2.3.68 Problems 6701 to 6800

Table 2.667: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

6701

6540

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

0.569

6702

8295

\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (0\right ) &= -4 \\ \end{align*}

0.569

6703

15408

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

0.569

6704

16346

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

0.569

6705

19026

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

0.569

6706

25382

\begin{align*} y_{1}^{\prime }&=5 y_{1}+2 y_{2}+t \\ y_{2}^{\prime }&=-8 y_{1}-3 y_{2}-2 t \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}

0.569

6707

1894

\begin{align*} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Series expansion around \(x=0\).

0.570

6708

6325

\begin{align*} y^{\prime \prime }&=\operatorname {f4} \left (x \right )+\operatorname {f3} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\left (\operatorname {f1} \left (x \right )-2 y\right ) y^{\prime } \\ \end{align*}

0.570

6709

6579

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

0.570

6710

7173

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

0.570

6711

9187

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

0.570

6712

9695

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

0.570

6713

10940

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

0.570

6714

16843

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

0.570

6715

22879

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (\frac {1}{2}\right ) &= 10 \\ \end{align*}
Series expansion around \(x={\frac {1}{2}}\).

0.570

6716

23677

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

0.570

6717

2743

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

0.571

6718

6444

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

0.571

6719

6541

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

0.571

6720

9587

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

0.571

6721

10963

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

0.571

6722

14760

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

0.571

6723

15273

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

0.571

6724

15459

\begin{align*} x^{\prime }&=-4 x-10 y \\ y^{\prime }&=x-2 y \\ \end{align*}

0.571

6725

20911

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

0.571

6726

3827

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

0.572

6727

10949

\begin{align*} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\ \end{align*}

0.572

6728

12892

\begin{align*} y^{\prime \prime } x +a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y}&=0 \\ \end{align*}

0.572

6729

12907

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

0.572

6730

14634

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

0.572

6731

15654

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

0.572

6732

19259

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

0.572

6733

22976

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

0.572

6734

1870

\begin{align*} \left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y&=0 \\ \end{align*}
Series expansion around \(x=2\).

0.573

6735

11009

\begin{align*} 16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \\ \end{align*}

0.573

6736

15395

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

0.573

6737

16038

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

0.573

6738

18444

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

0.573

6739

22213

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

0.573

6740

24965

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

0.573

6741

454

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

0.574

6742

1427

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

0.574

6743

2449

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

0.574

6744

3585

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

0.574

6745

9510

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

0.574

6746

11252

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

0.574

6747

13021

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

0.574

6748

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*}

0.574

6749

14790

\begin{align*} x^{\prime }&=5 x+2 y+5 t \\ y^{\prime }&=3 x+4 y+17 t \\ \end{align*}

0.574

6750

18013

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

0.574

6751

25353

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

0.574

6752

985

\begin{align*} x_{1}^{\prime }&=5 x_{1}-6 x_{3} \\ x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3} \\ x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3} \\ \end{align*}

0.575

6753

1877

\begin{align*} \left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \\ y \left (-1\right ) &= 3 \\ y^{\prime }\left (-1\right ) &= -3 \\ \end{align*}
Series expansion around \(x=-1\).

0.575

6754

1901

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

0.575

6755

2831

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

0.575

6756

16261

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

0.575

6757

24082

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +56 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.575

6758

24086

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

0.575

6759

9858

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

0.576

6760

11124

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

0.576

6761

21103

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

0.576

6762

23701

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

0.576

6763

24084

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

0.576

6764

6

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

0.577

6765

2446

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

0.577

6766

5403

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

0.577

6767

2626

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

0.578

6768

3182

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

0.578

6769

7092

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

0.578

6770

7167

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

0.578

6771

16931

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

0.578

6772

508

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

0.579

6773

1874

\begin{align*} \left (3 x^{2}-6 x +5\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+12 y&=0 \\ y \left (1\right ) &= -1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}
Series expansion around \(x=1\).

0.579

6774

6435

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

0.579

6775

8193

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

0.579

6776

20387

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

0.579

6777

1871

\begin{align*} \left (3 x^{2}+6 x +5\right ) y^{\prime \prime }+9 \left (x +1\right ) y^{\prime }+3 y&=0 \\ \end{align*}
Series expansion around \(x=-1\).

0.580

6778

1907

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

0.580

6779

8505

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

0.580

6780

11323

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

0.580

6781

16669

\begin{align*} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right ) \\ \end{align*}

0.580

6782

17232

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

0.580

6783

3997

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

0.581

6784

9515

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

0.581

6785

11122

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

0.581

6786

11133

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

0.581

6787

16040

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

0.581

6788

20033

\begin{align*} \left (8 {y^{\prime }}^{3}-27\right ) x&=12 y {y^{\prime }}^{2} \\ \end{align*}

0.581

6789

21778

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

0.581

6790

23721

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

0.581

6791

4171

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

0.582

6792

6420

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

0.582

6793

6737

\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=24 x \sin \left (x \right ) \\ \end{align*}

0.582

6794

9512

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

0.582

6795

10414

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

0.582

6796

15445

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

0.582

6797

15474

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

0.582

6798

15888

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

0.582

6799

24554

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

0.582

6800

24946

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

0.582