2.3.108 Problems 10701 to 10800

Table 2.759: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10701

23586

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

0.759

10702

1988

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.760

10703

2593

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

0.760

10704

3299

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

0.760

10705

8530

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

0.760

10706

10069

\begin{align*} z^{\prime \prime }+3 z^{\prime }+2 z&=24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \\ \end{align*}

0.760

10707

23080

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

0.760

10708

9565

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

0.761

10709

16022

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

0.761

10710

17513

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

0.761

10711

18207

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

0.761

10712

20484

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

0.761

10713

3287

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

0.762

10714

3395

\begin{align*} 9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=x^{4}+x^{2} \\ \end{align*}
Series expansion around \(x=0\).

0.762

10715

4593

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

0.762

10716

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*}

0.762

10717

8935

\begin{align*} y^{\prime \prime \prime }-8 y&={\mathrm e}^{i x} \\ \end{align*}

0.762

10718

12646

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

0.762

10719

15409

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

0.762

10720

18839

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

0.762

10721

990

\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{3} \\ x_{2}^{\prime }&=9 x_{1}-x_{2}+2 x_{3} \\ x_{3}^{\prime }&=-9 x_{1}+4 x_{2}-x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 17 \\ \end{align*}

0.763

10722

2048

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

0.763

10723

2105

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.763

10724

3867

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

0.763

10725

6193

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

0.763

10726

7086

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

0.763

10727

9396

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

0.763

10728

9855

\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+11 y^{\prime } x +9 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.763

10729

16883

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

0.763

10730

19613

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

0.763

10731

21515

\begin{align*} y^{\prime \prime }&=9 x^{2}+2 x -1 \\ \end{align*}

0.763

10732

23698

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

0.763

10733

2461

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

0.764

10734

2749

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

0.764

10735

5522

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

0.765

10736

8562

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

0.765

10737

14600

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

0.765

10738

15439

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

0.765

10739

19147

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

0.765

10740

23574

\begin{align*} x^{\prime }&=5 x-6 y+1 \\ y^{\prime }&=6 x-7 y+1 \\ \end{align*}

0.765

10741

645

\begin{align*} x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3} \\ x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3} \\ \end{align*}

0.766

10742

3512

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

0.766

10743

5729

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

0.766

10744

18994

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\ x_{2}^{\prime }&=2 x_{2}+2 x_{3} \\ x_{3}^{\prime }&=-x_{1}+x_{2}+3 x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 11 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 5 \\ \end{align*}

0.766

10745

21551

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

0.766

10746

22830

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

0.766

10747

23934

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

0.766

10748

3438

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

0.767

10749

9388

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

0.767

10750

18246

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

0.767

10751

22082

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

0.767

10752

23531

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

0.767

10753

25962

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

0.767

10754

1977

\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.768

10755

7760

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

0.768

10756

9077

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

0.768

10757

19063

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

0.768

10758

22268

\begin{align*} x^{\prime }&=y \\ y^{\prime }&=8 x-2 y+{\mathrm e}^{t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -4 \\ \end{align*}

0.768

10759

24648

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

0.768

10760

597

\begin{align*} -x^{\prime }+2 y^{\prime }&=x+3 y+{\mathrm e}^{t} \\ 3 x^{\prime }-4 y^{\prime }&=x-15 y+{\mathrm e}^{-t} \\ \end{align*}

0.769

10761

5577

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

0.769

10762

8096

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

0.769

10763

8392

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

0.769

10764

19264

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

0.769

10765

19734

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

0.769

10766

20117

\begin{align*} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y&=x^{4}+2 x -5 \\ \end{align*}

0.769

10767

20659

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

0.769

10768

1850

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

0.770

10769

3397

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

0.770

10770

6099

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

0.770

10771

11719

\begin{align*} \left (\operatorname {a2} x +\operatorname {c2} \right ) {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {a0} x +\operatorname {b0} y+\operatorname {c0}&=0 \\ \end{align*}

0.770

10772

19178

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

0.770

10773

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*}

0.771

10774

8513

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

0.771

10775

9174

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

0.771

10776

9803

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

0.771

10777

12657

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

0.771

10778

13254

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

0.771

10779

15301

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

0.771

10780

18414

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

0.771

10781

22883

\begin{align*} u^{\prime }&=2 v-1 \\ v^{\prime }&=1+2 u \\ \end{align*}

0.771

10782

25585

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

0.771

10783

1299

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

0.772

10784

3349

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

0.772

10785

7079

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right ) \\ \end{align*}

0.772

10786

12544

\begin{align*} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x -\left (4 x^{2}+12 x +3\right ) y&=0 \\ \end{align*}

0.772

10787

16177

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

0.772

10788

16874

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

0.772

10789

1528

\begin{align*} y^{\prime }&=x \sin \left (x^{2}\right ) \\ y \left (\frac {\sqrt {2}\, \sqrt {\pi }}{2}\right ) &= 1 \\ \end{align*}

0.773

10790

2666

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

0.773

10791

2713

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y&=0 \\ 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 \\ \end{align*}

0.773

10792

8423

\begin{align*} 3 y^{\prime }+12 y&=4 \\ \end{align*}

0.773

10793

9682

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

0.773

10794

12589

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

0.773

10795

14338

\begin{align*} x^{\prime \prime }-x&=\frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}} \\ \end{align*}

0.773

10796

15447

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

0.773

10797

19610

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

0.773

10798

23508

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

0.773

10799

25417

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

0.773

10800

1436

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

0.774