2.3.49 Problems 4801 to 4900

Table 2.671: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

4801

14748

\begin{align*} \left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.381

4802

16029

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

With initial conditions

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

0.381

4803

18258

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

0.381

4804

18764

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

0.381

4805

19550

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

0.381

4806

20925

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

0.381

4807

21569

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

0.381

4808

21870

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

0.381

4809

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 \(x=1\).

0.381

4810

24469

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

0.381

4811

25060

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

Using Laplace transform method.

0.381

4812

25067

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

Using Laplace transform method.

0.381

4813

25910

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

0.381

4814

27189

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

0.381

4815

27574

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

0.381

4816

448

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

Series expansion around \(x=0\).

0.382

4817

10497

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

0.382

4818

15999

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

With initial conditions

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

0.382

4819

16824

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

Series expansion around \(x=0\).

0.382

4820

16850

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

Series expansion around \(x=0\).

0.382

4821

17740

\begin{align*} y^{\prime \prime }-10 y^{\prime }+34 y&=0 \\ \end{align*}

0.382

4822

20883

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

Series expansion around \(x=0\).

0.382

4823

22231

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

Using Laplace transform method.

0.382

4824

23692

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

Series expansion around \(x=0\).

0.382

4825

24079

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

Series expansion around \(x=0\).

0.382

4826

25164

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

0.382

4827

25238

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

Using Laplace transform method.

0.382

4828

26713

\begin{align*} y^{\prime \prime }-y \,{\mathrm e}^{x}&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.382

4829

393

\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*}

0.383

4830

1074

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.383

4831

2615

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

Series expansion around \(t=0\).

0.383

4832

7049

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

0.383

4833

7233

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

0.383

4834

21206

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

0.383

4835

21537

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

0.383

4836

23364

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

0.383

4837

27116

\(\left [\begin {array}{ccc} -2 & 0 & 1 \\ 1 & 1 & 0 \\ 0 & 0 & -2 \end {array}\right ]\)

N/A

N/A

N/A

0.383

4838

27678

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

0.383

4839

573

\begin{align*} x^{\prime \prime }+6 x^{\prime }+9 x&=f \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.384

4840

1382

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

Series expansion around \(x=0\).

0.384

4841

3929

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

Using Laplace transform method.

0.384

4842

7460

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

0.384

4843

21705

\begin{align*} y^{\prime }-5 y&={\mathrm e}^{5 t} \\ y \left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.384

4844

23061

\begin{align*} \sin \left (\theta \right )^{2} r^{\prime }&=-b \cos \left (\theta \right ) \\ \end{align*}

0.384

4845

27780

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

Series expansion around \(x=0\).

0.384

4846

385

\begin{align*} x^{\prime \prime }+100 x&=225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \\ x \left (0\right ) &= 375 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.385

4847

450

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

Series expansion around \(x=0\).

0.385

4848

901

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

0.385

4849

2230

\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=x \left (x +1\right ) \\ y \left (-1\right ) &= -6 \\ y^{\prime }\left (-1\right ) &= {\frac {43}{6}} \\ y^{\prime \prime }\left (-1\right ) &= -{\frac {5}{2}} \\ \end{align*}

0.385

4850

3175

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

0.385

4851

3581

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

0.385

4852

7335

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

0.385

4853

8566

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

Series expansion around \(x=0\).

0.385

4854

9652

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

Using Laplace transform method.

0.385

4855

10052

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

0.385

4856

10362

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

0.385

4857

10470

\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\ \end{align*}

0.385

4858

11068

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y&=0 \\ \end{align*}

0.385

4859

16170

\begin{align*} 1&=x^{2}-9 y^{\prime } \\ \end{align*}

0.385

4860

17384

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

0.385

4861

18755

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

0.385

4862

18882

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

0.385

4863

19623

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

Using Laplace transform method.

0.385

4864

20089

\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=20 x \\ \end{align*}

0.385

4865

25639

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

Using Laplace transform method.

0.385

4866

25640

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

Using Laplace transform method.

0.385

4867

522

\begin{align*} 16 x^{2} y^{\prime \prime }-\left (-144 x^{3}+5\right ) y&=0 \\ \end{align*}

0.386

4868

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*}

0.386

4869

3854

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

0.386

4870

8480

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

Series expansion around \(x=0\).

0.386

4871

10501

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

0.386

4872

10943

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

0.386

4873

15475

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

0.386

4874

15752

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

0.386

4875

16961

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

0.386

4876

23589

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

0.386

4877

27734

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

0.386

4878

3883

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

0.387

4879

7075

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=12 \,{\mathrm e}^{x} \\ \end{align*}

0.387

4880

10648

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y&=0 \\ \end{align*}

0.387

4881

15743

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

N/A

N/A

N/A

0.387

4882

17416

\begin{align*} y^{\prime \prime }+6 y^{\prime }+2 y&=0 \\ \end{align*}

0.387

4883

18318

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

0.387

4884

23591

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

0.387

4885

23610

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

0.387

4886

403

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

Series expansion around \(x=0\).

0.388

4887

2253

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

0.388

4888

2386

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

0.388

4889

2676

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.388

4890

3930

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

Using Laplace transform method.

0.388

4891

3985

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

Series expansion around \(x=0\).

0.388

4892

7943

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

0.388

4893

8554

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

Series expansion around \(x=0\).

0.388

4894

10551

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

0.388

4895

16023

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

With initial conditions

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

0.388

4896

16401

\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 15 \\ \end{align*}

0.388

4897

16728

\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }+y&=0 \\ \end{align*}

0.388

4898

18360

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

0.388

4899

18779

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

0.388

4900

19023

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

0.388