2.3.49 Problems 4801 to 4900

Table 2.629: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

4801

7979

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}

0.257

4802

8023

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

0.257

4803

8481

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

0.257

4804

9130

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

0.257

4805

10231

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

0.257

4806

10331

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

0.257

4807

10475

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

0.257

4808

10597

\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \\ \end{align*}

0.257

4809

10709

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

0.257

4810

10772

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

0.257

4811

11025

\begin{align*} 4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}

0.257

4812

13145

\(\left [\begin {array}{cc} 7 & -6 \\ 12 & -10 \end {array}\right ]\)

N/A

N/A

N/A

0.257

4813

13177

\(\left [\begin {array}{cc} 10 & -6 \\ 12 & -7 \end {array}\right ]\)

N/A

N/A

N/A

0.257

4814

15831

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

0.257

4815

18049

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

0.257

4816

20157

\begin{align*} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 y^{\prime } x +4 y&=\frac {2}{x^{3}} \\ \end{align*}

0.257

4817

22820

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=6 \delta \left (t -2\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.257

4818

23791

\begin{align*} x^{\prime }&=5 x-6 y \\ y^{\prime }&=6 x-7 y \\ \end{align*}

0.257

4819

423

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

0.258

4820

767

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

0.258

4821

1452

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

0.258

4822

2194

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

0.258

4823

3340

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

0.258

4824

6876

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

0.258

4825

7049

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

0.258

4826

9221

\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}

0.258

4827

10777

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

0.258

4828

13179

\(\left [\begin {array}{cc} 11 & -15 \\ 6 & -8 \end {array}\right ]\)

N/A

N/A

N/A

0.258

4829

14131

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

0.258

4830

14991

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

N/A

N/A

N/A

0.258

4831

17018

\begin{align*} y^{\prime \prime }-6 y^{\prime }+45 y&=0 \\ \end{align*}

0.258

4832

19624

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

0.258

4833

21963

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

0.258

4834

23704

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

0.258

4835

23928

\begin{align*} 6 y^{\prime \prime }+11 y^{\prime }+4 y&=2 \\ \end{align*}

0.258

4836

24470

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

0.258

4837

24694

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

0.258

4838

241

\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align*}

0.259

4839

437

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

0.259

4840

1282

\begin{align*} y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4}&=0 \\ \end{align*}

0.259

4841

6696

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

0.259

4842

8116

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

0.259

4843

9738

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

0.259

4844

10493

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

0.259

4845

10688

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

0.259

4846

10815

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

0.259

4847

10889

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

0.259

4848

13149

\(\left [\begin {array}{cc} 13 & -15 \\ 6 & -6 \end {array}\right ]\)

N/A

N/A

N/A

0.259

4849

14996

\(\left [\begin {array}{cc} 6 & 0 \\ 0 & -13 \end {array}\right ]\)

N/A

N/A

N/A

0.259

4850

16516

\begin{align*} 9 y^{\prime \prime }+18 y^{\prime }+10 y&=0 \\ \end{align*}

0.259

4851

16989

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

0.259

4852

18133

\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+5 y&=0 \\ \end{align*}

0.259

4853

18683

\begin{align*} i^{\prime }&=\frac {i}{2}-\frac {v}{8} \\ v^{\prime }&=2 i-\frac {v}{2} \\ \end{align*}

0.259

4854

20419

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

0.259

4855

22096

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

0.259

4856

23708

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

0.259

4857

23714

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

0.259

4858

23771

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

0.259

4859

24047

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

0.259

4860

366

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

0.260

4861

1054

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

0.260

4862

1310

\begin{align*} 16 y^{\prime \prime }+24 y^{\prime }+9 y&=0 \\ \end{align*}

0.260

4863

2387

\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}

0.260

4864

5392

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

0.260

4865

5494

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

0.260

4866

5778

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

0.260

4867

5793

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}

0.260

4868

6770

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

0.260

4869

6867

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

0.260

4870

8627

\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=29 \cos \left (2 t \right ) \\ y \left (0\right ) &= {\frac {16}{5}} \\ y^{\prime }\left (0\right ) &= {\frac {31}{5}} \\ \end{align*}
Using Laplace transform method.

0.260

4871

8790

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

0.260

4872

8902

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

0.260

4873

9061

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

0.260

4874

10481

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

0.260

4875

10561

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

0.260

4876

10670

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

0.260

4877

10679

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

0.260

4878

10702

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

0.260

4879

10757

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

0.260

4880

10892

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

0.260

4881

10953

\begin{align*} x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \\ \end{align*}

0.260

4882

10956

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

0.260

4883

10976

\begin{align*} x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (4 x +3\right ) y&=0 \\ \end{align*}

0.260

4884

12738

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

0.260

4885

13141

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

N/A

N/A

N/A

0.260

4886

14399

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

0.260

4887

16336

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

0.260

4888

17699

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

0.260

4889

19572

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

0.260

4890

20046

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

0.260

4891

20916

\begin{align*} y^{\prime \prime }-3 y^{\prime }-4 y&=t^{2} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.260

4892

23062

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

0.260

4893

23109

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

0.260

4894

23695

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

0.260

4895

25549

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

0.260

4896

435

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

0.261

4897

4160

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

0.261

4898

4750

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

0.261

4899

7565

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

0.261

4900

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*}

0.261