2.3.67 Problems 6601 to 6700

Table 2.665: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

6601

16637

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=8 \,{\mathrm e}^{-3 x} \\ \end{align*}

0.339

6602

17436

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

0.339

6603

18097

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

0.339

6604

18692

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

0.339

6605

24753

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

0.339

6606

1416

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

0.340

6607

3502

\begin{align*} z y^{\prime \prime }-2 y^{\prime }+9 z^{5} y&=0 \\ \end{align*}
Series expansion around \(z=0\).

0.340

6608

8572

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

0.340

6609

8573

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

0.340

6610

9690

\begin{align*} x^{\prime }&=12 x-9 y \\ y^{\prime }&=4 x \\ \end{align*}

0.340

6611

10590

\begin{align*} 9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y&=0 \\ \end{align*}

0.340

6612

10784

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

0.340

6613

14975

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

0.340

6614

15011

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

0.340

6615

15707

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

0.340

6616

20401

\begin{align*} 3 {y^{\prime }}^{5}-y^{\prime } y+1&=0 \\ \end{align*}

0.340

6617

21299

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

0.340

6618

24798

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

0.340

6619

3717

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

0.341

6620

3741

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

0.341

6621

7721

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

0.341

6622

8105

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

0.341

6623

8112

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

0.341

6624

9235

\begin{align*} y^{\prime \prime }+8 y^{\prime }-9 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}

0.341

6625

10792

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

0.341

6626

12934

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

0.341

6627

15515

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

0.341

6628

18650

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

0.341

6629

18662

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

0.341

6630

22615

\begin{align*} s^{\prime \prime }+b s^{\prime }+\omega ^{2} s&=0 \\ \end{align*}

0.341

6631

23514

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

0.341

6632

24029

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

0.341

6633

24626

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

0.341

6634

24862

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

0.341

6635

25113

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=7 \,{\mathrm e}^{2 t} \\ \end{align*}

0.341

6636

901

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

0.342

6637

1012

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

0.342

6638

1096

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

0.342

6639

2423

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

0.342

6640

2699

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

0.342

6641

3737

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=40 \sin \left (x \right )^{2} \\ \end{align*}

0.342

6642

3893

\begin{align*} x_{1}^{\prime }&=9 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=5 x_{1}-2 x_{2} \\ \end{align*}

0.342

6643

4526

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=\delta \left (t -2\right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.342

6644

4527

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

0.342

6645

6317

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

0.342

6646

9457

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

0.342

6647

10523

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

0.342

6648

10555

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*}

0.342

6649

10780

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

0.342

6650

10786

\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \\ \end{align*}

0.342

6651

14729

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

0.342

6652

15228

\begin{align*} y^{\prime \prime }+9 y&=24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.342

6653

17399

\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

0.342

6654

19025

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

0.342

6655

19028

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

0.342

6656

21641

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

0.342

6657

21727

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

0.342

6658

22195

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

0.342

6659

23066

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

0.342

6660

24082

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +56 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.342

6661

24083

\begin{align*} 4 \left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +3 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.342

6662

24697

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=24 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \\ \end{align*}

0.342

6663

24869

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

0.342

6664

25234

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

0.342

6665

25575

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

0.342

6666

446

\begin{align*} \left (4 x^{2}+16 x +17\right ) y^{\prime \prime }&=8 y \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= 0 \\ \end{align*}
Series expansion around \(x=-2\).

0.343

6667

1258

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

0.343

6668

1458

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

0.343

6669

2253

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

0.343

6670

3718

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

0.343

6671

8486

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

0.343

6672

12507

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

0.343

6673

16704

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

0.343

6674

20783

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

0.343

6675

21483

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

0.343

6676

22833

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

0.343

6677

24719

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

0.343

6678

444

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

0.344

6679

1633

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

0.344

6680

3796

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=4 \,{\mathrm e}^{-3 x} \\ \end{align*}

0.344

6681

14997

\(\left [\begin {array}{cc} 4 & -2 \\ 1 & 2 \end {array}\right ]\)

N/A

N/A

N/A

0.344

6682

15009

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

0.344

6683

15388

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

0.344

6684

22197

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

0.344

6685

22802

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

0.344

6686

22847

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

0.344

6687

23035

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

0.344

6688

23068

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

0.344

6689

23454

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2}+3 \\ \end{align*}

0.344

6690

325

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

0.345

6691

334

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

0.345

6692

880

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

0.345

6693

2255

\begin{align*} y_{1}^{\prime }&=-7 y_{1}+4 y_{2} \\ y_{2}^{\prime }&=-y_{1}-11 y_{2} \\ \end{align*}

0.345

6694

2396

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

0.345

6695

2426

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

0.345

6696

2549

\begin{align*} 2 y^{\prime \prime }+y^{\prime }-10 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}

0.345

6697

5509

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

0.345

6698

6440

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

0.345

6699

7281

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

0.345

6700

9463

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

0.345