2.3.33 Problems 3201 to 3300

Table 2.639: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

3201

13193

\(\left [\begin {array}{ccc} 2 & -2 & 1 \\ -1 & 2 & 0 \\ -5 & 7 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.266

3202

17647

\begin{align*} x^{3} y^{\prime \prime \prime }+10 x^{2} y^{\prime \prime }-20 x y^{\prime }+20 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= -1 \\ y^{\prime \prime }\left (1\right ) &= 1 \\ \end{align*}

0.266

3203

20036

\begin{align*} y^{\prime \prime }+3 y^{\prime }-54 y&=0 \\ \end{align*}

0.266

3204

23009

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

0.266

3205

27041

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

With initial conditions

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

0.266

3206

414

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

Series expansion around \(x=0\).

0.267

3207

6602

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

0.267

3208

6605

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

0.267

3209

6766

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

0.267

3210

7041

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

0.267

3211

7269

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

0.267

3212

8507

\begin{align*} x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (5+x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.267

3213

10099

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

0.267

3214

10464

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y&=0 \\ \end{align*}

0.267

3215

10555

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align*}

0.267

3216

10772

\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ \end{align*}

0.267

3217

11065

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

0.267

3218

11110

\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y&=0 \\ \end{align*}

0.267

3219

18277

\begin{align*} y^{\prime \prime \prime \prime }-y&=8 \,{\mathrm e}^{x} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}

0.267

3220

20381

\begin{align*} {y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\ \end{align*}

0.267

3221

20382

\begin{align*} {y^{\prime }}^{2}-9 y^{\prime }+18&=0 \\ \end{align*}

0.267

3222

23017

\begin{align*} y^{\prime \prime }+8 y^{\prime }+4 y&=0 \\ \end{align*}

0.267

3223

24058

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

Using Laplace transform method.

0.267

3224

27104

\(\left [\begin {array}{cc} 4 & -2 \\ -2 & 1 \end {array}\right ]\)

N/A

N/A

N/A

0.267

3225

415

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

Series expansion around \(x=0\).

0.268

3226

1275

\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=0 \\ \end{align*}

0.268

3227

3945

\begin{align*} y^{\prime \prime }-9 y&=13 \sin \left (2 t \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

0.268

3228

10335

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

Using Laplace transform method.

0.268

3229

10569

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

0.268

3230

10928

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

0.268

3231

11236

\begin{align*} 2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y&=0 \\ \end{align*}

0.268

3232

14129

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

0.268

3233

14947

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

0.268

3234

26442

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

0.268

3235

27635

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

0.268

3236

27708

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

0.268

3237

2185

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+15 y&={\mathrm e}^{2 x} \left (15 x \cos \left (2 x \right )+32 \sin \left (2 x \right )\right ) \\ \end{align*}

0.269

3238

7259

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

0.269

3239

8065

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

0.269

3240

10152

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

0.269

3241

10533

\begin{align*} x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \\ \end{align*}

0.269

3242

10910

\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \\ \end{align*}

0.269

3243

11033

\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*}

0.269

3244

11101

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

0.269

3245

11107

\begin{align*} \left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y&=0 \\ \end{align*}

0.269

3246

14952

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

0.269

3247

16033

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

0.269

3248

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.

0.269

3249

831

\begin{align*} 6 y^{\prime \prime }-7 y^{\prime }-20 y&=0 \\ \end{align*}

0.270

3250

3059

\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=0 \\ \end{align*}

0.270

3251

3339

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

Series expansion around \(x=1\).

0.270

3252

4366

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

0.270

3253

10097

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

0.270

3254

10243

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

Series expansion around \(x=0\).

0.270

3255

10453

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

0.270

3256

10531

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

0.270

3257

10638

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

0.270

3258

11054

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y&=0 \\ \end{align*}

0.270

3259

11168

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

0.270

3260

14948

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

0.270

3261

15669

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

0.270

3262

15740

\(\left [\begin {array}{cc} -2 & -4 \\ 1 & 3 \end {array}\right ]\)

N/A

N/A

N/A

0.270

3263

16032

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

0.270

3264

17648

\begin{align*} x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+54 x y^{\prime }+42 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}

0.270

3265

18622

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

0.270

3266

20161

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

0.270

3267

22509

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

0.270

3268

23664

\begin{align*} y^{\prime \prime }+7 y^{\prime }+6 y&=250 \,{\mathrm e}^{t} \cos \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -7 \\ \end{align*}

Using Laplace transform method.

0.270

3269

26006

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

Series expansion around \(x=0\).

0.270

3270

26707

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

Series expansion around \(x=0\).

0.270

3271

459

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

Series expansion around \(x=0\).

0.271

3272

828

\begin{align*} 4 y^{\prime \prime }+8 y^{\prime }+3 y&=0 \\ \end{align*}

0.271

3273

3942

\begin{align*} y^{\prime \prime }+4 y&=10 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.271

3274

10100

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

0.271

3275

10102

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

0.271

3276

10677

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

0.271

3277

10678

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

0.271

3278

10791

\begin{align*} 16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y&=0 \\ \end{align*}

0.271

3279

10814

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

0.271

3280

11149

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

0.271

3281

14123

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

0.271

3282

19459

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

0.271

3283

1251

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

0.272

3284

10666

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

0.272

3285

10684

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

0.272

3286

10712

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y&=0 \\ \end{align*}

0.272

3287

10940

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

0.272

3288

11043

\begin{align*} 9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y&=0 \\ \end{align*}

0.272

3289

12594

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

0.272

3290

12804

\begin{align*} 6 x y^{\prime \prime }+6 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

0.272

3291

19464

\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

0.272

3292

19476

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

0.272

3293

549

\begin{align*} x^{\prime \prime \prime \prime }+8 x^{\prime \prime }+16 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ x^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

0.273

3294

1490

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

Using Laplace transform method.

0.273

3295

2293

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

0.273

3296

3946

\begin{align*} y^{\prime \prime }-y&=8 \sin \left (t \right )-6 \cos \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

Using Laplace transform method.

0.273

3297

3947

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=10 \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

Using Laplace transform method.

0.273

3298

7235

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

0.273

3299

7268

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

0.273

3300

7454

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

0.273