2.3.58 Problems 5701 to 5800

Table 2.647: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

5701

12957

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

0.454

5702

14807

\(\left [\begin {array}{ccc} -2 & 5 & 5 \\ -1 & 4 & 5 \\ 3 & -3 & 2 \end {array}\right ]\)

N/A

N/A

N/A

0.454

5703

15306

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

0.454

5704

16759

\begin{align*} -2 y+y^{\prime }&=t^{3} \\ y \left (0\right ) &= 4 \\ \end{align*}
Using Laplace transform method.

0.454

5705

19881

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

0.454

5706

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*}

0.454

5707

22919

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

0.454

5708

22935

\begin{align*} x^{\prime }+x-5 y&=0 \\ y^{\prime }+4 x+5 y&=0 \\ \end{align*}

0.454

5709

1032

\begin{align*} x_{1}^{\prime }&=-2 x_{1}+17 x_{2}+4 x_{3} \\ x_{2}^{\prime }&=-x_{1}+6 x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{2}+2 x_{3} \\ \end{align*}

0.455

5710

4098

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

0.455

5711

4172

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

0.455

5712

4186

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

0.455

5713

15110

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

0.455

5714

15731

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

0.455

5715

16001

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

0.455

5716

22856

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

0.455

5717

23561

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

0.455

5718

24079

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

0.455

5719

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.

0.456

5720

4373

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

0.456

5721

4559

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

0.456

5722

6863

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

0.456

5723

16761

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

0.456

5724

17595

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

0.456

5725

18673

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

0.456

5726

19028

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

0.456

5727

22170

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

0.456

5728

23821

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

0.456

5729

23827

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

0.456

5730

25027

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

0.456

5731

449

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

0.457

5732

1415

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

0.457

5733

2620

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

0.457

5734

2833

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

0.457

5735

3856

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

0.457

5736

8476

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

0.457

5737

9599

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

0.457

5738

18671

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

0.457

5739

19657

\begin{align*} x^{\prime }&=4 x-2 y \\ y^{\prime }&=5 x+2 y \\ \end{align*}

0.457

5740

20584

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

0.457

5741

21747

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

0.457

5742

21901

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

0.457

5743

655

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

0.458

5744

977

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

0.458

5745

1021

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

0.458

5746

3582

\begin{align*} y^{\prime }&=\frac {1}{x^{{2}/{3}}} \\ \end{align*}

0.458

5747

6385

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

0.458

5748

8560

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

0.458

5749

14802

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

N/A

N/A

N/A

0.458

5750

16866

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

0.458

5751

1033

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

0.459

5752

1394

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

0.459

5753

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 \(x=0\).

0.459

5754

7950

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

0.459

5755

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*}

0.459

5756

12895

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

0.459

5757

14744

\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 \(x=0\).

0.459

5758

17642

\begin{align*} x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+70 y^{\prime } x +80 y&=\frac {1}{x^{13}} \\ \end{align*}

0.459

5759

22419

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

0.459

5760

25246

\begin{align*} t y^{\prime \prime }+2 y^{\prime }+9 t y&=0 \\ \end{align*}
Using Laplace transform method.

0.459

5761

1856

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

0.460

5762

2179

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }+12 y&=8 \cos \left (2 x \right )-16 \sin \left (2 x \right ) \\ \end{align*}

0.460

5763

2728

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

0.460

5764

6611

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

0.460

5765

8496

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

0.460

5766

20415

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

0.460

5767

21739

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

0.460

5768

23823

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

0.460

5769

25159

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

0.460

5770

979

\begin{align*} x_{1}^{\prime }&=7 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\ \end{align*}

0.461

5771

3884

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

0.461

5772

3926

\begin{align*} x_{1}^{\prime }&=10 x_{1}-8 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\ \end{align*}

0.461

5773

10623

\begin{align*} 9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y&=0 \\ \end{align*}

0.461

5774

14750

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

0.461

5775

21551

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

0.461

5776

22872

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

0.461

5777

1905

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

0.462

5778

2697

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

0.462

5779

9381

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

0.462

5780

9620

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=1+t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}
Using Laplace transform method.

0.462

5781

11688

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

0.462

5782

22196

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

0.462

5783

22706

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

0.462

5784

23689

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

0.462

5785

23809

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

0.462

5786

1863

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

0.463

5787

2468

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

0.463

5788

2734

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

0.463

5789

6549

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

0.463

5790

10771

\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}

0.463

5791

12777

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

0.463

5792

15145

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

0.463

5793

16059

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

0.463

5794

16937

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

0.463

5795

17001

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

0.463

5796

19034

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

0.463

5797

21649

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

0.463

5798

22916

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

0.463

5799

2060

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

0.464

5800

2461

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

0.464