2.3.107 Problems 10601 to 10700

Table 2.787: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10601

12467

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

0.805

10602

14611

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+37 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}

0.805

10603

14979

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

Series expansion around \(x=0\).

0.805

10604

15272

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

0.805

10605

17358

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

0.805

10606

372

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

0.806

10607

1524

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

0.806

10608

1729

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

0.806

10609

8595

\begin{align*} 2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y&=0 \\ \end{align*}

Series expansion around \(t=0\).

0.806

10610

12395

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

0.806

10611

14610

\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.806

10612

15211

\begin{align*} y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 5 \\ y^{\prime \prime \prime }\left (0\right ) &= 19 \\ \end{align*}

Using Laplace transform method.

0.806

10613

18441

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

0.806

10614

18629

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

0.806

10615

19600

\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 \(x=0\).

0.806

10616

23262

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

0.806

10617

23458

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

0.806

10618

25975

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

0.806

10619

26028

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

Series expansion around \(x=0\).

0.806

10620

3822

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

0.807

10621

7455

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

0.807

10622

13070

\begin{align*} x^{\prime }+y-t^{2}+6 t +1&=0 \\ -x+y^{\prime }&=-3 t^{2}+3 t +1 \\ \end{align*}

0.807

10623

15250

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 3 \\ \end{align*}

Using Laplace transform method.

0.807

10624

16423

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

0.807

10625

17431

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

0.807

10626

23734

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

Series expansion around \(x=0\).

0.807

10627

2468

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

Series expansion around \(t=0\).

0.808

10628

4026

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

Series expansion around \(x=0\).

0.808

10629

12465

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

0.808

10630

14602

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

0.808

10631

17516

\begin{align*} y^{\prime \prime }+16 y&=\tan \left (2 t \right ) \\ \end{align*}

0.808

10632

19437

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

0.808

10633

20896

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

Series expansion around \(x=0\).

0.808

10634

22882

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

With initial conditions

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

0.808

10635

23501

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

0.808

10636

23682

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

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

0.808

10637

26017

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

Series expansion around \(x=0\).

0.808

10638

26423

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

0.808

10639

4055

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

Series expansion around \(x=0\).

0.809

10640

5561

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

0.809

10641

7375

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

0.809

10642

12880

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

0.809

10643

13723

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

0.809

10644

20642

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

0.809

10645

20909

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

Series expansion around \(x=0\).

0.809

10646

22810

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

Using Laplace transform method.

0.809

10647

26022

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

Series expansion around \(x=0\).

0.809

10648

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*}

0.810

10649

6640

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

0.810

10650

7644

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

Series expansion around \(x=1\).

0.810

10651

8083

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

Series expansion around \(x=0\).

0.810

10652

9464

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

0.810

10653

12459

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

0.810

10654

22256

\begin{align*} w^{\prime }+y&=\sin \left (t \right ) \\ y^{\prime }-z&={\mathrm e}^{t} \\ w+y+z^{\prime }&=1 \\ \end{align*}

With initial conditions

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

0.810

10655

561

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

Using Laplace transform method.

0.811

10656

8386

\begin{align*} y^{\prime }&=\left (-1+y\right )^{2}+\frac {1}{100} \\ y \left (0\right ) &= 1 \\ \end{align*}

0.811

10657

10529

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

0.811

10658

22148

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

0.811

10659

27177

\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2}+3 \,{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=9 x_{1}-3 x_{2}+{\mathrm e}^{2 t} \\ \end{align*}

0.811

10660

6413

\begin{align*} \sqrt {x}\, y^{\prime \prime }&=y^{{3}/{2}} \\ \end{align*}

0.812

10661

8416

\begin{align*} y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\ y \left (-1\right ) &= -3 \\ \end{align*}

0.812

10662

19667

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

0.812

10663

19983

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

0.812

10664

20440

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

0.812

10665

21228

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

0.812

10666

22689

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x}+15 x \\ \end{align*}

0.812

10667

910

\begin{align*} x^{\prime \prime }+100 x&=225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \\ x \left (0\right ) &= 375 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.813

10668

1517

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

0.813

10669

1976

\begin{align*} 3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.813

10670

1983

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

Series expansion around \(x=0\).

0.813

10671

12464

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

0.813

10672

12868

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

0.813

10673

14609

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

0.813

10674

15753

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

0.813

10675

16883

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

Series expansion around \(x=0\).

0.813

10676

17206

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

0.813

10677

18416

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

0.813

10678

20627

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

0.813

10679

20792

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

0.813

10680

22166

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

0.813

10681

22716

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

0.813

10682

23279

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

0.813

10683

24030

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

0.813

10684

8844

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

0.814

10685

9747

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

0.814

10686

14663

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

0.814

10687

19006

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

0.814

10688

19041

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

0.814

10689

20479

\begin{align*} 4 {y^{\prime }}^{2} x^{2} \left (x -1\right )-4 y^{\prime } x y \left (4 x -3\right )+\left (16 x -9\right ) y^{2}&=0 \\ \end{align*}

0.814

10690

3119

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

0.815

10691

5788

\begin{align*} -4 y-3 y^{\prime }+y^{\prime \prime }&=10 \cos \left (2 x \right ) \\ \end{align*}

0.815

10692

5795

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

0.815

10693

7166

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

Series expansion around \(x=0\).

0.815

10694

14935

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

0.815

10695

16172

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

0.815

10696

21658

\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 \(x=-1\).

0.815

10697

24735

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

0.815

10698

27101

\(\left [\begin {array}{cccc} -2 & 1 & 0 & 0 \\ 1 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end {array}\right ]\)

N/A

N/A

N/A

0.815

10699

245

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

0.816

10700

3137

\begin{align*} 4 y+y^{\prime \prime }&=12 \cos \left (x \right )^{2} \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\ \end{align*}

0.816