2.3.66 Problems 6501 to 6600

Table 2.675: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

6501

15085

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

0.420

6502

20542

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

0.420

6503

20848

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=5+10 \sin \left (2 x \right ) \\ \end{align*}

0.420

6504

22281

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=9 x \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}

0.420

6505

25625

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

0.420

6506

1856

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +20 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.421

6507

2412

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

0.421

6508

2569

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

0.421

6509

3826

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

0.421

6510

8490

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

0.421

6511

9465

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

0.421

6512

9616

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

0.421

6513

16525

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

0.421

6514

16622

\begin{align*} y^{\prime \prime }+9 y&=54 x^{2} {\mathrm e}^{3 x} \\ \end{align*}

0.421

6515

16638

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

0.421

6516

18659

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

0.421

6517

18824

\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=16 \,{\mathrm e}^{\frac {t}{2}} \\ \end{align*}

0.421

6518

19058

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

0.421

6519

19502

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

0.421

6520

20894

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

0.421

6521

24773

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

0.421

6522

1806

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {4}{1+{\mathrm e}^{-x}} \\ \end{align*}

0.422

6523

1929

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

0.422

6524

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 \(x=0\).

0.422

6525

8577

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= {\frac {15}{8}} \\ \end{align*}
Series expansion around \(x=0\).

0.422

6526

9258

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

0.422

6527

18327

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

0.422

6528

18819

\begin{align*} y^{\prime \prime }+9 y&=t^{2} {\mathrm e}^{3 t}+6 \\ \end{align*}

0.422

6529

19843

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

0.422

6530

21558

\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y&=4 \ln \left (x \right ) \\ \end{align*}

0.422

6531

21591

\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&={\mathrm e}^{x} x^{2} \\ \end{align*}

0.422

6532

25114

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

0.422

6533

1406

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

0.423

6534

2266

\begin{align*} y_{1}^{\prime }&=15 y_{1}-9 y_{2} \\ y_{2}^{\prime }&=16 y_{1}-9 y_{2} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= 5 \\ y_{2} \left (0\right ) &= 8 \\ \end{align*}

0.423

6535

9448

\begin{align*} y^{\prime \prime }+3 y^{\prime }-5 y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.423

6536

12843

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

0.423

6537

15700

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x}-3 x^{2} \\ \end{align*}
Using Laplace transform method.

0.423

6538

17438

\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=32 t \\ \end{align*}

0.423

6539

19894

\begin{align*} v^{\prime \prime }+\frac {2 v^{\prime }}{r}&=0 \\ \end{align*}

0.423

6540

23318

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

0.423

6541

24597

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

0.423

6542

24783

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

0.423

6543

232

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

0.424

6544

495

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

0.424

6545

3233

\begin{align*} 3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 y^{\prime } x +10 y&=\frac {4}{x^{2}} \\ \end{align*}

0.424

6546

3717

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

0.424

6547

7621

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -{\frac {17}{2}} \\ \end{align*}

0.424

6548

7632

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

0.424

6549

8285

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

0.424

6550

8849

\begin{align*} x_{1}^{\prime }&=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-9 x_{2} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}

0.424

6551

9168

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

0.424

6552

9280

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

0.424

6553

12360

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

0.424

6554

15575

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

0.424

6555

15752

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

0.424

6556

16000

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

0.424

6557

17994

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

0.424

6558

18660

\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=3 x-2 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 5 \\ \end{align*}

0.424

6559

18823

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

0.424

6560

20440

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

0.424

6561

21883

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y+8 \,{\mathrm e}^{-x}+3 x&=0 \\ \end{align*}

0.424

6562

2224

\begin{align*} 16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 y^{\prime } x +9 y&=96 x^{{5}/{2}} \\ \end{align*}

0.425

6563

3797

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=4 \,{\mathrm e}^{-2 x} \\ \end{align*}

0.425

6564

3809

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

0.425

6565

3811

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

0.425

6566

6931

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

0.425

6567

8797

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

0.425

6568

10400

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

0.425

6569

12550

\begin{align*} \left (3 x -1\right )^{2} y^{\prime \prime }+3 \left (3 x -1\right ) y^{\prime }-9 y-\ln \left (3 x -1\right )^{2}&=0 \\ \end{align*}

0.425

6570

15973

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

0.425

6571

16024

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

0.425

6572

16554

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

0.425

6573

18816

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

0.425

6574

19495

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

0.425

6575

21774

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

0.425

6576

2571

\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 2 \\ \end{align*}

0.426

6577

6128

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

0.426

6578

7277

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

0.426

6579

8963

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

0.426

6580

13150

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

N/A

N/A

N/A

0.426

6581

15242

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=3 \delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.426

6582

16835

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

0.426

6583

18243

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

0.426

6584

18293

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

0.426

6585

18862

\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=16 \,{\mathrm e}^{\frac {t}{2}} \\ \end{align*}

0.426

6586

21725

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

0.426

6587

24588

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

0.426

6588

25083

\begin{align*} y^{\prime \prime }+9 y&=36 t \sin \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

0.426

6589

25120

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

0.426

6590

1289

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

0.427

6591

3111

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

0.427

6592

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 \(x=0\).

0.427

6593

4133

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

0.427

6594

6095

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

0.427

6595

6107

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

0.427

6596

11288

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

0.427

6597

14637

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=3 \,{\mathrm e}^{x} x^{2}-7 \,{\mathrm e}^{x} \\ \end{align*}

0.427

6598

19880

\begin{align*} z^{\prime }+7 y-3 z&=0 \\ 7 y^{\prime }+63 y-36 z&=0 \\ \end{align*}

0.427

6599

20206

\begin{align*} x^{\prime }-7 x+y&=0 \\ y^{\prime }-2 x-5 y&=0 \\ \end{align*}

0.427

6600

23389

\begin{align*} 2 x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y&=0 \\ \end{align*}

0.427