2.3.28 Problems 2701 to 2800

Table 2.587: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

2701

11269

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

0.202

2702

13149

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

N/A

N/A

N/A

0.202

2703

14060

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

0.202

2704

18471

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

0.202

2705

19630

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

0.202

2706

22822

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

0.202

2707

4002

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

0.203

2708

8143

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

0.203

2709

10621

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

0.203

2710

10841

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

0.203

2711

10853

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

0.203

2712

11013

\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*}

0.203

2713

17735

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

0.203

2714

20374

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y&=16 x^{2}+256 \\ \end{align*}

0.203

2715

21960

\begin{align*} b^{\left (7\right )}&=3 p \\ \end{align*}

0.203

2716

22233

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

0.203

2717

24040

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

0.203

2718

24684

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

0.203

2719

532

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

0.204

2720

1053

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

0.204

2721

2198

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=12 \,{\mathrm e}^{-x}+9 \cos \left (2 x \right )-13 \sin \left (2 x \right ) \\ \end{align*}

0.204

2722

2221

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

0.204

2723

3693

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

0.204

2724

4369

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

0.204

2725

6875

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

0.204

2726

9307

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

0.204

2727

9600

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

0.204

2728

9978

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

0.204

2729

10616

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

0.204

2730

10659

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

0.204

2731

11015

\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y&=0 \\ \end{align*}

0.204

2732

11079

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

0.204

2733

11108

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

0.204

2734

14795

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

N/A

N/A

N/A

0.204

2735

15208

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 5 \\ y^{\prime \prime }\left (0\right ) &= -20 \\ \end{align*}
Using Laplace transform method.

0.204

2736

16055

\(\left [\begin {array}{cc} 1 & 0 \\ 2 & 3 \end {array}\right ]\)

N/A

N/A

N/A

0.204

2737

17532

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

0.204

2738

17598

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }-11 y^{\prime }+30 y&={\mathrm e}^{4 t} \\ \end{align*}

0.204

2739

17599

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-10 y^{\prime }-24 y&={\mathrm e}^{-3 t} \\ \end{align*}

0.204

2740

19190

\begin{align*} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{x} \left (x +1\right ) \\ \end{align*}

0.204

2741

24528

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

0.204

2742

169

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

0.205

2743

10861

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

0.205

2744

11031

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

0.205

2745

13143

\(\left [\begin {array}{cc} 6 & -4 \\ 3 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.205

2746

15740

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

N/A

N/A

N/A

0.205

2747

17582

\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=1 \\ \end{align*}

0.205

2748

20197

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

0.205

2749

21205

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

0.205

2750

22262

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

0.205

2751

24523

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

0.205

2752

24553

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

0.205

2753

24650

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

0.205

2754

2174

\begin{align*} y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y&={\mathrm e}^{2 x} \left (-5 x^{2}-8 x +3\right ) \\ \end{align*}

0.206

2755

4493

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=12 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{3 x} \\ \end{align*}

0.206

2756

7881

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

0.206

2757

8763

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

0.206

2758

9029

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

0.206

2759

10578

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

0.206

2760

10836

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

0.206

2761

10859

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

0.206

2762

17600

\begin{align*} y^{\prime \prime \prime }-13 y^{\prime }+12 y&=\cos \left (t \right ) \\ \end{align*}

0.206

2763

20487

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

0.206

2764

23999

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=x^{4} {\mathrm e}^{2 x} \\ \end{align*}

0.206

2765

339

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

0.207

2766

1051

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

0.207

2767

8073

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

0.207

2768

12712

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

0.207

2769

13142

\(\left [\begin {array}{cc} 10 & -9 \\ 6 & -5 \end {array}\right ]\)

N/A

N/A

N/A

0.207

2770

14996

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

N/A

N/A

N/A

0.207

2771

15064

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

0.207

2772

15221

\begin{align*} y^{\prime \prime }+8 y^{\prime }+20 y&=\sin \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}
Using Laplace transform method.

0.207

2773

16755

\begin{align*} y^{\left (6\right )}-64 y&={\mathrm e}^{-2 x} \\ \end{align*}

0.207

2774

17993

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

0.207

2775

22824

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

0.207

2776

23094

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

0.207

2777

23386

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

0.207

2778

24682

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

0.207

2779

4463

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

0.208

2780

10747

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

0.208

2781

10762

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

0.208

2782

10988

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

0.208

2783

11016

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \\ \end{align*}

0.208

2784

11208

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

0.208

2785

14771

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

0.208

2786

16052

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

N/A

N/A

N/A

0.208

2787

16314

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

0.208

2788

18297

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

0.208

2789

18899

\begin{align*} y^{\prime \prime }-8 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

0.208

2790

19579

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

0.208

2791

20130

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

0.208

2792

20386

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

0.208

2793

21289

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

0.208

2794

533

\begin{align*} x^{\prime \prime }+8 x^{\prime }+15 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= -3 \\ \end{align*}
Using Laplace transform method.

0.209

2795

1485

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

0.209

2796

2418

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

0.209

2797

6962

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

0.209

2798

7728

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

0.209

2799

10931

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

0.209

2800

11059

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \\ \end{align*}

0.209