2.3.86 Problems 8501 to 8600

Table 2.703: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

8501

9000

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

0.826

8502

21696

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

0.826

8503

23239

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

0.826

8504

990

\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{3} \\ x_{2}^{\prime }&=9 x_{1}-x_{2}+2 x_{3} \\ x_{3}^{\prime }&=-9 x_{1}+4 x_{2}-x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 17 \\ \end{align*}

0.827

8505

1962

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

0.827

8506

2487

\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}

0.827

8507

6433

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

0.827

8508

8051

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

0.827

8509

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 \(x=0\).

0.827

8510

25319

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=\delta \left (t -3\right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}
Using Laplace transform method.

0.827

8511

1267

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

0.828

8512

3860

\begin{align*} x_{1}^{\prime }&=15 x_{1}-32 x_{2}+12 x_{3} \\ x_{2}^{\prime }&=8 x_{1}-17 x_{2}+6 x_{3} \\ x_{3}^{\prime }&=-x_{3} \\ \end{align*}

0.828

8513

9837

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+10 y^{\prime } x +20 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.828

8514

22967

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

0.828

8515

1985

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.829

8516

2203

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

0.829

8517

3363

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

0.829

8518

7153

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

0.829

8519

9480

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

0.829

8520

1271

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

0.830

8521

14214

\begin{align*} u^{\prime }&=\frac {1}{5-2 u} \\ \end{align*}

0.830

8522

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*}

0.831

8523

4544

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

0.831

8524

16877

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

0.831

8525

23

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

0.832

8526

2719

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

0.832

8527

3857

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

0.832

8528

10170

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

0.832

8529

10490

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

0.832

8530

14641

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+7 y^{\prime \prime }-5 y^{\prime }+6 y&=5 \sin \left (x \right )-12 \sin \left (2 x \right ) \\ \end{align*}

0.832

8531

16869

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

0.832

8532

18178

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

0.832

8533

18965

\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*}

0.832

8534

20160

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

0.832

8535

21755

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

0.832

8536

24950

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

0.832

8537

3361

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

0.833

8538

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 \(x=0\).

0.833

8539

8330

\begin{align*} y^{\prime }&=10+3 y-y^{2} \\ \end{align*}

0.833

8540

14181

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

0.833

8541

15066

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

0.833

8542

18995

\begin{align*} x_{1}^{\prime }&=-x_{3} \\ x_{2}^{\prime }&=2 x_{1} \\ x_{3}^{\prime }&=-x_{1}+2 x_{2}+4 x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 7 \\ x_{2} \left (0\right ) &= 5 \\ x_{3} \left (0\right ) &= 5 \\ \end{align*}

0.833

8543

25313

\begin{align*} y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.833

8544

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 \(x=0\).

0.834

8545

9950

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

0.834

8546

12988

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

0.834

8547

15451

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

0.834

8548

19011

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }&=-8 x_{1}-5 x_{2}-3 x_{3} \\ \end{align*}

0.834

8549

23670

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

0.834

8550

23676

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

0.834

8551

25384

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

0.834

8552

25658

\begin{align*} y^{\prime }+20 y&=24 \\ \end{align*}

0.834

8553

2527

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

0.835

8554

3325

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

0.835

8555

6543

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

0.835

8556

9058

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

0.835

8557

9985

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

0.835

8558

15855

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

0.835

8559

19222

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

0.835

8560

19621

\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 \(x=\infty \).

0.835

8561

24936

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

0.835

8562

1955

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

0.836

8563

18450

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

0.836

8564

21335

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

0.836

8565

2663

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

0.837

8566

5355

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

0.837

8567

5865

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

0.837

8568

1428

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

0.838

8569

1430

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

0.838

8570

3438

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

0.838

8571

5886

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

0.838

8572

9409

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

0.838

8573

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 \(x=0\).

0.838

8574

17138

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

0.838

8575

25402

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

0.838

8576

7135

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

0.839

8577

8586

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

0.839

8578

19219

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

0.839

8579

24105

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

0.839

8580

3148

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

0.840

8581

8588

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

0.840

8582

14064

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

0.840

8583

15760

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

0.840

8584

21738

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

0.840

8585

25342

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

0.840

8586

4000

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

0.841

8587

10884

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

0.841

8588

10886

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

0.841

8589

17897

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

0.841

8590

18388

\begin{align*} 9 \left (1-x \right ) x y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.841

8591

25487

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

0.841

8592

4600

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

0.842

8593

14920

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

0.842

8594

20122

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

0.842

8595

2723

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

0.844

8596

2736

\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}+2 x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{1}+10 x_{2}+2 x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= -1 \\ x_{2} \left (0\right ) &= -4 \\ x_{3} \left (0\right ) &= 13 \\ \end{align*}

0.844

8597

9077

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

0.844

8598

10959

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

0.844

8599

13041

\begin{align*} y^{\prime \prime \prime }-a^{2} \left ({y^{\prime }}^{5}+2 {y^{\prime }}^{3}+y^{\prime }\right )&=0 \\ \end{align*}

0.844

8600

15439

\begin{align*} a^{4} y+2 a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=8 \cos \left (a x \right ) \\ \end{align*}

0.844