2.3.67 Problems 6601 to 6700

Table 2.677: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

6601

24631

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

0.427

6602

24671

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

0.427

6603

24806

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

0.427

6604

1879

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

0.428

6605

3810

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

0.428

6606

3824

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

0.428

6607

3834

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

0.428

6608

3835

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

0.428

6609

4131

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

0.428

6610

6728

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

0.428

6611

8136

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

0.428

6612

8493

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

0.428

6613

9690

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

0.428

6614

11734

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

0.428

6615

15181

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

0.428

6616

18669

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

0.428

6617

19110

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

0.428

6618

19577

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

0.428

6619

21736

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

0.428

6620

23281

\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=0 \\ \end{align*}

0.428

6621

24624

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=36 x \,{\mathrm e}^{2 x} \\ \end{align*}

0.428

6622

24694

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

0.428

6623

7890

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

0.429

6624

8001

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

0.429

6625

8473

\begin{align*} x^{\prime }&=-\lambda _{1} x \\ y^{\prime }&=\lambda _{1} x-\lambda _{2} y \\ \end{align*}

0.429

6626

8843

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

0.429

6627

14991

\(\left [\begin {array}{cc} 2 & 2 \\ 0 & -4 \end {array}\right ]\)

N/A

N/A

N/A

0.429

6628

16824

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

0.429

6629

18661

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

0.429

6630

18699

\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=8 x \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -1 \\ \end{align*}

0.429

6631

20189

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

0.429

6632

21151

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

0.429

6633

21642

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

0.429

6634

22253

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

0.429

6635

22272

\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=9 x+y \\ \end{align*}

0.429

6636

24006

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

0.429

6637

24539

\begin{align*} 4 y+y^{\prime \prime }&=15 \,{\mathrm e}^{x}-8 x \\ \end{align*}

0.429

6638

24587

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

0.429

6639

25513

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

0.429

6640

478

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

0.430

6641

1863

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

0.430

6642

2237

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

0.430

6643

8901

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

0.430

6644

10402

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

0.430

6645

10516

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x +28 y&=0 \\ \end{align*}

0.430

6646

15033

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

0.430

6647

15730

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

0.430

6648

17851

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

0.430

6649

18265

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

0.430

6650

19645

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

0.430

6651

20517

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

0.430

6652

20941

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

0.430

6653

22737

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{x}+{\mathrm e}^{-x} \\ \end{align*}

0.430

6654

24748

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

0.430

6655

479

\begin{align*} 6 x^{2} y^{\prime \prime }+7 y^{\prime } x -\left (x^{2}+2\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.431

6656

1866

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

0.431

6657

1868

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

0.431

6658

2827

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

0.431

6659

3737

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

0.431

6660

6148

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

0.431

6661

6549

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

0.431

6662

6779

\begin{align*} \operatorname {A4} y+\operatorname {A3} x y^{\prime }+\operatorname {A2} \,x^{2} y^{\prime \prime }+\operatorname {A1} \,x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

0.431

6663

9172

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

0.431

6664

9377

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

0.431

6665

9697

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

0.431

6666

14949

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

0.431

6667

15053

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

0.431

6668

16511

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}

0.431

6669

17409

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

0.431

6670

18333

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

0.431

6671

18432

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

0.431

6672

18675

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

0.431

6673

18729

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

0.431

6674

19756

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

0.431

6675

24747

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

0.431

6676

152

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

0.432

6677

591

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

0.432

6678

1387

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

0.432

6679

3813

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

0.432

6680

6923

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

0.432

6681

7998

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

0.432

6682

9250

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \\ \end{align*}

0.432

6683

10949

\begin{align*} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\ \end{align*}

0.432

6684

15771

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

0.432

6685

18263

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=9 x^{2}-12 x +2 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

0.432

6686

18397

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

0.432

6687

20369

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

0.432

6688

21163

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

0.432

6689

24615

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=12 \,{\mathrm e}^{-2 x} x \\ \end{align*}

0.432

6690

1014

\begin{align*} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=-7 x_{1}+9 x_{2}+7 x_{3} \\ x_{3}^{\prime }&=2 x_{3} \\ \end{align*}

0.433

6691

3215

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

0.433

6692

7952

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

0.433

6693

8095

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

0.433

6694

16149

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

0.433

6695

23996

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

0.433

6696

24543

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

0.433

6697

25117

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

0.433

6698

875

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

0.434

6699

914

\begin{align*} x^{\prime \prime }+3 x^{\prime }+5 x&=-4 \cos \left (5 t \right ) \\ \end{align*}

0.434

6700

1923

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

0.434