2.3.131 Problems 13001 to 13100

Table 2.835: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13001

9480

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

1.050

13002

16229

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

1.050

13003

21038

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

1.050

13004

17489

\begin{align*} y^{\prime \prime }+2 y^{\prime }+50 y&={\mathrm e}^{-t} \csc \left (7 t \right ) \\ \end{align*}

1.051

13005

3770

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

1.052

13006

9002

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

Series expansion around \(x=0\).

1.052

13007

9562

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

1.052

13008

22792

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

1.052

13009

26470

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

1.052

13010

7915

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

1.053

13011

9544

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

Series expansion around \(x=0\).

1.053

13012

10166

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

Series expansion around \(x=0\).

1.053

13013

12583

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

1.053

13014

16868

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

Series expansion around \(x=1\).

1.053

13015

22574

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

1.053

13016

2543

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

1.054

13017

9733

\begin{align*} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\ \end{align*}

1.054

13018

6399

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

1.055

13019

9879

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

Series expansion around \(x=0\).

1.055

13020

20945

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

With initial conditions

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

1.055

13021

21566

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

1.055

13022

3218

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

1.056

13023

3369

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

Series expansion around \(x=0\).

1.056

13024

8363

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

1.056

13025

8757

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

1.056

13026

9766

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

1.056

13027

12475

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

1.056

13028

15163

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

1.056

13029

17432

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

1.056

13030

19851

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

1.056

13031

20657

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

1.056

13032

20873

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

1.056

13033

21434

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

1.056

13034

23647

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

Using Laplace transform method.

1.056

13035

2645

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

Series expansion around \(t=0\).

1.057

13036

6117

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

1.057

13037

9563

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

1.057

13038

19757

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

1.057

13039

19863

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

1.057

13040

25682

\begin{align*} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=0 \\ \end{align*}

1.057

13041

2007

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.058

13042

2539

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

1.058

13043

6225

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

1.058

13044

9542

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

Series expansion around \(x=0\).

1.058

13045

25556

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

1.058

13046

1851

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

Series expansion around \(x=0\).

1.059

13047

3874

\begin{align*} x_{1}^{\prime }&=-x_{1}+2 x_{2}+54 t \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=-2 x_{1}+4 x_{2}+9 \,{\mathrm e}^{3 t} \\ \end{align*}

1.059

13048

9826

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

1.059

13049

9986

\begin{align*} x^{\prime }&=6 x-7 y+10 \\ y^{\prime }&=x-2 y-2 \,{\mathrm e}^{t} \\ \end{align*}

1.059

13050

13069

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

1.059

13051

6205

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

1.060

13052

10032

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

1.060

13053

12903

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

1.060

13054

17462

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=4 \\ y \left (0\right ) &= {\frac {5}{4}} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.060

13055

18867

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

1.060

13056

20515

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

1.060

13057

22776

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

1.060

13058

24579

\begin{align*} y^{\prime \prime }+9 y&=4 \cos \left (x \right ) \\ \end{align*}

1.060

13059

25583

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

1.060

13060

20513

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

1.061

13061

23578

\begin{align*} N_{1}^{\prime }&=4 N_{1}-6 N_{2} \\ N_{2}^{\prime }&=8 N_{1}-10 N_{2} \\ \end{align*}

With initial conditions

\begin{align*} N_{1} \left (0\right ) &= 100000 \\ N_{2} \left (0\right ) &= 1000 \\ \end{align*}

1.061

13062

2373

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

1.062

13063

4038

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

Series expansion around \(x=0\).

1.062

13064

9000

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

Series expansion around \(x=0\).

1.062

13065

9112

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

1.062

13066

12536

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

1.062

13067

16410

\begin{align*} -y^{\prime }+x y^{\prime \prime }&=6 x^{5} \\ \end{align*}

1.062

13068

18100

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

1.062

13069

20909

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

Series expansion around \(x=0\).

1.062

13070

24433

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= {\mathrm e}^{3} \\ \end{align*}

1.062

13071

27562

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

1.062

13072

2812

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

1.063

13073

3260

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

1.063

13074

6408

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

1.063

13075

7151

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

1.063

13076

8975

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

1.063

13077

17486

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

1.063

13078

23096

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

With initial conditions

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

1.063

13079

23458

\begin{align*} y^{\prime \prime }+9 y&=\cos \left (3 x \right )-\sin \left (3 x \right ) \\ \end{align*}

1.063

13080

25425

\begin{align*} y^{\prime }+y&=8 \,{\mathrm e}^{-3 t} \\ y \left (0\right ) &= 2 \\ \end{align*}

1.063

13081

3141

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

1.064

13082

9668

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

1.064

13083

15251

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y&=-t^{2}+2 t -10 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.064

13084

1125

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

1.065

13085

5939

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

1.065

13086

6536

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

1.065

13087

9749

\begin{align*} x^{6} {y^{\prime }}^{3}-3 x y^{\prime }-3 y&=0 \\ \end{align*}

1.065

13088

19666

\begin{align*} x^{\prime }&=b \,{\mathrm e}^{x} \\ x \left (0\right ) &= 1 \\ \end{align*}

1.065

13089

19874

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

1.065

13090

21459

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

1.065

13091

21563

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

1.065

13092

23277

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

1.065

13093

2189

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+32 y^{\prime \prime }+64 y^{\prime }+39 y&={\mathrm e}^{-2 x} \left (\left (4-15 x \right ) \cos \left (3 x \right )-\left (4+15 x \right ) \sin \left (3 x \right )\right ) \\ \end{align*}

1.066

13094

7799

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

1.066

13095

8987

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

Series expansion around \(x=1\).

1.066

13096

15469

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

1.066

13097

20176

\begin{align*} 3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+2\right ) y^{\prime }-4 y&=0 \\ \end{align*}

1.066

13098

23995

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

1.066

13099

24013

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

1.066

13100

24065

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{x}+{\mathrm e}^{2 x}+{\mathrm e}^{3 x} \\ \end{align*}

1.066