2.3.101 Problems 10001 to 10100

Table 2.775: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10001

995

\begin{align*} x_{1}^{\prime }&=-40 x_{1}-12 x_{2}+54 x_{3} \\ x_{2}^{\prime }&=35 x_{1}+13 x_{2}-46 x_{3} \\ x_{3}^{\prime }&=-25 x_{1}-7 x_{2}+34 x_{3} \\ \end{align*}

0.747

10002

3342

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

Series expansion around \(x=\frac {\pi }{2}\).

0.747

10003

4878

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

0.747

10004

5390

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

0.747

10005

9748

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

0.747

10006

14820

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

Using Laplace transform method.

0.747

10007

18448

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

0.747

10008

19517

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

0.747

10009

20349

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

0.747

10010

20854

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

0.747

10011

21154

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

0.747

10012

22753

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

0.747

10013

24746

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

0.747

10014

3692

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

0.748

10015

3753

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

0.748

10016

3766

\begin{align*} y^{\prime \prime }-9 y&=F \left (x \right ) \\ \end{align*}

0.748

10017

11379

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

0.748

10018

12878

\begin{align*} y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r}&=0 \\ \end{align*}

0.748

10019

14958

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

0.748

10020

20379

\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=24 x \cos \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 12 \\ \end{align*}

0.748

10021

21856

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

0.748

10022

23938

\begin{align*} y^{\prime }&=x^{2}+6 y+4 z \\ z^{\prime }&=y+3 z \\ \end{align*}

0.748

10023

26472

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

0.748

10024

482

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

Series expansion around \(x=0\).

0.749

10025

1826

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

0.749

10026

10373

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

0.749

10027

13771

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

0.749

10028

21148

\begin{align*} x^{\prime \prime }-4 x^{\prime }+3 x&=2 \,{\mathrm e}^{t}-5 \,{\mathrm e}^{2 t} \\ \end{align*}

0.749

10029

26439

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

0.749

10030

2051

\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*}

Series expansion around \(x=0\).

0.750

10031

3744

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=4 \,{\mathrm e}^{3 x} \ln \left (x \right ) \\ \end{align*}

0.750

10032

9271

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

0.750

10033

10220

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

Series expansion around \(x=0\).

0.750

10034

14934

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

0.750

10035

16122

\begin{align*} y^{\prime \prime }+6 y^{\prime }+20 y&=-3 \sin \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.750

10036

16926

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

Series expansion around \(x=0\).

0.750

10037

18703

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

0.750

10038

20397

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

0.750

10039

21468

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

0.750

10040

22749

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

0.750

10041

24098

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

Series expansion around \(x=0\).

0.750

10042

24763

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

0.750

10043

25381

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

With initial conditions

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

0.750

10044

25946

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

0.750

10045

986

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

0.751

10046

10046

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

0.751

10047

17218

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

0.751

10048

20345

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

0.751

10049

25524

\begin{align*} y^{\prime \prime }+100 y&=\cos \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.751

10050

2803

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

0.752

10051

5563

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

0.752

10052

10199

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

Series expansion around \(x=0\).

0.752

10053

15433

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

0.752

10054

17767

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

0.752

10055

22730

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

0.752

10056

22787

\begin{align*} r^{\prime \prime }-2 r&=-{\mathrm e}^{-2 t} \\ \end{align*}

0.752

10057

3293

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

0.753

10058

5647

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

0.753

10059

7197

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

Series expansion around \(x=0\).

0.753

10060

9858

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

Series expansion around \(x=1\).

0.753

10061

10366

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

0.753

10062

22644

\begin{align*} 4 i^{\prime \prime }-12 i^{\prime }+9 i&=0 \\ \end{align*}

0.753

10063

23730

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

Series expansion around \(x=0\).

0.753

10064

25580

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

0.753

10065

26066

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

0.753

10066

490

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

Series expansion around \(x=0\).

0.754

10067

1385

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

Series expansion around \(x=1\).

0.754

10068

2275

\begin{align*} y_{1}^{\prime }&=-5 y_{1}-y_{2}+11 y_{3} \\ y_{2}^{\prime }&=-7 y_{1}+y_{2}+13 y_{3} \\ y_{3}^{\prime }&=-4 y_{1}+8 y_{3} \\ \end{align*}

With initial conditions

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

0.754

10069

9525

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

Series expansion around \(x=0\).

0.754

10070

9593

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

Series expansion around \(x=0\).

0.754

10071

12585

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

0.754

10072

13240

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

0.754

10073

16760

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

Using Laplace transform method.

0.754

10074

17507

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

0.754

10075

18432

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

With initial conditions

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

0.754

10076

19040

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

0.754

10077

20638

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

0.754

10078

21650

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

Series expansion around \(x=0\).

0.754

10079

22613

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

0.754

10080

25334

\begin{align*} y^{\prime \prime }+\frac {t y^{\prime }}{-t^{2}+1}+\frac {y}{t +1}&=0 \\ \end{align*}

Series expansion around \(t=0\).

0.754

10081

27173

\begin{align*} x_{1}^{\prime }&=-2 x_{1}+x_{2} \\ x_{2}^{\prime }&=-4 x_{1}+3 x_{2}+10 \cos \left (t \right ) \\ \end{align*}

0.754

10082

4577

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

0.755

10083

7133

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

0.755

10084

7673

\begin{align*} y^{\prime \prime }+16 y&=16 \cos \left (4 x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.755

10085

8621

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

Series expansion around \(x=0\).

0.755

10086

16352

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

0.755

10087

22626

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

0.755

10088

23526

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

0.755

10089

25128

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

0.755

10090

3751

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=\frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4} \\ \end{align*}

0.756

10091

4576

\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}+27 t \\ x_{2}^{\prime }&=-x_{1}+4 x_{2} \\ \end{align*}

0.756

10092

7888

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

0.756

10093

9421

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

Series expansion around \(x=0\).

0.756

10094

10168

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

Series expansion around \(x=0\).

0.756

10095

10215

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

Series expansion around \(x=0\).

0.756

10096

16636

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=24 \sin \left (3 x \right ) \\ \end{align*}

0.756

10097

18446

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

With initial conditions

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

0.756

10098

18830

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

0.756

10099

20073

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

0.756

10100

22876

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

Series expansion around \(x=0\).

0.756