2.3.29 Problems 2801 to 2900

Table 2.589: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

2801

14798

\(\left [\begin {array}{cc} -2 & 7 \\ 3 & 2 \end {array}\right ]\)

N/A

N/A

N/A

0.209

2802

18463

\begin{align*} x^{\prime \prime }&=\cos \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.209

2803

1045

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

0.210

2804

1061

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

0.210

2805

3799

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime }&=\sin \left (4 x \right ) \\ \end{align*}

0.210

2806

5391

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

0.210

2807

5398

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

0.210

2808

8071

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

0.210

2809

13148

\(\left [\begin {array}{cc} 19 & -10 \\ 21 & -10 \end {array}\right ]\)

N/A

N/A

N/A

0.210

2810

13164

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

N/A

N/A

N/A

0.210

2811

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.

0.210

2812

16580

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 y^{\prime } x +16 y&=0 \\ \end{align*}

0.210

2813

16593

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

0.210

2814

16667

\begin{align*} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}

0.210

2815

18459

\begin{align*} 2 x^{\prime }+6 x&=t \,{\mathrm e}^{-3 t} \\ x \left (0\right ) &= -{\frac {1}{2}} \\ \end{align*}
Using Laplace transform method.

0.210

2816

20008

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

0.210

2817

22513

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

0.210

2818

22889

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

0.210

2819

24688

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=16 x^{3}+20 x^{2} \\ \end{align*}

0.210

2820

414

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

0.211

2821

564

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

0.211

2822

1757

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

0.211

2823

5390

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

0.211

2824

10809

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

0.211

2825

11029

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

0.211

2826

14800

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

N/A

N/A

N/A

0.211

2827

16673

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

0.211

2828

17601

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

0.211

2829

19975

\begin{align*} {y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\ \end{align*}

0.211

2830

22823

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

0.211

2831

24524

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+4 y&=14 \\ \end{align*}

0.211

2832

1396

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

0.212

2833

2223

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

0.212

2834

3193

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

0.212

2835

6930

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

0.212

2836

6937

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

0.212

2837

9384

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

0.212

2838

17569

\begin{align*} 8 y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+66 y^{\prime \prime \prime }-41 y^{\prime \prime }-37 y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -14 \\ y^{\prime \prime }\left (0\right ) &= -14 \\ y^{\prime \prime \prime }\left (0\right ) &= 139 \\ y^{\prime \prime \prime \prime }\left (0\right ) &= -{\frac {29}{4}} \\ \end{align*}

0.212

2839

4380

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

0.213

2840

6927

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

0.213

2841

8130

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

0.213

2842

9716

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

0.213

2843

10283

\begin{align*} f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi &=0 \\ \end{align*}

0.213

2844

25241

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

0.213

2845

1047

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

0.214

2846

1050

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

0.214

2847

1758

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

0.214

2848

5386

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

0.214

2849

9527

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

0.214

2850

10683

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

0.214

2851

14359

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

0.214

2852

14796

\(\left [\begin {array}{cc} 3 & 2 \\ 6 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.214

2853

20352

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

0.214

2854

22247

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

0.214

2855

22795

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

0.214

2856

1048

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

0.215

2857

1484

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

0.215

2858

5393

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

0.215

2859

6300

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

0.215

2860

9022

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

0.215

2861

13165

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

N/A

N/A

N/A

0.215

2862

18049

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

0.215

2863

20381

\begin{align*} {y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\ \end{align*}

0.215

2864

22874

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

0.215

2865

24534

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }&=12 \\ \end{align*}

0.215

2866

24664

\begin{align*} y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y&=36 \,{\mathrm e}^{3 x} \\ \end{align*}

0.215

2867

25323

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

0.215

2868

3800

\begin{align*} y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y&=8 \,{\mathrm e}^{-x}+1 \\ \end{align*}

0.216

2869

6947

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

0.216

2870

10728

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

0.216

2871

13167

\(\left [\begin {array}{cc} 0 & -12 \\ 12 & 0 \end {array}\right ]\)

N/A

N/A

N/A

0.216

2872

14797

\(\left [\begin {array}{cc} 3 & 1 \\ 12 & 2 \end {array}\right ]\)

N/A

N/A

N/A

0.216

2873

14799

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

N/A

N/A

N/A

0.216

2874

17536

\begin{align*} 4 t^{2} y^{\prime \prime }+4 y^{\prime } t +\left (16 t^{2}-1\right ) y&=0 \\ \end{align*}

0.216

2875

18315

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

0.216

2876

20383

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

0.216

2877

24610

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

0.216

2878

3370

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

0.217

2879

5407

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

0.217

2880

7457

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

0.217

2881

7459

\begin{align*} \cos \left (\theta \right ) r^{\prime }-r \sin \left (\theta \right )+{\mathrm e}^{\theta }&=0 \\ \end{align*}

0.217

2882

10301

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

0.217

2883

10770

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

0.217

2884

10973

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

0.217

2885

11061

\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (4 x +1\right ) y^{\prime }-\left (49+27 x \right ) y&=0 \\ \end{align*}

0.217

2886

14822

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=36 t \,{\mathrm e}^{4 t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -6 \\ \end{align*}
Using Laplace transform method.

0.217

2887

15705

\begin{align*} y^{\prime \prime }-y^{\prime }+6 y&=-2 \sin \left (3 x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

0.217

2888

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.

0.217

2889

16461

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

0.217

2890

20490

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

0.217

2891

20667

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

0.217

2892

22762

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

0.217

2893

24530

\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime }&=11 \\ \end{align*}

0.217

2894

24531

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }&=12 \\ \end{align*}

0.217

2895

24633

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

0.217

2896

11169

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

0.218

2897

12754

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime \prime }+8 y^{\prime \prime } x +10 y^{\prime }-3+\frac {1}{x^{2}}-2 \ln \left (x \right )&=0 \\ \end{align*}

0.218

2898

14817

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=18 \,{\mathrm e}^{-t} \sin \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

0.218

2899

15248

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y&=8 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -3 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ \end{align*}
Using Laplace transform method.

0.218

2900

18458

\begin{align*} x^{\prime }-x&=\cos \left (t \right )-\sin \left (t \right ) \\ x \left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.218