2.3.108 Problems 10701 to 10800

Table 2.789: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10701

5409

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

0.816

10702

6636

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

0.816

10703

6711

\begin{align*} -4 y-14 x y^{\prime }+\left (-8 x^{2}+3\right ) y^{\prime \prime }+x \left (-x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}

0.816

10704

7772

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

0.816

10705

9263

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

0.816

10706

10378

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

0.816

10707

14684

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

0.816

10708

16944

\begin{align*} x^{\prime }&=4 x+3 y-6 \,{\mathrm e}^{3 t} \\ y^{\prime }&=x+6 y+2 \,{\mathrm e}^{3 t} \\ \end{align*}

With initial conditions

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

0.816

10709

17509

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

0.816

10710

23628

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

With initial conditions

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

0.816

10711

25367

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

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}

0.816

10712

26993

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=4 \cos \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}

0.816

10713

17681

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

Series expansion around \(x=-2\).

0.817

10714

22841

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

Series expansion around \(x=0\).

0.817

10715

4171

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

0.818

10716

11602

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

0.818

10717

12534

\begin{align*} \left (2 x^{2}+6 x +4\right ) y^{\prime \prime }+\left (10 x^{2}+21 x +8\right ) y^{\prime }+\left (12 x^{2}+17 x +8\right ) y&=0 \\ \end{align*}

0.818

10718

14688

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

0.818

10719

17011

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

0.818

10720

5750

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

0.819

10721

7674

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

0.819

10722

8090

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

Series expansion around \(x=0\).

0.819

10723

8097

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

Series expansion around \(x=0\).

0.819

10724

9952

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

Series expansion around \(x=0\).

0.819

10725

14293

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

0.819

10726

19617

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

Series expansion around \(x=0\).

0.819

10727

20879

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

0.819

10728

22934

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

With initial conditions

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

0.819

10729

2599

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

0.820

10730

3250

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

0.820

10731

5726

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

0.820

10732

6534

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

0.820

10733

7124

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

0.820

10734

7672

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

0.820

10735

15575

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

0.820

10736

20657

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

0.820

10737

22195

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

Series expansion around \(x=1\).

0.820

10738

25989

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

0.820

10739

27180

\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2}+5 \sin \left (t \right ) \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 10 \\ x_{2} \left (0\right ) &= 5 \\ \end{align*}

0.820

10740

5393

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

0.821

10741

9514

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

Series expansion around \(x=0\).

0.821

10742

9960

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

Series expansion around \(x=0\).

0.821

10743

22187

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

Series expansion around \(x=-1\).

0.821

10744

24640

\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&={\mathrm e}^{-3 x} \sec \left (x \right )^{2} \left (1+2 \tan \left (x \right )\right ) \\ \end{align*}

0.821

10745

4473

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

0.822

10746

5720

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

0.822

10747

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*}

0.822

10748

9702

\begin{align*} x^{\prime }&=4 x+5 y \\ y^{\prime }&=-2 x+6 y \\ \end{align*}

0.822

10749

10034

\begin{align*} \left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime }&=0 \\ y \left (3\right ) &= 2 \pi \\ y^{\prime }\left (3\right ) &= {\frac {2}{3}} \\ \end{align*}

0.822

10750

12927

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

0.822

10751

14605

\begin{align*} 9 y^{\prime \prime }-6 y^{\prime }+y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

0.822

10752

14608

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

0.822

10753

18454

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

0.822

10754

19367

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

0.822

10755

22823

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

Series expansion around \(x=0\).

0.822

10756

24730

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

0.822

10757

1548

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

0.823

10758

1994

\begin{align*} 8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.823

10759

6926

\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*}

0.823

10760

9478

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

0.823

10761

10272

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

0.823

10762

16896

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

Series expansion around \(x=0\).

0.823

10763

16914

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

Series expansion around \(x=0\).

0.823

10764

17832

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

0.823

10765

24731

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

0.823

10766

2205

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y&={\mathrm e}^{x} \left (12 x -2 \cos \left (x \right )+2 \sin \left (x \right )\right ) \\ \end{align*}

0.824

10767

3808

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

0.824

10768

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*}

0.824

10769

7193

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

Series expansion around \(x=0\).

0.824

10770

7898

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

0.824

10771

18248

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

0.824

10772

18861

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

0.824

10773

618

\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}+x_{3} \\ x_{2}^{\prime }&=6 x_{1}-x_{2} \\ x_{3}^{\prime }&=-x_{1}-2 x_{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 ) &= 3 \\ \end{align*}

0.825

10774

997

\begin{align*} x_{1}^{\prime }&=147 x_{1}+23 x_{2}-202 x_{3} \\ x_{2}^{\prime }&=-90 x_{1}-9 x_{2}+129 x_{3} \\ x_{3}^{\prime }&=90 x_{1}+15 x_{2}-123 x_{3} \\ \end{align*}

0.825

10775

1980

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

Series expansion around \(x=0\).

0.825

10776

7196

\begin{align*} x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.825

10777

7216

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

0.825

10778

8077

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

Series expansion around \(x=0\).

0.825

10779

14279

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

0.825

10780

19441

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

0.825

10781

21577

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x}+7 x -2 \\ \end{align*}

0.825

10782

26641

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

0.825

10783

2020

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

Series expansion around \(x=0\).

0.826

10784

2195

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

0.826

10785

3897

\begin{align*} x_{1}^{\prime }&=-3 x_{1}-x_{2} \\ x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\ x_{3}^{\prime }&=6 x_{1}+6 x_{2}+4 x_{3} \\ \end{align*}

0.826

10786

8807

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

0.826

10787

18122

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

0.826

10788

23103

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

0.826

10789

26996

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

0.826

10790

27359

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

0.826

10791

782

\begin{align*} 6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}

0.827

10792

7374

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

Series expansion around \(x=0\).

0.827

10793

13076

\begin{align*} 4 x^{\prime }+9 y^{\prime }+44 x+49 y&=t \\ 3 x^{\prime }+7 y^{\prime }+34 x+38 y&={\mathrm e}^{t} \\ \end{align*}

0.827

10794

20848

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=5+10 \sin \left (2 x \right ) \\ \end{align*}

0.827

10795

26461

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

0.827

10796

890

\begin{align*} y^{\prime \prime }+9 y&=\sin \left (x \right )^{4} \\ \end{align*}

0.828

10797

5920

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

0.828

10798

12628

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

0.828

10799

14664

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=x \,{\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \\ \end{align*}

0.828

10800

23545

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

0.828