

7374

10707

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \\ \end{align*}

0.649

7375

10971

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

0.649

7376

2024

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.650

7377

10447

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

0.650

7378

10697

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

0.650

7379

11130

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

0.650

7380

13160

\(\left [\begin {array}{cccc} 1 & 2 & 2 & 2 \\ 0 & 2 & 2 & 2 \\ 0 & 0 & 3 & 2 \\ 0 & 0 & 0 & 4 \end {array}\right ]\)

N/A

N/A

N/A

0.650

7381

13163

\(\left [\begin {array}{cccc} 4 & 0 & 0 & -3 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 6 & 0 & 0 & -5 \end {array}\right ]\)

N/A

N/A

N/A

0.650

7382

17825

\begin{align*} x_{1}^{\prime }&=-3 x_{1} \\ x_{2}^{\prime }&=1 \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= -1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}

0.650

7383

18121

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

0.650

7384

24259

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

0.650

7385

618

\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}+x_{3} \\ x_{2}^{\prime }&=6 x_{1}-x_{2} \\ x_{3}^{\prime }&=-x_{1}-2 x_{2}-x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ x_{3} \left (0\right ) &= 3 \\ \end{align*}

0.651

7386

638

\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=2 x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }&=2 x_{1}+x_{2}+7 x_{3} \\ \end{align*}

0.651

7387

6546

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

0.651

7388

11082

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

0.651

7389

11098

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

0.651

7390

13020

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

0.651

7391

17003

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

0.651

7392

19841

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

0.651

7393

21471

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

0.651

7394

21630

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

0.651

7395

640

\begin{align*} x_{1}^{\prime }&=5 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }&=3 x_{1}+x_{2}+5 x_{3} \\ \end{align*}

0.652

7396

9691

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

0.652

7397

9839

\begin{align*} \left (x^{2}-9\right ) y^{\prime \prime }+3 y^{\prime } x -3 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.652

7398

19604

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

0.652

7399

25348

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

0.652

7400

1841

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

0.653