2.3.67 Problems 6601 to 6700

Table 2.683: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

6601

14600

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

0.503

6602

15702

\begin{align*} y^{\prime }-y&=2 \,{\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.503

6603

16079

\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=3 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.503

6604

16625

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\left (12 x -4\right ) {\mathrm e}^{-5 x} \\ \end{align*}

0.503

6605

17806

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

0.503

6606

18128

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

0.503

6607

19637

\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=3 x+y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 5 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.503

6608

20885

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

0.503

6609

22139

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

0.503

6610

26347

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

0.503

6611

918

\begin{align*} x^{\prime \prime }+6 x^{\prime }+13 x&=10 \sin \left (5 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.504

6612

1448

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

0.504

6613

1915

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

0.504

6614

1933

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

0.504

6615

2015

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

0.504

6616

2050

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.504

6617

2258

\begin{align*} y_{1}^{\prime }&=-10 y_{1}+9 y_{2} \\ y_{2}^{\prime }&=-4 y_{1}+2 y_{2} \\ \end{align*}

0.504

6618

3407

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

0.504

6619

3710

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=18 \,{\mathrm e}^{5 x} \\ \end{align*}

0.504

6620

5898

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

0.504

6621

6238

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

0.504

6622

6285

\begin{align*} a y-x^{5} y^{\prime }+x^{6} y^{\prime \prime }&=0 \\ \end{align*}

0.504

6623

7260

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

0.504

6624

8493

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

0.504

6625

8909

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

0.504

6626

9683

\begin{align*} x^{\prime }&=\frac {x}{2} \\ y^{\prime }&=x-\frac {y}{2} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 5 \\ \end{align*}

0.504

6627

11290

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

0.504

6628

14321

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

0.504

6629

14572

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

0.504

6630

14860

\begin{align*} x^{\prime }&=x+7 y \\ y^{\prime }&=3 x+5 y \\ \end{align*}

0.504

6631

14917

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

0.504

6632

14920

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

0.504

6633

14924

\begin{align*} 2 z^{\prime \prime }+7 z^{\prime }-4 z&=0 \\ z \left (0\right ) &= 0 \\ z^{\prime }\left (0\right ) &= 9 \\ \end{align*}

0.504

6634

14939

\begin{align*} x^{\prime \prime }+2 x^{\prime }+10 x&={\mathrm e}^{-t} \\ \end{align*}

0.504

6635

16086

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&={\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.504

6636

17756

\begin{align*} y^{\prime \prime }+9 y^{\prime }+20 y&=-2 \,{\mathrm e}^{t} t \\ \end{align*}

0.504

6637

18782

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

0.504

6638

22141

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

0.504

6639

22186

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

0.504

6640

1358

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

0.505

6641

1881

\begin{align*} \left (-2 x^{3}+1\right ) y^{\prime \prime }-10 x^{2} y^{\prime }-8 y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.505

6642

1884

\begin{align*} \left (-x^{3}+1\right ) y^{\prime \prime }+15 x^{2} y^{\prime }-36 y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.505

6643

3179

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

0.505

6644

3335

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

0.505

6645

3690

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

0.505

6646

6712

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

0.505

6647

8913

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

0.505

6648

14927

\begin{align*} 4 x^{\prime \prime }-20 x^{\prime }+21 x&=0 \\ x \left (0\right ) &= -4 \\ x^{\prime }\left (0\right ) &= -12 \\ \end{align*}

0.505

6649

15714

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

0.505

6650

21217

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

0.505

6651

21704

\begin{align*} y^{\prime }-5 y&=0 \\ y \left (\pi \right ) &= 2 \\ \end{align*}
Using Laplace transform method.

0.505

6652

26014

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

0.505

6653

26196

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

0.505

6654

1411

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

0.506

6655

1893

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

0.506

6656

2040

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }+\left (12 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.506

6657

2560

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

0.506

6658

3343

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

0.506

6659

3953

\begin{align*} y^{\prime \prime }+9 y&=7 \sin \left (4 t \right )+14 \cos \left (4 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

0.506

6660

4510

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

0.506

6661

9992

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

0.506

6662

15002

\begin{align*} x^{\prime }&=11 x-2 y \\ y^{\prime }&=3 x+4 y \\ \end{align*}

0.506

6663

15471

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

0.506

6664

16008

\begin{align*} x^{\prime }&=2 x+2 y \\ y^{\prime }&=-4 x+6 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.506

6665

16187

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

0.506

6666

17863

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

0.506

6667

19590

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

0.506

6668

22764

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+y^{\prime } x -y&=1 \\ \end{align*}

0.506

6669

23043

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

0.506

6670

23077

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

0.506

6671

24029

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

0.506

6672

24469

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

0.506

6673

4

\begin{align*} y^{\prime }&=\frac {1}{x^{2}} \\ y \left (1\right ) &= 5 \\ \end{align*}

0.507

6674

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*}

0.507

6675

2782

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

0.507

6676

5425

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

0.507

6677

5811

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

0.507

6678

5871

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

0.507

6679

6398

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

0.507

6680

8815

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

0.507

6681

9502

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

0.507

6682

15073

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

0.507

6683

16186

\begin{align*} y^{\prime }&=3 \sqrt {x +3} \\ y \left (1\right ) &= 20 \\ \end{align*}

0.507

6684

16864

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

0.507

6685

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*}

0.507

6686

22832

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

0.507

6687

24774

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

0.507

6688

24775

\begin{align*} x^{2} {y^{\prime }}^{2}-7 y y^{\prime } x +12 y^{2}&=0 \\ \end{align*}

0.507

6689

25369

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

0.507

6690

25586

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

0.507

6691

26566

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

0.507

6692

462

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

0.508

6693

1395

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

0.508

6694

2033

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

0.508

6695

2055

\begin{align*} 9 \left (x +3\right ) x^{2} y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (4 x +3\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.508

6696

4129

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

0.508

6697

4377

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

0.508

6698

6032

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

0.508

6699

7593

\begin{align*} 3 y^{\prime \prime }+11 y^{\prime }-7 y&=0 \\ \end{align*}

0.508

6700

8813

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

0.508