2.3.27 Problems 2601 to 2700

Table 2.585: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

2601

22232

\begin{align*} y^{\prime \prime }-3 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}
Using Laplace transform method.

0.194

2602

24779

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

0.194

2603

24861

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

0.194

2604

2106

\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (-1\right ) &= -4 \\ y^{\prime }\left (-1\right ) &= -14 \\ y^{\prime \prime }\left (-1\right ) &= -20 \\ \end{align*}

0.195

2605

3685

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

0.195

2606

3798

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime }&=x^{2} \\ \end{align*}

0.195

2607

4471

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }-y&=44 \sin \left (3 x \right ) \\ \end{align*}

0.195

2608

6948

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

0.195

2609

7820

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

0.195

2610

7913

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

0.195

2611

8629

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= {\frac {81}{10}} \\ y^{\prime }\left (0\right ) &= {\frac {39}{10}} \\ \end{align*}
Using Laplace transform method.

0.195

2612

10856

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

0.195

2613

11177

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

0.195

2614

11191

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

0.195

2615

15206

\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+13 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -6 \\ \end{align*}
Using Laplace transform method.

0.195

2616

15209

\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= -24 \\ \end{align*}
Using Laplace transform method.

0.195

2617

16133

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

0.195

2618

22230

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

0.195

2619

4490

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

0.196

2620

5477

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

0.196

2621

10300

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

0.196

2622

11199

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

0.196

2623

13176

\(\left [\begin {array}{cc} 9 & -8 \\ 6 & -5 \end {array}\right ]\)

N/A

N/A

N/A

0.196

2624

13179

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

N/A

N/A

N/A

0.196

2625

17364

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=0 \\ \end{align*}

0.196

2626

18277

\begin{align*} y^{\prime \prime \prime \prime }-y&=8 \,{\mathrm e}^{x} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}

0.196

2627

18470

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

0.196

2628

1043

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

0.197

2629

6650

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

0.197

2630

8631

\begin{align*} y^{\prime \prime }+\frac {y}{25}&=\frac {t^{2}}{50} \\ y \left (0\right ) &= -25 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.197

2631

10745

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

0.197

2632

11156

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

0.197

2633

11193

\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \\ \end{align*}

0.197

2634

13178

\(\left [\begin {array}{cc} 6 & -10 \\ 2 & -3 \end {array}\right ]\)

N/A

N/A

N/A

0.197

2635

15249

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

0.197

2636

16582

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

0.197

2637

17366

\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=0 \\ \end{align*}

0.197

2638

17576

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+30 y^{\prime \prime }-56 y^{\prime }+49 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ y^{\prime \prime \prime }\left (0\right ) &= -1 \\ \end{align*}

0.197

2639

19623

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

0.197

2640

20533

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

0.197

2641

22838

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

0.197

2642

23518

\begin{align*} e i u^{\prime \prime \prime \prime }&=\cos \left (x \right ) \\ \end{align*}

0.197

2643

25080

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

0.197

2644

25085

\begin{align*} y^{\prime \prime }+4 y&=32 \cos \left (2 t \right ) t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

0.197

2645

8120

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

0.198

2646

11176

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

0.198

2647

13177

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

N/A

N/A

N/A

0.198

2648

14189

\begin{align*} y^{\prime }+8 y^{\prime \prime } x +4 x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}

0.198

2649

16583

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}

0.198

2650

16956

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

0.198

2651

17375

\begin{align*} 4 t^{2} y^{\prime \prime }+4 y^{\prime } t +\left (36 t^{2}-1\right ) y&=0 \\ \end{align*}

0.198

2652

22255

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

0.198

2653

24526

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

0.198

2654

3765

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=12 \,{\mathrm e}^{3 x} \\ \end{align*}

0.199

2655

4062

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

0.199

2656

6961

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

0.199

2657

7718

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

0.199

2658

12741

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

0.199

2659

17218

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

0.199

2660

17368

\begin{align*} y^{\prime \prime }+49 y&=0 \\ \end{align*}

0.199

2661

22837

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

0.199

2662

22849

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

0.199

2663

24069

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

0.199

2664

24527

\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+14 y^{\prime }-8 y&=2 \\ \end{align*}

0.199

2665

24924

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

0.199

2666

2441

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

0.200

2667

8109

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

0.200

2668

10673

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

0.200

2669

10800

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

0.200

2670

11039

\begin{align*} 16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \\ \end{align*}

0.200

2671

11685

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

0.200

2672

12829

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

0.200

2673

13145

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

N/A

N/A

N/A

0.200

2674

14872

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

0.200

2675

15328

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

0.200

2676

15400

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

0.200

2677

16151

\begin{align*} y^{\prime \prime }+16 y&=t \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.200

2678

17602

\begin{align*} y^{\left (6\right )}+y^{\prime \prime \prime \prime }&=-24 \\ \end{align*}

0.200

2679

20612

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

0.200

2680

22031

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

0.200

2681

22493

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

0.200

2682

24612

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

0.200

2683

25084

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

0.200

2684

7450

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

0.201

2685

7897

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

0.201

2686

8188

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

0.201

2687

8624

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 11 \\ y^{\prime }\left (0\right ) &= 28 \\ \end{align*}
Using Laplace transform method.

0.201

2688

10696

\begin{align*} x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y&=0 \\ \end{align*}

0.201

2689

11152

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

0.201

2690

14779

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

0.201

2691

19572

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

0.201

2692

19627

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=3 \sin \left (x \right ) {\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

0.201

2693

21890

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

0.201

2694

22250

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=3 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.201

2695

24649

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

0.201

2696

25079

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=50 \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

0.201

2697

1052

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

0.202

2698

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*}

0.202

2699

8127

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

0.202

2700

9402

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

0.202