2.3.118 Problems 11701 to 11800

Table 2.767: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11701

9758

\begin{align*} 5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y&=0 \\ \end{align*}

0.646

11702

21877

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

0.646

11703

22717

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

0.646

11704

24836

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

0.646

11705

25295

\begin{align*} y^{\prime }+5 y&=\left \{\begin {array}{cc} -5 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.646

11706

1852

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

0.647

11707

5517

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

0.647

11708

5773

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

0.647

11709

6499

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

0.647

11710

9393

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

0.647

11711

14776

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

0.647

11712

15488

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

0.647

11713

16960

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

0.647

11714

19881

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

0.647

11715

982

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

0.648

11716

1965

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

0.648

11717

2590

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

0.648

11718

4539

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

0.648

11719

4685

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

0.648

11720

5962

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

0.648

11721

6434

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

0.648

11722

8601

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

0.648

11723

10207

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

0.648

11724

12524

\begin{align*} x \left (x -1\right ) y^{\prime \prime }+\left (\left (\operatorname {a1} +\operatorname {b1} +1\right ) x -\operatorname {d1} \right ) y^{\prime }+\operatorname {a1} \operatorname {b1} \operatorname {d1}&=0 \\ \end{align*}

0.648

11725

12987

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

0.648

11726

17724

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

0.648

11727

17768

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

0.648

11728

19662

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

0.648

11729

21233

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

0.648

11730

9708

\begin{align*} x^{\prime }&=2 x+3 y-7 \\ y^{\prime }&=-x-2 y+5 \\ \end{align*}

0.649

11731

9761

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

0.649

11732

13672

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

0.649

11733

14333

\begin{align*} t^{2} x^{\prime \prime }-2 x&=t^{3} \\ \end{align*}

0.649

11734

14790

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

0.649

11735

19496

\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=14 \,{\mathrm e}^{-5 x} \\ \end{align*}

0.649

11736

20376

\begin{align*} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y&=96 \sin \left (2 x \right ) \cos \left (x \right ) \\ \end{align*}

0.649

11737

20854

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

0.649

11738

22916

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

0.649

11739

489

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

0.650

11740

981

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

0.650

11741

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 \(x=0\).

0.650

11742

14072

\begin{align*} 3 x {y^{\prime }}^{2}-6 y^{\prime } y+x +2 y&=0 \\ \end{align*}

0.650

11743

14631

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

0.650

11744

15723

\begin{align*} y^{\prime }+3 y&=\delta \left (x -2\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.650

11745

18330

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

0.650

11746

19732

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

0.650

11747

20348

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

0.650

11748

20522

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

0.650

11749

23746

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

0.650

11750

1030

\begin{align*} x_{1}^{\prime }&=39 x_{1}+8 x_{2}-16 x_{3} \\ x_{2}^{\prime }&=-36 x_{1}-5 x_{2}+16 x_{3} \\ x_{3}^{\prime }&=72 x_{1}+16 x_{2}-29 x_{3} \\ \end{align*}

0.651

11751

3206

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

0.651

11752

6020

\begin{align*} \left (\operatorname {b2} \,x^{2}+\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

0.651

11753

12642

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

0.651

11754

12893

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

0.651

11755

15300

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

0.651

11756

16123

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

0.651

11757

16945

\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=4 x+24 t \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.651

11758

25415

\begin{align*} y+y^{\prime }&=7 \operatorname {Heaviside}\left (t -4\right ) \\ \end{align*}

0.651

11759

1962

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

0.652

11760

3495

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

0.652

11761

3967

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=30 \operatorname {Heaviside}\left (-1+t \right ) {\mathrm e}^{1-t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}
Using Laplace transform method.

0.652

11762

3976

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\delta \left (-1+t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.652

11763

7131

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

0.652

11764

7209

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

0.652

11765

12563

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

0.652

11766

13069

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

0.652

11767

22276

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=6 x_{1}+4 \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}

0.652

11768

25293

\begin{align*} y^{\prime }&=\left \{\begin {array}{cc} 0 & t =0 \\ \sin \left (\frac {1}{t}\right ) & \operatorname {otherwise} \end {array}\right . \\ \end{align*}
Using Laplace transform method.

0.652

11769

620

\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2}-2 x_{4} \\ x_{2}^{\prime }&=x_{2} \\ x_{3}^{\prime }&=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\ x_{4}^{\prime }&=-4 x_{2}-x_{4} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ x_{4} \left (0\right ) &= 1 \\ \end{align*}

0.653

11770

3213

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

0.653

11771

3260

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

0.653

11772

6363

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

0.653

11773

11723

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

0.653

11774

12992

\begin{align*} 8 \left (-x^{3}+1\right ) y y^{\prime \prime }-4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}-12 x^{2} y y^{\prime }+3 x y^{2}&=0 \\ \end{align*}

0.653

11775

18964

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

0.653

11776

19521

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

0.653

11777

24881

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

0.653

11778

25335

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

0.653

11779

1031

\begin{align*} x_{1}^{\prime }&=28 x_{1}+50 x_{2}+100 x_{3} \\ x_{2}^{\prime }&=15 x_{1}+33 x_{2}+60 x_{3} \\ x_{3}^{\prime }&=-15 x_{1}-30 x_{2}-57 x_{3} \\ \end{align*}

0.654

11780

1455

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

0.654

11781

2383

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

0.654

11782

2456

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

0.654

11783

5758

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

0.654

11784

5998

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

0.654

11785

6103

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

0.654

11786

9584

\begin{align*} 16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y&=0 \\ \end{align*}

0.654

11787

12885

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

0.654

11788

14372

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

0.654

11789

17710

\begin{align*} 5 y^{\prime \prime } x +8 y^{\prime }-y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.654

11790

18995

\begin{align*} x_{1}^{\prime }&=-x_{3} \\ x_{2}^{\prime }&=2 x_{1} \\ x_{3}^{\prime }&=-x_{1}+2 x_{2}+4 x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 7 \\ x_{2} \left (0\right ) &= 5 \\ x_{3} \left (0\right ) &= 5 \\ \end{align*}

0.654

11791

19126

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

0.654

11792

21169

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

0.654

11793

22550

\begin{align*} n^{\prime }&=-a n \\ n \left (0\right ) &= n_{0} \\ \end{align*}

0.654

11794

23573

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

0.654

11795

24874

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

0.654

11796

502

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

0.655

11797

2645

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

0.655

11798

2737

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

0.655

11799

4486

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

0.655

11800

7119

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

0.655