2.3.69 Problems 6801 to 6900

Table 2.711: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

6801

18678

\begin{align*} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }&=a x+\frac {5 y}{4} \\ \end{align*}

0.851

6802

20853

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

0.851

6803

23324

\begin{align*} 2 y^{\prime \prime }+14 y^{\prime }+25 y&=0 \\ \end{align*}

0.851

6804

24777

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

0.851

6805

3815

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

0.852

6806

3998

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

Series expansion around \(x=0\).

0.852

6807

4018

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

Series expansion around \(x=0\).

0.852

6808

6584

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

0.852

6809

7987

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

0.852

6810

9071

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

0.852

6811

9367

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

Series expansion around \(x=0\).

0.852

6812

14861

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

0.852

6813

15970

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

0.852

6814

19562

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

0.852

6815

19836

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

0.852

6816

20703

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

0.852

6817

21537

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

0.852

6818

21912

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

Using Laplace transform method.

0.852

6819

22243

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

Using Laplace transform method.

0.852

6820

25142

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

0.852

6821

2528

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

0.853

6822

19026

\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2} \\ x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\ \end{align*}

0.853

6823

19266

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

0.853

6824

19877

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

0.853

6825

27575

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

0.853

6826

1441

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

With initial conditions

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

0.854

6827

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*}

0.854

6828

5317

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

0.854

6829

5465

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

0.854

6830

7214

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

0.854

6831

245

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

0.855

6832

14395

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

With initial conditions

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

0.855

6833

14854

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

0.855

6834

19428

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

0.855

6835

25251

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

0.855

6836

1344

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

0.856

6837

4388

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

0.856

6838

5718

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

0.856

6839

7281

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

0.856

6840

9355

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

Series expansion around \(x=0\).

0.856

6841

18028

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

0.856

6842

18861

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

0.856

6843

24663

\begin{align*} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }-8 y^{\prime \prime }&=48 \,{\mathrm e}^{2 x} \\ \end{align*}

0.856

6844

14990

\begin{align*} x^{\prime }&=8 x+14 y \\ y^{\prime }&=7 x+y \\ \end{align*}

With initial conditions

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

0.857

6845

15692

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

0.857

6846

502

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

Series expansion around \(x=0\).

0.858

6847

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.

0.858

6848

7790

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

0.858

6849

13934

\begin{align*} y^{\prime \prime }+a y^{\prime }+\left (b \,{\mathrm e}^{\lambda x}+c \right ) y&=0 \\ \end{align*}

0.858

6850

16790

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

Using Laplace transform method.

0.858

6851

18824

\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=16 \,{\mathrm e}^{\frac {t}{2}} \\ \end{align*}

0.858

6852

18863

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

0.858

6853

20915

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

Using Laplace transform method.

0.858

6854

21876

\begin{align*} 9 y^{\prime \prime }-30 y^{\prime }+25 y&=0 \\ \end{align*}

0.858

6855

5953

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

0.859

6856

6522

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

0.859

6857

8985

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime }+3 x^{2} y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.859

6858

12333

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

0.859

6859

14953

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

0.859

6860

18321

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

0.859

6861

25258

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

0.859

6862

3243

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

0.860

6863

3416

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

0.860

6864

3740

\begin{align*} y^{\prime \prime }-4 y&=100 \,{\mathrm e}^{x} \sin \left (x \right ) x \\ \end{align*}

0.860

6865

6407

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

0.860

6866

6417

\begin{align*} f \left (x \right )^{2} y^{\prime \prime }&=-24 f \left (x \right )^{4}+\left (3 f \left (x \right )^{3}-f \left (x \right )^{2} y+3 f \left (x \right ) f^{\prime }\left (x \right )\right ) y^{\prime } \\ \end{align*}

0.860

6867

15263

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

0.860

6868

19261

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

0.860

6869

24781

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

0.860

6870

2763

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

0.861

6871

3321

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

0.861

6872

7631

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

Series expansion around \(x=0\).

0.861

6873

7765

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=100 \sin \left (4 x \right ) \\ \end{align*}

0.861

6874

8629

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= {\frac {81}{10}} \\ y^{\prime }\left (0\right ) &= {\frac {39}{10}} \\ \end{align*}

Using Laplace transform method.

0.861

6875

18737

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

0.861

6876

26441

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

0.861

6877

26524

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

0.861

6878

921

\begin{align*} x^{\prime \prime }+8 x^{\prime }+25 x&=200 \cos \left (t \right )+520 \sin \left (t \right ) \\ x \left (0\right ) &= -30 \\ x^{\prime }\left (0\right ) &= -10 \\ \end{align*}

0.862

6879

1903

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

Series expansion around \(x=1\).

0.862

6880

2003

\begin{align*} x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (7 x^{2}+6 x +3\right ) y^{\prime }+\left (-3 x^{2}+6 x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.862

6881

2005

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

Series expansion around \(x=0\).

0.862

6882

3248

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

0.862

6883

3838

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

0.862

6884

6779

\begin{align*} \operatorname {A4} y+\operatorname {A3} x y^{\prime }+\operatorname {A2} \,x^{2} y^{\prime \prime }+\operatorname {A1} \,x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

0.862

6885

7049

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

0.862

6886

7787

\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=50 t^{3}-36 t^{2}-63 t +18 \\ \end{align*}

0.862

6887

9683

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

With initial conditions

\begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 5 \\ \end{align*}

0.862

6888

14658

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=x^{3}+x +{\mathrm e}^{-2 x} \\ \end{align*}

0.862

6889

14804

\(\left [\begin {array}{ccc} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end {array}\right ]\)

N/A

N/A

N/A

0.862

6890

18829

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

0.862

6891

20938

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

0.862

6892

22110

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

0.862

6893

2248

\begin{align*} y_{1}^{\prime }&=y_{1}-y_{2}+2 y_{3} \\ y_{2}^{\prime }&=12 y_{1}-4 y_{2}+10 y_{3} \\ y_{3}^{\prime }&=-6 y_{1}+y_{2}-7 y_{3} \\ \end{align*}

0.863

6894

12663

\begin{align*} y^{\prime \prime }&=\frac {y^{\prime }}{x}-\frac {a y}{x^{6}} \\ \end{align*}

0.863

6895

14398

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

0.863

6896

15442

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

0.863

6897

16672

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

0.863

6898

24012

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

0.863

6899

4512

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

0.864

6900

5980

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

0.864