2.3.107 Problems 10601 to 10700

Table 2.745: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10601

19865

\begin{align*} \left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y&=x^{3} \\ \end{align*}

0.557

10602

20160

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

0.557

10603

22213

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

0.557

10604

22927

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

0.557

10605

24820

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

0.557

10606

25454

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

0.557

10607

1391

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

0.558

10608

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 \(t=0\).

0.558

10609

5959

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

0.558

10610

8594

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

0.558

10611

14313

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

0.558

10612

14744

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

0.558

10613

18856

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (6 t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.558

10614

19187

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

0.558

10615

21935

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

0.558

10616

22990

\begin{align*} p^{\prime }&=15-20 p \\ p \left (0\right ) &= {\frac {7}{10}} \\ \end{align*}

0.558

10617

25519

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

0.558

10618

488

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

0.559

10619

1410

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

0.559

10620

1954

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

0.559

10621

2001

\begin{align*} x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.559

10622

2800

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

0.559

10623

3771

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

0.559

10624

7769

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

0.559

10625

7970

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

0.559

10626

8509

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

0.559

10627

9051

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

0.559

10628

9581

\begin{align*} y^{\prime \prime } x +y^{\prime }-7 x^{3} y&=0 \\ \end{align*}

0.559

10629

12675

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

0.559

10630

15405

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

0.559

10631

15728

\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (x \right ) \delta \left (x -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.559

10632

16406

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

0.559

10633

23583

\begin{align*} x^{\prime }&=5 x-6 y+1 \\ y^{\prime }&=6 x-7 y+1 \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.559

10634

25345

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

0.559

10635

392

\begin{align*} x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.560

10636

3851

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

0.560

10637

4459

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

0.560

10638

7672

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

0.560

10639

9705

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

0.560

10640

12877

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

0.560

10641

15239

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

0.560

10642

16011

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

0.560

10643

21491

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

0.560

10644

21581

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

0.560

10645

4487

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

0.561

10646

9426

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

0.561

10647

9522

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

0.561

10648

17492

\begin{align*} y^{\prime \prime }+12 y^{\prime }+37 y&={\mathrm e}^{-6 t} \csc \left (t \right ) \\ \end{align*}

0.561

10649

18243

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

0.561

10650

23402

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

0.561

10651

5385

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

0.562

10652

6039

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

0.562

10653

6501

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

0.562

10654

7201

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

0.562

10655

9878

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

0.562

10656

10057

\begin{align*} x^{\prime }&=9 x+4 y \\ y^{\prime }&=-6 x-y \\ z^{\prime }&=6 x+4 y+3 z \\ \end{align*}

0.562

10657

12660

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

0.562

10658

16815

\begin{align*} y^{\prime \prime }+4 y^{\prime }-12 y&=\delta \left (t -3\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.562

10659

17605

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

0.562

10660

21148

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

0.562

10661

21490

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

0.562

10662

22482

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

0.562

10663

23377

\begin{align*} x^{2} y^{\prime \prime }+\frac {7 y^{\prime } x}{2}-\frac {3 y}{2}&=0 \\ \end{align*}

0.562

10664

23379

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

0.562

10665

1992

\begin{align*} 28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.563

10666

2046

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

0.563

10667

5841

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

0.563

10668

5943

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

0.563

10669

6894

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

0.563

10670

7817

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

0.563

10671

8326

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

0.563

10672

8649

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

0.563

10673

10079

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

0.563

10674

10141

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

0.563

10675

10228

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

0.563

10676

15658

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

0.563

10677

20414

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

0.563

10678

21230

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

0.563

10679

22160

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

0.563

10680

23827

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

0.563

10681

594

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

0.564

10682

2047

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

0.564

10683

4184

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

0.564

10684

5964

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

0.564

10685

14750

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

0.564

10686

14828

\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right . \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

0.564

10687

16010

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

0.564

10688

16432

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

0.564

10689

16726

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -30 y&=0 \\ \end{align*}

0.564

10690

17503

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 t}}{t} \\ \end{align*}

0.564

10691

18433

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

0.564

10692

18872

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

0.564

10693

21898

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

0.564

10694

21945

\begin{align*} y^{\prime \prime }+4 y&=2 t -8 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.564

10695

23076

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

0.564

10696

1024

\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=18 x_{1}+7 x_{2}+4 x_{3} \\ x_{3}^{\prime }&=-27 x_{1}-9 x_{2}-5 x_{3} \\ \end{align*}

0.565

10697

3185

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

0.565

10698

5840

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

0.565

10699

8945

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

0.565

10700

10203

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

0.565