2.3.98 Problems 9701 to 9800

Table 2.769: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9701

26593

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=10 \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.720

9702

26640

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

0.720

9703

1420

\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*}

0.721

9704

2283

\begin{align*} y_{1}^{\prime }&=-3 y_{1}-3 y_{2}+4 y_{3} \\ y_{2}^{\prime }&=4 y_{1}+5 y_{2}-8 y_{3} \\ y_{3}^{\prime }&=2 y_{1}+3 y_{2}-5 y_{3} \\ \end{align*}

0.721

9705

4165

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

0.721

9706

9370

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

Series expansion around \(x=0\).

0.721

9707

12624

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

0.721

9708

17021

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

0.721

9709

17683

\begin{align*} y^{\prime \prime }+3 y^{\prime }-18 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.721

9710

17769

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

0.721

9711

21478

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

0.721

9712

21886

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

0.721

9713

22617

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

0.721

9714

23616

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

0.721

9715

27072

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

Series expansion around \(x=0\).

0.721

9716

2042

\begin{align*} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-9 x^{2}+5\right ) y^{\prime }+\left (-3 x^{2}+4\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.722

9717

2382

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

0.722

9718

9187

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

0.722

9719

15221

\begin{align*} y^{\prime \prime }+8 y^{\prime }+20 y&=\sin \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}

Using Laplace transform method.

0.722

9720

17831

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

0.722

9721

26708

\begin{align*} 9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.722

9722

1816

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

0.723

9723

9632

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

Using Laplace transform method.

0.723

9724

15314

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

0.723

9725

23615

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

0.723

9726

25763

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

0.723

9727

26975

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=3 x +25 \sin \left (3 x \right ) \\ \end{align*}

0.723

9728

485

\begin{align*} 4 x y^{\prime \prime }+8 y^{\prime }+y x&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.724

9729

2735

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= -2 \\ x_{3} \left (0\right ) &= -1 \\ \end{align*}

0.724

9730

6659

\begin{align*} \operatorname {a3} y+\operatorname {a2} y^{\prime }+\operatorname {a1} y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}

0.724

9731

6694

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

0.724

9732

10164

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

Series expansion around \(x=0\).

0.724

9733

10613

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

0.724

9734

12707

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

0.724

9735

14105

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

0.724

9736

16638

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

0.724

9737

16930

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

0.724

9738

17003

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

0.724

9739

17530

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&={\mathrm e}^{-\frac {t}{2}} \\ y \left (0\right ) &= a \\ y^{\prime }\left (0\right ) &= b \\ \end{align*}

0.724

9740

18383

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

Series expansion around \(x=0\).

0.724

9741

21654

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

Series expansion around \(x=1\).

0.724

9742

22283

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

0.724

9743

23534

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

0.724

9744

23572

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

0.724

9745

25276

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

0.724

9746

2059

\begin{align*} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.725

9747

2252

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

0.725

9748

9074

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

0.725

9749

10167

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

Series expansion around \(x=0\).

0.725

9750

18898

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

Using Laplace transform method.

0.725

9751

20111

\begin{align*} y+3 x y^{\prime }+9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=\left (1+\ln \left (x \right )\right )^{2} \\ \end{align*}

0.725

9752

21855

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

0.725

9753

24705

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

0.725

9754

24752

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

0.725

9755

24769

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

0.725

9756

26054

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

0.725

9757

27413

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

0.725

9758

2197

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+9 y^{\prime }-10 y&=10 \,{\mathrm e}^{2 x}+20 \,{\mathrm e}^{x} \sin \left (2 x \right )-10 \\ \end{align*}

0.726

9759

9289

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

0.726

9760

18651

\begin{align*} x^{\prime }&=4 x-3 y \\ y^{\prime }&=8 x-6 y \\ \end{align*}

0.726

9761

19247

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

0.726

9762

20808

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

0.726

9763

24719

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

0.726

9764

363

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

0.727

9765

2036

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

Series expansion around \(x=0\).

0.727

9766

2262

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

0.727

9767

9742

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

0.727

9768

9980

\begin{align*} y^{\prime \prime }+16 y&=4 \cos \left (x \right ) \\ \end{align*}

0.727

9769

11778

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

0.727

9770

14860

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

0.727

9771

14932

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

0.727

9772

15977

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

0.727

9773

15978

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

0.727

9774

16942

\begin{align*} x^{\prime }&=8 x+2 y-17 \\ y^{\prime }&=4 x+y-13 \\ \end{align*}

With initial conditions

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

0.727

9775

17522

\begin{align*} y^{\prime \prime }-16 y&=16 t \,{\mathrm e}^{-4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.727

9776

17721

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

Series expansion around \(x=0\).

0.727

9777

22304

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

0.727

9778

23737

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

Series expansion around \(x=1\).

0.727

9779

23828

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

0.727

9780

23964

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

0.727

9781

24105

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

Series expansion around \(x=0\).

0.727

9782

478

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

Series expansion around \(x=0\).

0.728

9783

479

\begin{align*} 6 x^{2} y^{\prime \prime }+7 x y^{\prime }-\left (x^{2}+2\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.728

9784

2251

\begin{align*} y_{1}^{\prime }&=3 y_{1}+2 y_{2}-2 y_{3} \\ y_{2}^{\prime }&=-2 y_{1}+7 y_{2}-2 y_{3} \\ y_{3}^{\prime }&=-10 y_{1}+10 y_{2}-5 y_{3} \\ \end{align*}

0.728

9785

18647

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

0.728

9786

22188

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

Series expansion around \(x=2\).

0.728

9787

22849

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

Series expansion around \(x=0\).

0.728

9788

26438

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

0.728

9789

2281

\begin{align*} y_{1}^{\prime }&=-y_{1}-12 y_{2}+8 y_{3} \\ y_{2}^{\prime }&=y_{1}-9 y_{2}+4 y_{3} \\ y_{3}^{\prime }&=y_{1}-6 y_{2}+y_{3} \\ \end{align*}

0.729

9790

11610

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

0.729

9791

15482

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

0.729

9792

18665

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

0.729

9793

21659

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+3 x y^{\prime }+y x&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}

Series expansion around \(x=0\).

0.729

9794

24749

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

0.729

9795

477

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

Series expansion around \(x=0\).

0.730

9796

2043

\begin{align*} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (-x^{2}+14\right ) y^{\prime }+2 \left (x^{2}+9\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.730

9797

3735

\begin{align*} y^{\prime \prime }-y&=10 \,{\mathrm e}^{2 x} \cos \left (x \right ) \\ \end{align*}

0.730

9798

3756

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

0.730

9799

3820

\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}+5 \,{\mathrm e}^{4 t} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}

0.730

9800

6865

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

0.730