2.3.69 Problems 6801 to 6900

Table 2.669: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

6801

18636

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

0.349

6802

19024

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

0.349

6803

21993

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

0.349

6804

22648

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

0.349

6805

22834

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

0.349

6806

23483

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

0.349

6807

23929

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

0.349

6808

24636

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=18 \,{\mathrm e}^{-2 x} \cos \left (3 x \right ) \\ \end{align*}

0.349

6809

1092

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

0.350

6810

2618

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

0.350

6811

3629

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

0.350

6812

5783

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

0.350

6813

6504

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

0.350

6814

8131

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

0.350

6815

8842

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

0.350

6816

9273

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

0.350

6817

18391

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {y}{9}&=0 \\ \end{align*}

0.350

6818

18392

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

0.350

6819

18670

\begin{align*} x^{\prime }&=2 x-5 y \\ y^{\prime }&=x-2 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 2 \\ \end{align*}

0.350

6820

20167

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

0.350

6821

21707

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

0.350

6822

22221

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

0.350

6823

22650

\begin{align*} s^{\prime \prime }+16 s^{\prime }+64 s&=0 \\ s \left (0\right ) &= 0 \\ s^{\prime }\left (0\right ) &= -4 \\ \end{align*}

0.350

6824

23034

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

0.350

6825

24021

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

0.350

6826

24577

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

0.350

6827

25246

\begin{align*} t y^{\prime \prime }+2 y^{\prime }+9 t y&=0 \\ \end{align*}
Using Laplace transform method.

0.350

6828

25564

\begin{align*} y^{\prime \prime }+2 z \omega _{n} y^{\prime }+\omega _{n}^{2} y&={\mathrm e}^{c t} \\ \end{align*}

0.350

6829

322

\begin{align*} y^{\prime \prime }+16 y&={\mathrm e}^{3 x} \\ \end{align*}

0.351

6830

2257

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

0.351

6831

2393

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

0.351

6832

3817

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

0.351

6833

4174

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

0.351

6834

5770

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

0.351

6835

7378

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

0.351

6836

7651

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

0.351

6837

7997

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

0.351

6838

8385

\begin{align*} y^{\prime }&=\left (y-1\right )^{2} \\ y \left (0\right ) &= {\frac {101}{100}} \\ \end{align*}

0.351

6839

8635

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=50 t -100 \\ y \left (2\right ) &= -4 \\ y^{\prime }\left (2\right ) &= 14 \\ \end{align*}
Using Laplace transform method.

0.351

6840

8969

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

0.351

6841

9070

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

0.351

6842

10607

\begin{align*} 9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y&=0 \\ \end{align*}

0.351

6843

13194

\(\left [\begin {array}{ccc} -2 & 4 & -1 \\ -3 & 5 & -1 \\ -1 & 1 & 1 \end {array}\right ]\)

N/A

N/A

N/A

0.351

6844

14927

\begin{align*} 4 x^{\prime \prime }-20 x^{\prime }+21 x&=0 \\ x \left (0\right ) &= -4 \\ x^{\prime }\left (0\right ) &= -12 \\ \end{align*}

0.351

6845

14934

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

0.351

6846

14962

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

0.351

6847

16954

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

0.351

6848

17396

\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

0.351

6849

17641

\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-11 y^{\prime } x +16 y&=\frac {1}{x^{3}} \\ \end{align*}

0.351

6850

18283

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

0.351

6851

18858

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5}&=\cos \left (t w \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.351

6852

19019

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

0.351

6853

21120

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

0.351

6854

22698

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

0.351

6855

22819

\begin{align*} y^{\prime \prime }+y&=3 \delta \left (t -\pi \right ) \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.351

6856

23721

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

0.351

6857

24558

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

0.351

6858

1069

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.352

6859

1086

\begin{align*} \left (4 x^{2}+16 x +17\right ) y^{\prime \prime }&=8 y \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= 0 \\ \end{align*}
Series expansion around \(x=-2\).

0.352

6860

1382

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

0.352

6861

3186

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

0.352

6862

3818

\begin{align*} x_{1}^{\prime }&=2 x_{1}+5 x_{2} \\ x_{2}^{\prime }&=-x_{1}-2 x_{2} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}

0.352

6863

4068

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

0.352

6864

4162

\begin{align*} 25 y^{\prime \prime }-30 y^{\prime }+9 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}

0.352

6865

5792

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

0.352

6866

7345

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

0.352

6867

7999

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

0.352

6868

8492

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

0.352

6869

8866

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

0.352

6870

9499

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

0.352

6871

9675

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

0.352

6872

9787

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

0.352

6873

9805

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=12 x^{2} \\ \end{align*}

0.352

6874

13771

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

0.352

6875

13932

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

0.352

6876

14161

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

0.352

6877

14853

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

0.352

6878

15472

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

0.352

6879

16061

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

0.352

6880

16566

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

0.352

6881

16605

\begin{align*} y^{\prime \prime }+9 y&=52 \,{\mathrm e}^{2 x} \\ \end{align*}

0.352

6882

18114

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

0.352

6883

18199

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

0.352

6884

18429

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

0.352

6885

20943

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

0.352

6886

21774

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

0.352

6887

22206

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

0.352

6888

22272

\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=9 x+y \\ \end{align*}

0.352

6889

23515

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

0.352

6890

23978

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

0.352

6891

25558

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

0.352

6892

4158

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&=2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x} \\ \end{align*}

0.353

6893

6102

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

0.353

6894

6165

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

0.353

6895

8006

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

0.353

6896

8491

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

0.353

6897

9254

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

0.353

6898

10133

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

0.353

6899

20748

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

0.353

6900

20934

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

0.353