2.3.99 Problems 9801 to 9900

Table 2.741: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9801

7656

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

0.665

9802

9840

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

0.665

9803

12378

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

0.665

9804

12493

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

0.665

9805

12889

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

0.665

9806

14303

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

0.665

9807

17232

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

0.665

9808

17897

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

0.665

9809

21470

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

0.665

9810

23070

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

0.665

9811

1991

\begin{align*} 6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.666

9812

16019

\begin{align*} x^{\prime }&=-\frac {9 x}{10}-2 y \\ y^{\prime }&=x+\frac {11 y}{10} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.666

9813

21630

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

0.666

9814

22154

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

0.666

9815

22279

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=x_{3} \\ x_{3}^{\prime }&=6 t \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 12 \\ \end{align*}

0.666

9816

23530

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

0.666

9817

23535

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

0.666

9818

25197

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

0.666

9819

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*}

0.667

9820

4473

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

0.667

9821

7378

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

0.667

9822

10158

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

0.667

9823

14299

\begin{align*} x^{\prime \prime }+x^{\prime }+x&=5 \sin \left (7 t \right ) \\ \end{align*}

0.667

9824

17502

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=\frac {{\mathrm e}^{-4 t}}{t^{4}} \\ \end{align*}

0.667

9825

20516

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

0.667

9826

2199

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=4 \,{\mathrm e}^{-x} \left (1-6 x \right )-2 \cos \left (x \right ) x +2 \left (x +1\right ) \sin \left (x \right ) \\ \end{align*}

0.668

9827

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*}

0.668

9828

7381

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

0.668

9829

8656

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=25 t -100 \delta \left (t -\pi \right ) \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}
Using Laplace transform method.

0.668

9830

14601

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

0.668

9831

14917

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

0.668

9832

18640

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

0.668

9833

18826

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

0.668

9834

23075

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

0.668

9835

1844

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

0.669

9836

2421

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

0.669

9837

7796

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

0.669

9838

8407

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

0.669

9839

14098

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

0.669

9840

19269

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

0.669

9841

20513

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

0.669

9842

22809

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}
Using Laplace transform method.

0.669

9843

1845

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

0.670

9844

3501

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

0.670

9845

5774

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

0.670

9846

5892

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

0.670

9847

5893

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

0.670

9848

6184

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

0.670

9849

6273

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

0.670

9850

10289

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

0.670

9851

16086

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

0.670

9852

18721

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

0.670

9853

23074

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

0.670

9854

3361

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

0.671

9855

3362

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

0.671

9856

3381

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

0.671

9857

9665

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

0.671

9858

14716

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

0.671

9859

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*}

0.671

9860

17030

\begin{align*} y^{\prime \prime }+4 y&=t \\ y \left (\frac {\pi }{4}\right ) &= 1 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= \frac {\pi }{16} \\ \end{align*}

0.671

9861

17501

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

0.671

9862

22501

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

0.671

9863

26041

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

0.671

9864

2799

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

0.672

9865

2805

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

0.672

9866

6498

\begin{align*} x y y^{\prime \prime }&=y \left (\operatorname {a2} +\operatorname {a3} y^{2}\right )+x \left (\operatorname {a0} +\operatorname {a1} y^{4}\right )-y y^{\prime }+x {y^{\prime }}^{2} \\ \end{align*}

0.672

9867

9464

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

0.672

9868

9793

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

0.672

9869

16352

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

0.672

9870

19650

\begin{align*} x^{\prime }&=x+y-5 t +2 \\ y^{\prime }&=4 x-2 y-8 t -8 \\ \end{align*}

0.672

9871

20714

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

0.672

9872

21584

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

0.672

9873

24738

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

0.672

9874

25041

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

0.672

9875

2016

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

0.673

9876

4532

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

0.673

9877

10062

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

0.673

9878

16620

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

0.673

9879

18450

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

0.673

9880

3584

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

0.674

9881

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*}

0.674

9882

10222

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

0.674

9883

11828

\begin{align*} 16 y^{2} {y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\ \end{align*}

0.674

9884

14688

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

0.674

9885

15313

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

0.674

9886

15964

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

0.674

9887

16081

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&={\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.674

9888

24464

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

0.674

9889

24735

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

0.674

9890

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*}

0.675

9891

1994

\begin{align*} 8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.675

9892

3358

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

0.675

9893

5391

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

0.675

9894

5728

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

0.675

9895

6176

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

0.675

9896

8844

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

0.675

9897

8994

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

0.675

9898

9526

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

0.675

9899

12455

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

0.675

9900

12896

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

0.675