2.3.124 Problems 12301 to 12400

Table 2.797: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12301

14057

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

1.086

12302

16734

\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }+3&=0 \\ \end{align*}

1.086

12303

21163

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

1.086

12304

25619

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

1.086

12305

9649

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

1.087

12306

12628

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

1.087

12307

20906

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

1.087

12308

10190

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

1.088

12309

10370

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

1.088

12310

12996

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

1.088

12311

1439

\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2}+\csc \left (t \right ) \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\sec \left (t \right ) \\ \end{align*}

1.089

12312

2436

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

1.089

12313

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 \(x=0\).

1.089

12314

3359

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

1.089

12315

3362

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

1.089

12316

6132

\begin{align*} 6 y-4 \left (a +x \right ) y^{\prime }+\left (\operatorname {a0} +x \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

1.089

12317

6883

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

1.089

12318

10205

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

1.089

12319

21621

\begin{align*} \theta ^{\prime \prime }+4 \theta &=15 \cos \left (3 t \right ) \\ \theta \left (0\right ) &= 0 \\ \theta ^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.089

12320

1437

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

1.090

12321

6363

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

1.090

12322

6852

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

1.090

12323

10181

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

1.090

12324

13723

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

1.090

12325

25401

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

1.090

12326

3354

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

1.091

12327

13108

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

1.091

12328

993

\begin{align*} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4} \\ x_{3}^{\prime }&=5 x_{3} \\ x_{4}^{\prime }&=-21 x_{3}-2 x_{4} \\ \end{align*}

1.092

12329

6323

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

1.092

12330

9783

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

1.092

12331

16491

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

1.092

12332

16608

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

1.092

12333

19150

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

1.092

12334

26377

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

1.092

12335

4487

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

1.093

12336

18245

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=6 x \,{\mathrm e}^{-x} \left (1-{\mathrm e}^{-x}\right ) \\ \end{align*}

1.093

12337

18854

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

1.093

12338

20947

\begin{align*} x^{\prime }&=2 x-y+\cos \left (t \right ) \\ y^{\prime }&=5 x-2 y+\sin \left (t \right ) \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}

1.093

12339

21162

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

1.093

12340

21661

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

1.093

12341

22220

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

1.093

12342

4020

\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (3 x +7\right ) y^{\prime }+\left (1+6 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.094

12343

4542

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

1.094

12344

5644

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

1.094

12345

6365

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

1.094

12346

15653

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

1.094

12347

15977

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

1.094

12348

18851

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

1.094

12349

13020

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

1.095

12350

26029

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

1.095

12351

178

\begin{align*} x^{\prime }&=7 x \left (x-13\right ) \\ x \left (0\right ) &= 17 \\ \end{align*}

1.096

12352

1516

\begin{align*} y^{\prime \prime }+y&=\frac {\operatorname {Heaviside}\left (t -4+k \right )-\operatorname {Heaviside}\left (t -4-k \right )}{2 k} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.096

12353

9963

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

1.096

12354

12685

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

1.096

12355

21750

\begin{align*} x^{\prime }&=7 x-y+6 z \\ y^{\prime }&=-10 x+4 y-12 z \\ z^{\prime }&=-2 x+y-z \\ \end{align*}

1.096

12356

2693

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.097

12357

16732

\begin{align*} 9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\ \end{align*}

1.097

12358

17489

\begin{align*} y^{\prime \prime }+2 y^{\prime }+50 y&={\mathrm e}^{-t} \csc \left (7 t \right ) \\ \end{align*}

1.097

12359

24551

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

1.097

12360

26482

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

1.097

12361

3381

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

1.098

12362

4017

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

1.098

12363

9571

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-64\right ) y&=0 \\ \end{align*}

1.098

12364

12585

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

1.098

12365

23687

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

1.098

12366

26567

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

1.098

12367

17728

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

1.099

12368

23144

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

1.099

12369

16392

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

1.100

12370

16713

\begin{align*} 16 y-7 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}

1.100

12371

19596

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

1.100

12372

4044

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

1.101

12373

6514

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

1.101

12374

10093

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

1.101

12375

6317

\begin{align*} y y^{\prime }+y^{\prime \prime }&=-12 f \left (x \right ) y+y^{3}+12 f^{\prime }\left (x \right ) \\ \end{align*}

1.102

12376

6417

\begin{align*} f \left (x \right )^{2} y^{\prime \prime }&=-24 f \left (x \right )^{4}+\left (3 f \left (x \right )^{3}-f \left (x \right )^{2} y+3 f \left (x \right ) f^{\prime }\left (x \right )\right ) y^{\prime } \\ \end{align*}

1.102

12377

9548

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

1.102

12378

21542

\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*}

1.102

12379

2177

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }-2 y&={\mathrm e}^{2 x} \left (\left (-x^{2}+5 x +27\right ) \cos \left (x \right )+\left (9 x^{2}+13 x +2\right ) \sin \left (x \right )\right ) \\ \end{align*}

1.103

12380

3755

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

1.103

12381

4030

\begin{align*} x^{2} y^{\prime \prime }+\left (-2 x^{5}+9 x \right ) y^{\prime }+\left (10 x^{4}+5 x^{2}+25\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.103

12382

18832

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

1.103

12383

19666

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

1.103

12384

20425

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

1.103

12385

21974

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

1.103

12386

2772

\begin{align*} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3}+2 \,{\mathrm e}^{8 t} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{3}+{\mathrm e}^{8 t} \\ x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3}+2 \,{\mathrm e}^{8 t} \\ \end{align*}

1.104

12387

3365

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

1.104

12388

10357

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

1.104

12389

12402

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

1.104

12390

26027

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

1.104

12391

9001

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

1.105

12392

9795

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

1.105

12393

9902

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

1.105

12394

10445

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

1.105

12395

19848

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

1.105

12396

3364

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

1.106

12397

4014

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.106

12398

15667

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

1.106

12399

18825

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

1.106

12400

20003

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

1.106