2.3.138 Problems 13701 to 13800

Table 2.807: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13701

15371

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

0.894

13702

15653

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

0.894

13703

18307

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

0.894

13704

18359

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

0.894

13705

22697

\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} x & 0\le x \le \pi \\ 0 & \pi <x \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.894

13706

989

\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*}

0.895

13707

4507

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

0.895

13708

12502

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

0.895

13709

13699

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

0.895

13710

19361

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

0.895

13711

20673

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

0.895

13712

24739

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

0.895

13713

1038

\begin{align*} x_{1}^{\prime }&=35 x_{1}-12 x_{2}+4 x_{3}+30 x_{4} \\ x_{2}^{\prime }&=22 x_{1}-8 x_{2}+3 x_{3}+19 x_{4} \\ x_{3}^{\prime }&=-10 x_{1}+3 x_{2}-9 x_{4} \\ x_{4}^{\prime }&=-27 x_{1}+9 x_{2}-3 x_{3}-23 x_{4} \\ \end{align*}

0.896

13714

6053

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

0.896

13715

8085

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

0.896

13716

13770

\begin{align*} \left (x +\gamma \right ) y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (x^{n -1} a n +b m \,x^{m -1}\right ) y&=0 \\ \end{align*}

0.896

13717

21025

\begin{align*} x^{\prime }-k^{2} x&=1 \\ \end{align*}

0.896

13718

21410

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

0.896

13719

1223

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

0.897

13720

16394

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

0.897

13721

20863

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

0.897

13722

9814

\begin{align*} 4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\ \end{align*}

0.898

13723

13773

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

0.898

13724

15117

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

0.898

13725

16385

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

0.898

13726

17158

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

0.898

13727

23617

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

0.898

13728

2768

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

0.899

13729

4547

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

0.899

13730

12896

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

0.899

13731

25420

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

0.899

13732

14726

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

0.900

13733

21100

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

0.900

13734

2190

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y&={\mathrm e}^{x} \left (\left (7+8 x \right ) \cos \left (2 x \right )+\left (8-4 x \right ) \sin \left (2 x \right )\right ) \\ \end{align*}

0.901

13735

3366

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

0.901

13736

4425

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

0.901

13737

16414

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=9 \,{\mathrm e}^{-3 x} \\ \end{align*}

0.901

13738

18147

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

0.901

13739

21681

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

0.901

13740

153

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

0.902

13741

10397

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

0.902

13742

15076

\begin{align*} x^{3} x^{\prime \prime }+1&=0 \\ \end{align*}

0.902

13743

19883

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

0.902

13744

20152

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

0.902

13745

13788

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

0.903

13746

19879

\begin{align*} V^{\prime \prime }+\frac {V^{\prime }}{r}&=0 \\ \end{align*}

0.903

13747

20560

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

0.903

13748

21682

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

0.903

13749

21693

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

0.903

13750

23105

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

0.903

13751

262

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

0.904

13752

1183

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

0.904

13753

2082

\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.904

13754

2384

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

0.904

13755

4040

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+7 \,{\mathrm e}^{x} y^{\prime } x +9 \left (1+\tan \left (x \right )\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.904

13756

5996

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

0.904

13757

6333

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

0.904

13758

15173

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

0.904

13759

19179

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

0.904

13760

20986

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

0.904

13761

25336

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

0.904

13762

3379

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

0.905

13763

9541

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

0.905

13764

14699

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

0.905

13765

14717

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*}

0.905

13766

20527

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

0.905

13767

22981

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

0.905

13768

16717

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

0.906

13769

22097

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

0.906

13770

25383

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

0.906

13771

25473

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

0.906

13772

814

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

0.907

13773

3627

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

0.907

13774

16993

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

0.907

13775

21750

\begin{align*} x^{\prime }&=7 x-y+6 z \\ y^{\prime }&=-10 x+4 y-12 z \\ z^{\prime }&=-2 x+y-z \\ \end{align*}

0.907

13776

24858

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

0.907

13777

2400

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

0.908

13778

2435

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

0.908

13779

3165

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

0.908

13780

6378

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

0.908

13781

14489

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

0.908

13782

23621

\begin{align*} x^{\prime }&=-10 x+y+7 z \\ y^{\prime }&=-9 x+4 y+5 z \\ z^{\prime }&=-17 x+y+12 z \\ \end{align*}

0.908

13783

24563

\begin{align*} y^{\prime \prime }+3 y^{\prime }&=-18 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

0.908

13784

17

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

0.909

13785

5870

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

0.909

13786

6519

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

0.909

13787

12921

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

0.909

13788

13108

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

0.909

13789

18009

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

0.909

13790

18632

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

0.909

13791

25494

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

0.909

13792

1596

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

0.910

13793

5969

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

0.910

13794

15288

\begin{align*} x^{\prime }&=3 x-2 y+24 \sin \left (t \right ) \\ y^{\prime }&=9 x-3 y+12 \cos \left (t \right ) \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}

0.910

13795

19639

\begin{align*} x^{\prime }&=x+2 y+t -1 \\ y^{\prime }&=3 x+2 y-5 t -2 \\ \end{align*}

0.910

13796

22065

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

0.910

13797

2189

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+32 y^{\prime \prime }+64 y^{\prime }+39 y&={\mathrm e}^{-2 x} \left (\left (4-15 x \right ) \cos \left (3 x \right )-\left (4+15 x \right ) \sin \left (3 x \right )\right ) \\ \end{align*}

0.911

13798

2700

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

0.911

13799

12974

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

0.911

13800

14143

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

0.911