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

6421

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

2.253

13002

9891

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

Series expansion around \(x=0\).

2.255

13003

25763

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=-12 x +8 \\ y \left (1\right ) &= -2 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*}

2.255

13004

4912

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

2.256

13005

5516

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

2.256

13006

9371

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

Series expansion around \(x=0\).

2.256

13007

3563

\begin{align*} y^{\prime \prime }-9 y&=0 \\ \end{align*}

2.257

13008

4296

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

2.257

13009

4776

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

2.257

13010

14164

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

2.257

13011

22843

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

Series expansion around \(x=0\).

2.257

13012

16696

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

2.259

13013

20501

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

2.259

13014

26561

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

2.259

13015

22707

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

2.260

13016

27676

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

2.260

13017

23094

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

With initial conditions

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

2.261

13018

27358

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

2.261

13019

9833

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

Series expansion around \(x=0\).

2.263

13020

13300

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

2.263

13021

23250

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

2.263

13022

24883

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

2.263

13023

4900

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

2.264

13024

9595

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

Series expansion around \(x=1\).

2.264

13025

14225

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

2.264

13026

20087

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

2.264

13027

25686

\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y&=10 \\ \end{align*}

2.264

13028

10249

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

Series expansion around \(x=0\).

2.265

13029

18161

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

2.266

13030

23659

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t}+5 t \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

Using Laplace transform method.

2.266

13031

25111

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}

2.266

13032

27634

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

2.266

13033

4051

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

Series expansion around \(x=0\).

2.267

13034

5978

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

2.267

13035

8220

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

2.267

13036

12644

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

2.267

13037

19150

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

2.267

13038

19524

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

2.267

13039

21559

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

2.268

13040

4919

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

2.269

13041

15889

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

2.269

13042

17802

\begin{align*} x^{\prime \prime }+16 x&=0 \\ x \left (0\right ) &= -2 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

2.269

13043

22621

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

2.269

13044

4216

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

2.270

13045

9840

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

Series expansion around \(x=0\).

2.270

13046

10340

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

Using Laplace transform method.

2.270

13047

13764

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

2.270

13048

21924

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

With initial conditions

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

2.270

13049

23627

\begin{align*} x^{\prime }&=-10 x+y+7 z \\ y^{\prime }&=-9 x+4 y+5 z \\ z^{\prime }&=-17 x+y+12 z \\ \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) &= 6 \\ y \left (0\right ) &= 1 \\ z \left (0\right ) &= 10 \\ \end{align*}

2.270

13050

25372

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

With initial conditions

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

2.270

13051

5009

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

2.271

13052

14047

\begin{align*} \left (2 y^{\prime } x -y\right )^{2}&=8 x^{3} \\ \end{align*}

2.271

13053

27587

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

2.271

13054

23663

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

Using Laplace transform method.

2.273

13055

26515

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

2.273

13056

22694

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

2.274

13057

1235

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

2.276

13058

9850

\begin{align*} 2 y^{\prime \prime }+9 y^{\prime } x -36 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

2.276

13059

24796

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

2.276

13060

9533

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

Series expansion around \(x=0\).

2.277

13061

19196

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

2.277

13062

23080

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

2.277

13063

25140

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

2.277

13064

8524

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

Series expansion around \(x=0\).

2.278

13065

10424

\begin{align*} 10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )}&=0 \\ \end{align*}

2.278

13066

18239

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

2.279

13067

1716

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

2.280

13068

7206

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

2.280

13069

11863

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

2.280

13070

12104

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

2.280

13071

14725

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

2.280

13072

21941

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

2.280

13073

24805

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

2.280

13074

11569

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

2.281

13075

16838

\begin{align*} 6 y-2 y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}

Series expansion around \(x=0\).

2.282

13076

9404

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

Series expansion around \(x=0\).

2.283

13077

21936

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

2.283

13078

25818

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

2.283

13079

10391

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

2.284

13080

5048

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

2.286

13081

7729

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

2.286

13082

15185

\begin{align*} y^{\prime \prime }+\left (5+2 x \right ) y^{\prime }+\left (4 x +8\right ) y&={\mathrm e}^{-2 x} \\ \end{align*}

2.286

13083

20505

\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 }&=4 x \\ \end{align*}

2.286

13084

99

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

2.287

13085

15764

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

2.287

13086

1294

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

2.288

13087

14693

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

2.288

13088

9890

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

Series expansion around \(x=0\).

2.289

13089

10027

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

2.289

13090

11307

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

2.289

13091

23633

\begin{align*} y^{\prime }-3 y&=13 \cos \left (2 t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*}

Using Laplace transform method.

2.289

13092

26513

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

2.289

13093

2534

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

2.290

13094

14132

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

2.290

13095

21144

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

2.290

13096

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*}

2.290

13097

10164

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

Series expansion around \(x=0\).

2.291

13098

16901

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

Series expansion around \(x=0\).

2.291

13099

8103

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

Series expansion around \(x=0\).

2.292

13100

15169

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

2.292