2.3.99 Problems 9801 to 9900

Table 2.729: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9801

14677

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

0.503

9802

14680

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

0.503

9803

15025

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

0.503

9804

15070

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

0.503

9805

15742

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

N/A

N/A

N/A

0.503

9806

18865

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

0.503

9807

20532

\begin{align*} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y&=x^{4}+2 x -5 \\ \end{align*}

0.503

9808

23144

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

0.503

9809

24767

\begin{align*} v^{\prime }-2 v+2 w^{\prime }&=2-4 \,{\mathrm e}^{2 x} \\ 2 v^{\prime }-3 v+3 w^{\prime }-w&=0 \\ \end{align*}

0.503

9810

25194

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

0.503

9811

148

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

0.504

9812

2038

\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*}
Series expansion around \(x=0\).

0.504

9813

2040

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }+\left (12 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.504

9814

2427

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

0.504

9815

2609

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=t^{{3}/{2}} {\mathrm e}^{3 t} \\ \end{align*}

0.504

9816

3858

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

0.504

9817

5549

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

0.504

9818

9449

\begin{align*} y^{\prime \prime }+3 y^{\prime }-2 y&=-6 \,{\mathrm e}^{\pi -t} \\ y \left (\pi \right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 4 \\ \end{align*}
Using Laplace transform method.

0.504

9819

9576

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

0.504

9820

9839

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

0.504

9821

14644

\begin{align*} y^{\prime \prime }-8 y^{\prime }+15 y&=9 x \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}

0.504

9822

15744

\(\left [\begin {array}{ccc} 7 & -1 & 6 \\ -10 & 4 & -12 \\ -2 & 1 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.504

9823

17766

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

0.504

9824

17808

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

0.504

9825

21743

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

0.504

9826

25157

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

0.504

9827

25472

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

0.504

9828

25561

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

0.504

9829

25570

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

0.504

9830

7622

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

0.505

9831

9511

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

0.505

9832

10137

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

0.505

9833

10183

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

0.505

9834

10211

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

0.505

9835

15687

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y&=36 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \\ \end{align*}

0.505

9836

16927

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

0.505

9837

18831

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

0.505

9838

19498

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=20 \,{\mathrm e}^{-2 x} \\ \end{align*}

0.505

9839

20420

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

0.505

9840

21297

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

0.505

9841

22074

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

0.505

9842

22708

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

0.505

9843

25522

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{i \omega t} \\ \end{align*}

0.505

9844

3489

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

0.506

9845

4228

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

0.506

9846

5945

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

0.506

9847

8553

\begin{align*} y^{\prime \prime } x +y^{\prime }-7 x^{3} y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.506

9848

9725

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

0.506

9849

10268

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

0.506

9850

13666

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

0.506

9851

14172

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

0.506

9852

14392

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

0.506

9853

15257

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

0.506

9854

16060

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

0.506

9855

17774

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

0.506

9856

18200

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

0.506

9857

19194

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

0.506

9858

20463

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

0.506

9859

22176

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

0.506

9860

24637

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

0.506

9861

25196

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

0.506

9862

369

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

0.507

9863

882

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

0.507

9864

1900

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

0.507

9865

2037

\begin{align*} 4 x^{2} \left (4 x^{2}+1\right ) y^{\prime \prime }+32 x^{3} y^{\prime }+y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.507

9866

2161

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime }&=-16 \,{\mathrm e}^{-2 x} \left (-x^{3}+x^{2}+x +1\right ) \\ \end{align*}

0.507

9867

2749

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

0.507

9868

3321

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

0.507

9869

6095

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

0.507

9870

8007

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

0.507

9871

9842

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

0.507

9872

13150

\(\left [\begin {array}{ccc} 2 & 0 & 0 \\ 2 & -2 & -1 \\ -2 & 6 & 3 \end {array}\right ]\)

N/A

N/A

N/A

0.507

9873

14110

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

0.507

9874

15307

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

0.507

9875

15459

\begin{align*} x^{\prime }&=-4 x-10 y \\ y^{\prime }&=x-2 y \\ \end{align*}

0.507

9876

17098

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

0.507

9877

17450

\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=-648 t^{2} {\mathrm e}^{5 t} \\ \end{align*}

0.507

9878

17752

\begin{align*} y^{\prime \prime }-9 y&=\frac {1}{1+{\mathrm e}^{3 t}} \\ \end{align*}

0.507

9879

19515

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

0.507

9880

21246

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

0.507

9881

22792

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

0.507

9882

22923

\begin{align*} x^{\prime }+2 y&=4 \,{\mathrm e}^{2 t} \\ x+y^{\prime }-y&=2 \,{\mathrm e}^{2 t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 7 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.507

9883

22976

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

0.507

9884

24917

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

0.507

9885

3752

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=4 \,{\mathrm e}^{3 x} \sec \left (2 x \right )^{2} \\ \end{align*}

0.508

9886

12654

\begin{align*} y^{\prime \prime }&=\frac {\left (7 a \,x^{2}+5\right ) y^{\prime }}{x \left (a \,x^{2}+1\right )}-\frac {\left (15 a \,x^{2}+5\right ) y}{x^{2} \left (a \,x^{2}+1\right )} \\ \end{align*}

0.508

9887

19245

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

0.508

9888

19566

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

0.508

9889

19777

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

0.508

9890

22507

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

0.508

9891

1292

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

0.509

9892

1344

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

0.509

9893

4473

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

0.509

9894

6159

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

0.509

9895

6518

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

0.509

9896

8854

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}-8 \\ x_{2}^{\prime }&=x_{1}+x_{2}+3 \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}

0.509

9897

10062

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

0.509

9898

14645

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=4 x \,{\mathrm e}^{-3 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

0.509

9899

15395

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

0.509

9900

16739

\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=25 \sin \left (3 x \right ) \\ \end{align*}

0.509