2.3.108 Problems 10701 to 10800

Table 2.747: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10701

15102

\begin{align*} x^{\prime \prime }+10 x^{\prime }+25 x&=2^{t}+t \,{\mathrm e}^{-5 t} \\ \end{align*}

0.565

10702

18288

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right ) \\ y \left (\infty \right ) &= 0 \\ \end{align*}

0.565

10703

18826

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

0.565

10704

19635

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

0.565

10705

21546

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

0.565

10706

22888

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

0.565

10707

25313

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

0.565

10708

3

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

0.566

10709

640

\begin{align*} x_{1}^{\prime }&=5 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }&=3 x_{1}+x_{2}+5 x_{3} \\ \end{align*}

0.566

10710

1021

\begin{align*} x_{1}^{\prime }&=x_{3} \\ x_{2}^{\prime }&=-5 x_{1}-x_{2}-5 x_{3} \\ x_{3}^{\prime }&=4 x_{1}+x_{2}-2 x_{3} \\ \end{align*}

0.566

10711

1982

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

0.566

10712

2286

\begin{align*} y_{1}^{\prime }&=-11 y_{1}+4 y_{2} \\ y_{2}^{\prime }&=-26 y_{1}+9 y_{2} \\ \end{align*}

0.566

10713

2742

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

0.566

10714

3914

\begin{align*} x_{1}^{\prime }&=-6 x_{1}+x_{2}+1 \\ x_{2}^{\prime }&=6 x_{1}-5 x_{2}+{\mathrm e}^{-t} \\ \end{align*}

0.566

10715

4578

\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-x_{2}+35 \,{\mathrm e}^{t} t^{{3}/{2}} \\ \end{align*}

0.566

10716

5910

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

0.566

10717

7132

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

0.566

10718

8999

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

0.566

10719

16249

\begin{align*} y^{\prime }-2 y&=-10 \\ y \left (0\right ) &= 8 \\ \end{align*}

0.566

10720

18988

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

0.566

10721

20345

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

0.566

10722

24818

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

0.566

10723

2589

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

0.567

10724

9841

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

0.567

10725

12360

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

0.567

10726

19623

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

0.567

10727

565

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

0.568

10728

1404

\begin{align*} x_{1}^{\prime }&=2 x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=\frac {9 x_{1}}{5}-x_{2} \\ \end{align*}

0.568

10729

6107

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

0.568

10730

8280

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

0.568

10731

8394

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

0.568

10732

9241

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

0.568

10733

10369

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

0.568

10734

10962

\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}

0.568

10735

19479

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

0.568

10736

24771

\begin{align*} 3 v^{\prime }+2 v+w^{\prime }-6 w&=5 \,{\mathrm e}^{x} \\ 4 v^{\prime }+2 v+w^{\prime }-8 w&=5 \,{\mathrm e}^{x}+2 x -3 \\ \end{align*}

0.568

10737

1794

\begin{align*} y^{\prime }+y^{2}+8 y+7&=0 \\ \end{align*}

0.569

10738

2561

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

0.569

10739

3122

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

0.569

10740

3134

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

0.569

10741

3293

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

0.569

10742

4086

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

0.569

10743

4568

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

0.569

10744

5403

\begin{align*} {y^{\prime }}^{2}+a x y^{\prime }&=b c \,x^{2} \\ \end{align*}

0.569

10745

6032

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

0.569

10746

6246

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

0.569

10747

7304

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

0.569

10748

8595

\begin{align*} 2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y&=0 \\ \end{align*}
Series expansion around \(t=0\).

0.569

10749

8602

\begin{align*} \left (2 x +1\right )^{2} y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+16 \left (x +1\right ) x y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.569

10750

9327

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

0.569

10751

9709

\begin{align*} x^{\prime }&=5 x+9 y+2 \\ y^{\prime }&=-x+11 y+6 \\ \end{align*}

0.569

10752

10171

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

0.569

10753

12907

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

0.569

10754

14751

\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+\frac {8}{9}\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.569

10755

15731

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

0.569

10756

16155

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

0.569

10757

16912

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

0.569

10758

16918

\begin{align*} x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+9 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.569

10759

16920

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

0.569

10760

17592

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

0.569

10761

18413

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

0.569

10762

19428

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

0.569

10763

19627

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

0.569

10764

21493

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

0.569

10765

1384

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

0.570

10766

1975

\begin{align*} 4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.570

10767

3487

\begin{align*} f^{\prime \prime }+8 f^{\prime }+12 f&=12 \,{\mathrm e}^{-4 t} \\ f \left (0\right ) &= 0 \\ f^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.570

10768

5725

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

0.570

10769

6735

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

0.570

10770

8548

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

0.570

10771

14767

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

0.570

10772

16869

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

0.570

10773

16963

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

0.570

10774

17686

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

0.570

10775

19140

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

0.570

10776

21116

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

0.570

10777

22307

\begin{align*} s^{\prime }&=9 \sqrt {u} \\ s \left (4\right ) &= 16 \\ \end{align*}

0.570

10778

22728

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

0.570

10779

22846

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

0.570

10780

25338

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

0.570

10781

3759

\begin{align*} y^{\prime \prime }+2 y^{\prime }+17 y&=\frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}} \\ \end{align*}

0.571

10782

14679

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

0.571

10783

18333

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

0.571

10784

20210

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

0.571

10785

21315

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

0.571

10786

24859

\begin{align*} 9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-1&=0 \\ \end{align*}

0.571

10787

25314

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

0.571

10788

25749

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

0.571

10789

157

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

0.572

10790

592

\begin{align*} x^{\prime }&=x+9 y \\ y^{\prime }&=-2 x-5 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 2 \\ \end{align*}

0.572

10791

3500

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

0.572

10792

3761

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=15 \,{\mathrm e}^{-2 x} \ln \left (x \right )+25 \cos \left (x \right ) \\ \end{align*}

0.572

10793

4183

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

0.572

10794

5896

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

0.572

10795

7096

\begin{align*} y^{\prime \prime }+9 y&=8 \cos \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= -1 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}

0.572

10796

7639

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

0.572

10797

7649

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

0.572

10798

8497

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

0.572

10799

8514

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

0.572

10800

14190

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

0.572