2.3.141 Problems 14001 to 14100

Table 2.855: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14001

26459

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

1.415

14002

14320

\begin{align*} x^{\prime \prime }+3025 x&=\cos \left (45 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.416

14003

18396

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

1.416

14004

27025

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} -2 & 0\le t <3 \\ 0 & 3\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.416

14005

6169

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

1.417

14006

21052

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

1.417

14007

3164

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

1.418

14008

5891

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

1.418

14009

17524

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

1.418

14010

18096

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

1.418

14011

21673

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

Series expansion around \(x=0\).

1.418

14012

25410

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

1.418

14013

26743

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

With initial conditions

\begin{align*} x \left (0\right ) &= -{\frac {7}{9}} \\ y \left (0\right ) &= -{\frac {5}{9}} \\ \end{align*}

1.418

14014

27009

\begin{align*} x^{2} y^{\prime \prime }+25 x y^{\prime }+144 y&=0 \\ y \left (1\right ) &= -4 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}

1.418

14015

7971

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

1.419

14016

25211

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

1.419

14017

5825

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

1.420

14018

650

\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}+7 x_{4} \\ x_{2}^{\prime }&=x_{1}+4 x_{2}+10 x_{3}+x_{4} \\ x_{3}^{\prime }&=x_{1}+10 x_{2}+4 x_{3}+x_{4} \\ x_{4}^{\prime }&=7 x_{1}+x_{2}+x_{3}+4 x_{4} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 3 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ x_{4} \left (0\right ) &= 3 \\ \end{align*}

1.421

14019

3865

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

1.421

14020

22943

\begin{align*} x^{\prime }+2 x-y&=100 \sin \left (t \right ) \\ y^{\prime }-4 x-y&=36 t \\ \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) &= -8 \\ y \left (0\right ) &= -21 \\ \end{align*}

1.421

14021

23954

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

1.421

14022

25400

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

1.421

14023

22926

\begin{align*} 3 x-y^{\prime }-2 y&=8 t \\ x^{\prime }-2 x+y&=16 \,{\mathrm e}^{-t} \\ \end{align*}

1.423

14024

25935

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

1.423

14025

14410

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

1.424

14026

15278

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

1.424

14027

23138

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

1.424

14028

649

\begin{align*} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4} \\ x_{3}^{\prime }&=5 x_{3} \\ x_{4}^{\prime }&=-21 x_{3}-2 x_{4} \\ \end{align*}

1.425

14029

3266

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

1.425

14030

17512

\begin{align*} y^{\prime \prime }+9 y&=\tan \left (3 t \right )^{2} \\ \end{align*}

1.425

14031

18244

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

1.425

14032

25932

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

1.425

14033

6548

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

1.426

14034

15306

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

Series expansion around \(x=0\).

1.426

14035

8046

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

1.428

14036

8975

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

1.428

14037

19788

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

1.428

14038

27375

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

1.429

14039

17845

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

1.430

14040

35

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

1.431

14041

8529

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

Series expansion around \(x=0\).

1.431

14042

17448

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=-32 t^{2} \cos \left (2 t \right ) \\ \end{align*}

1.431

14043

7553

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

1.432

14044

8049

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

1.432

14045

11304

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

1.432

14046

12852

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

1.432

14047

22942

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

1.432

14048

6289

\begin{align*} \left (-2 x^{2}+1\right ) y+4 x^{3} \left (2 x^{2}+1\right ) y^{\prime }+4 x^{6} y^{\prime \prime }&=0 \\ \end{align*}

1.434

14049

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*}

1.434

14050

14183

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

1.434

14051

16183

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

1.434

14052

19173

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

1.434

14053

21803

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

1.434

14054

22792

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

1.434

14055

24934

\begin{align*} y^{\prime \prime }&=6 \sin \left (3 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

1.434

14056

25658

\begin{align*} y^{\prime }+20 y&=24 \\ \end{align*}

1.434

14057

6366

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

1.435

14058

16249

\begin{align*} y^{\prime }-2 y&=-10 \\ y \left (0\right ) &= 8 \\ \end{align*}

1.435

14059

24434

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

1.435

14060

12658

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

1.436

14061

18148

\begin{align*} y^{\prime \prime }-7 y^{\prime }&=\left (x -1\right )^{2} \\ \end{align*}

1.436

14062

20985

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

1.436

14063

455

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

Series expansion around \(x=0\).

1.437

14064

8169

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

1.437

14065

8926

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

1.437

14066

9949

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (x^{2}+3\right ) y^{\prime }+6 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.437

14067

14751

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+\frac {8}{9}\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.437

14068

16713

\begin{align*} 16 y-7 x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

1.437

14069

17535

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

1.437

14070

20648

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

1.437

14071

21885

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

1.437

14072

1036

\begin{align*} x_{1}^{\prime }&=-x_{1}+x_{2}+x_{3}-2 x_{4} \\ x_{2}^{\prime }&=7 x_{1}-4 x_{2}-6 x_{3}+11 x_{4} \\ x_{3}^{\prime }&=5 x_{1}-x_{2}+x_{3}+3 x_{4} \\ x_{4}^{\prime }&=6 x_{1}-2 x_{2}-2 x_{3}+6 x_{4} \\ \end{align*}

1.438

14073

14216

\begin{align*} Q^{\prime }&=\frac {Q}{4+Q^{2}} \\ \end{align*}

1.438

14074

21556

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

1.438

14075

25274

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

1.438

14076

25543

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

1.438

14077

9141

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

1.439

14078

11746

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

1.439

14079

15295

\begin{align*} x^{\prime }&=x+5 y+10 \sinh \left (t \right ) \\ y^{\prime }&=19 x-13 y+24 \sinh \left (t \right ) \\ \end{align*}

1.439

14080

6024

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

1.440

14081

6164

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

1.440

14082

11687

\begin{align*} {y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}}&=0 \\ \end{align*}

1.440

14083

27224

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

1.441

14084

27419

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

1.441

14085

4580

\begin{align*} x_{1}^{\prime }&=x_{1}-2 x_{2}-x_{3} \\ x_{2}^{\prime }&=-x_{1}+x_{2}+x_{3}+12 t \\ x_{3}^{\prime }&=x_{1}-x_{3} \\ \end{align*}

1.442

14086

13736

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

1.442

14087

15447

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

1.442

14088

24935

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

1.442

14089

27607

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

1.442

14090

5916

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

1.443

14091

23465

\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }-10 y&=x \ln \left (x \right ) \\ \end{align*}

1.443

14092

4579

\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{2}-x_{3}+6 \,{\mathrm e}^{-t} \\ x_{3}^{\prime }&=2 x_{1}-x_{2} \\ \end{align*}

1.444

14093

6075

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

1.444

14094

6242

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

1.444

14095

8996

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

Series expansion around \(x=0\).

1.444

14096

9407

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

Series expansion around \(x=0\).

1.444

14097

14239

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

1.444

14098

20026

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

1.444

14099

24436

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

1.444

14100

27042

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

With initial conditions

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

1.444