2.3.114 Problems 11301 to 11400

Table 2.759: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11301

9876

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

0.609

11302

10191

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

0.609

11303

12912

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

0.609

11304

15068

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

0.609

11305

15974

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

0.609

11306

16891

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

0.609

11307

18993

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

0.609

11308

20066

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

0.609

11309

21486

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

0.609

11310

23339

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

0.609

11311

25316

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

0.609

11312

1956

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

0.610

11313

2643

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

0.610

11314

15663

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

0.610

11315

18877

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

0.610

11316

18997

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

0.610

11317

22724

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }-6 y^{\prime }-12 y&=\sinh \left (x \right )^{4} \\ \end{align*}

0.610

11318

23099

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

0.610

11319

25350

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

0.610

11320

1998

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

0.611

11321

6547

\begin{align*} 2 \left (1-y\right ) y y^{\prime \prime }&=-\left (1-y\right )^{3} \left (\operatorname {F0} \left (x \right )^{2}-\operatorname {G0} \left (x \right )^{2} y^{2}\right )-4 \left (1-y\right ) y^{2} \left (f \left (x \right )^{2}-g \left (x \right )^{2}+f^{\prime }\left (x \right )+g^{\prime }\left (x \right )\right )-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*}

0.611

11322

14416

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

0.611

11323

15097

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

0.611

11324

17358

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

0.611

11325

20518

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

0.611

11326

20941

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

0.611

11327

25482

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

0.611

11328

1963

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

0.612

11329

5849

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

0.612

11330

8220

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

0.612

11331

8523

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

0.612

11332

8587

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

0.612

11333

8598

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

0.612

11334

9950

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x -18 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.612

11335

10363

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

0.612

11336

13010

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

0.612

11337

19843

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

0.612

11338

20523

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

0.612

11339

20617

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

0.612

11340

25583

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

0.612

11341

25660

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

0.612

11342

2647

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

0.613

11343

2828

\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=-8 x_{1}+4 x_{2} \\ \end{align*}

0.613

11344

7910

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

0.613

11345

8589

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

0.613

11346

8975

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

0.613

11347

9460

\begin{align*} x^{\prime }&=x+2 y+t -1 \\ y^{\prime }&=3 x+2 y-5 t -2 \\ \end{align*}

0.613

11348

18006

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

0.613

11349

24520

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

0.613

11350

619

\begin{align*} x_{1}^{\prime }&=-8 x_{1}-11 x_{2}-2 x_{3} \\ x_{2}^{\prime }&=6 x_{1}+9 x_{2}+2 x_{3} \\ x_{3}^{\prime }&=-6 x_{1}-6 x_{2}+x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 5 \\ x_{2} \left (0\right ) &= -7 \\ x_{3} \left (0\right ) &= 11 \\ \end{align*}

0.614

11351

1028

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

0.614

11352

1502

\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=1-\operatorname {Heaviside}\left (t -\pi \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.

0.614

11353

1812

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

0.614

11354

2652

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

0.614

11355

3848

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

0.614

11356

19659

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

0.614

11357

25527

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

0.614

11358

25531

\begin{align*} m y^{\prime \prime }-k y&={\mathrm e}^{i \omega t} \\ \end{align*}

0.614

11359

1359

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u&=3 \cos \left (6 t \right ) \\ u \left (0\right ) &= 2 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.615

11360

2729

\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*}

0.615

11361

3485

\begin{align*} f^{\prime \prime }+2 f^{\prime }+5 f&={\mathrm e}^{-t} \cos \left (3 t \right ) \\ f \left (0\right ) &= 0 \\ f^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.615

11362

3507

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

0.615

11363

6579

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

0.615

11364

8990

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

0.615

11365

10087

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

0.615

11366

13006

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

0.615

11367

15176

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

0.615

11368

17831

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

0.615

11369

20033

\begin{align*} \left (8 {y^{\prime }}^{3}-27\right ) x&=12 y {y^{\prime }}^{2} \\ \end{align*}

0.615

11370

20894

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

0.615

11371

23741

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

0.615

11372

25281

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

0.615

11373

1353

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

0.616

11374

3161

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

0.616

11375

6140

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

0.616

11376

6225

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

0.616

11377

7835

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

0.616

11378

8227

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

0.616

11379

9693

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

0.616

11380

10177

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

0.616

11381

18434

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

0.616

11382

18443

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

0.616

11383

19425

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

0.616

11384

22269

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

0.616

11385

23733

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

0.616

11386

23751

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

0.616

11387

23938

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

0.616

11388

24736

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

0.616

11389

25375

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

0.616

11390

1064

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

0.617

11391

3149

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

0.617

11392

8087

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

0.617

11393

12414

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

0.617

11394

15169

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

0.617

11395

19648

\begin{align*} x^{\prime }&=7 x+6 y \\ y^{\prime }&=2 x+6 y \\ \end{align*}

0.617

11396

21274

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

0.617

11397

24569

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

0.617

11398

24939

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

0.617

11399

25545

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

0.617

11400

505

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

0.618