2.3.64 Problems 6301 to 6400

Table 2.659: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

6301

4173

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

0.524

6302

10342

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

0.524

6303

14858

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

0.524

6304

16769

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

0.524

6305

17013

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

0.524

6306

6823

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

0.525

6307

8161

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

0.525

6308

8181

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

0.525

6309

8538

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

0.525

6310

14783

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

0.525

6311

23046

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

0.525

6312

314

\begin{align*} a \,x^{3} y^{\prime \prime \prime }+b \,x^{2} y^{\prime \prime }+c x y^{\prime }+d y&=0 \\ \end{align*}

0.526

6313

981

\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\ x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\ \end{align*}

0.526

6314

2014

\begin{align*} 36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.526

6315

2019

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

0.526

6316

2442

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

0.526

6317

4376

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

0.526

6318

5385

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

0.526

6319

6517

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

0.526

6320

10831

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

0.526

6321

16938

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

0.526

6322

19643

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

0.526

6323

3811

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

0.527

6324

3927

\begin{align*} -2 y+y^{\prime }&=6 \,{\mathrm e}^{5 t} \\ y \left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

0.527

6325

3988

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

0.527

6326

7803

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

0.527

6327

10828

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

0.527

6328

12900

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

0.527

6329

15896

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

0.527

6330

22164

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

0.527

6331

22848

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

0.527

6332

22927

\begin{align*} 2 x^{\prime }-x-y^{\prime }+y&=4 t \,{\mathrm e}^{-t}-3 \,{\mathrm e}^{-t} \\ x^{\prime }+4 x-2 y^{\prime }-4 y&=2 t \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{-t} \\ \end{align*}

0.527

6333

24857

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

0.527

6334

6319

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

0.528

6335

9474

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

0.528

6336

11255

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

0.528

6337

12945

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

0.528

6338

18680

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

0.528

6339

22863

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

0.528

6340

1395

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

0.529

6341

3919

\begin{align*} x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=8 x_{1}+x_{2} \\ \end{align*}

0.529

6342

12977

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

0.529

6343

16885

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

0.529

6344

22176

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

0.529

6345

23452

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

0.529

6346

982

\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*}

0.530

6347

1859

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

0.530

6348

1910

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

0.530

6349

10522

\begin{align*} \left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \\ \end{align*}

0.530

6350

10830

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

0.530

6351

12989

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

0.530

6352

15025

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

0.530

6353

15275

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

0.530

6354

20506

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 y^{\prime } x +2 y&=x^{2}+3 x -4 \\ \end{align*}

0.530

6355

20581

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

0.530

6356

22864

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

0.530

6357

24052

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=\cosh \left (2 x \right ) \\ \end{align*}
Using Laplace transform method.

0.530

6358

1882

\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.531

6359

5439

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

0.531

6360

6536

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

0.531

6361

6640

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

0.531

6362

6955

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

0.531

6363

9666

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

0.531

6364

9836

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.531

6365

10290

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

0.531

6366

15684

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=24 x^{2}-6 x +14+32 \cos \left (2 x \right ) \\ \end{align*}

0.531

6367

17722

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

0.531

6368

22923

\begin{align*} x^{\prime }+2 y&=4 \,{\mathrm e}^{2 t} \\ x+y^{\prime }-y&=2 \,{\mathrm e}^{2 t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 7 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.531

6369

23574

\begin{align*} x^{\prime }&=5 x-6 y+1 \\ y^{\prime }&=6 x-7 y+1 \\ \end{align*}

0.531

6370

987

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

0.532

6371

1412

\begin{align*} x_{1}^{\prime }&=-\frac {4 x_{1}}{5}+2 x_{2} \\ x_{2}^{\prime }&=-x_{1}+\frac {6 x_{2}}{5} \\ \end{align*}

0.532

6372

1875

\begin{align*} \left (4 x^{2}-24 x +37\right ) y^{\prime \prime }+y&=0 \\ y \left (3\right ) &= 4 \\ y^{\prime }\left (3\right ) &= -6 \\ \end{align*}
Series expansion around \(x=3\).

0.532

6373

8844

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

0.532

6374

9589

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

0.532

6375

23691

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

0.532

6376

23760

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

0.532

6377

23795

\begin{align*} x^{\prime }&=5 x-6 y+1 \\ y^{\prime }&=6 x-7 y+1 \\ \end{align*}

0.532

6378

513

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

0.533

6379

984

\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*}

0.533

6380

2717

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

0.533

6381

3920

\begin{align*} x_{1}^{\prime }&=-6 x_{2} \\ x_{2}^{\prime }&=x_{1}-5 x_{2} \\ \end{align*}

0.533

6382

4001

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

0.533

6383

8549

\begin{align*} 4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.533

6384

10834

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

0.533

6385

17611

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

0.533

6386

632

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

0.534

6387

639

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

0.534

6388

3346

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

0.534

6389

14078

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

0.534

6390

15890

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

0.534

6391

16266

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

0.534

6392

16936

\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=5 x-2 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 15 \\ \end{align*}

0.534

6393

21698

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

0.534

6394

24056

\begin{align*} y^{\left (5\right )}&=120 \\ 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 ) &= 6 \\ y^{\prime \prime \prime \prime }\left (0\right ) &= 24 \\ \end{align*}
Using Laplace transform method.

0.534

6395

24104

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

0.534

6396

3992

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

0.535

6397

4088

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

0.535

6398

8076

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

0.535

6399

11260

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

0.535

6400

17585

\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=2 \,{\mathrm e}^{-3 t}-t \,{\mathrm e}^{-t} \\ \end{align*}

0.535