2.3.133 Problems 13201 to 13300

Table 2.839: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13201

25399

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

1.214

13202

26660

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

1.214

13203

14769

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

Series expansion around \(x=0\).

1.215

13204

20006

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

1.215

13205

1514

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

Using Laplace transform method.

1.216

13206

4185

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

Series expansion around \(x=0\).

1.216

13207

5933

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

1.216

13208

8974

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

1.216

13209

3804

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

1.217

13210

9548

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

Series expansion around \(x=0\).

1.217

13211

9565

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

1.217

13212

9783

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

1.217

13213

21152

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

1.217

13214

26655

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

1.217

13215

27379

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

1.217

13216

3586

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

1.218

13217

10145

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

1.218

13218

14989

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

With initial conditions

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

1.218

13219

21330

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

1.218

13220

8353

\begin{align*} q^{\prime }&=k \left (q-70\right ) \\ \end{align*}

1.219

13221

26108

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

1.219

13222

27536

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

1.219

13223

9573

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

1.220

13224

12356

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

1.220

13225

18414

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

1.220

13226

19431

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

1.220

13227

20541

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

1.220

13228

24834

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

1.220

13229

6248

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

1.221

13230

16570

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*}

1.221

13231

3446

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

1.222

13232

9563

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

1.222

13233

9574

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

1.222

13234

27004

\begin{align*} x^{2} y^{\prime \prime }+25 x y^{\prime }+144 y&=0 \\ \end{align*}

1.222

13235

7151

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

1.223

13236

15325

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

Using Laplace transform method.

1.223

13237

18995

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 7 \\ x_{2} \left (0\right ) &= 5 \\ x_{3} \left (0\right ) &= 5 \\ \end{align*}

1.223

13238

315

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

1.224

13239

8592

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

Series expansion around \(x=0\).

1.224

13240

20621

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

1.224

13241

21932

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

1.224

13242

13063

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

1.225

13243

23021

\begin{align*} 9 y^{\prime \prime }+49 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

1.225

13244

2445

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

Series expansion around \(t=0\).

1.226

13245

3888

\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=6 x_{2}-7 x_{3}+3 x_{4} \\ x_{3}^{\prime }&=3 x_{3}-x_{4} \\ x_{4}^{\prime }&=-4 x_{2}+9 x_{3}-3 x_{4} \\ \end{align*}

1.226

13246

17329

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

1.226

13247

26922

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

1.226

13248

3977

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

Using Laplace transform method.

1.227

13249

7815

\begin{align*} y^{\prime \prime }-7 y^{\prime }&=-3 \\ \end{align*}

1.227

13250

9001

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

Series expansion around \(x=0\).

1.227

13251

9570

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y&=0 \\ \end{align*}

1.227

13252

12444

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

1.227

13253

13675

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

1.227

13254

15097

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

1.227

13255

22815

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

Using Laplace transform method.

1.227

13256

26076

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

1.227

13257

26921

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

1.227

13258

14107

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

1.228

13259

14191

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

1.228

13260

15083

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

1.228

13261

26170

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

1.228

13262

15867

\begin{align*} y^{\prime }&=y^{2}-4 y-12 \\ y \left (0\right ) &= 5 \\ \end{align*}

1.229

13263

18081

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

1.229

13264

18893

\begin{align*} y^{\prime \prime \prime \prime }-6 y&=t \,{\mathrm e}^{-t} \\ 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 ) &= 9 \\ \end{align*}

Using Laplace transform method.

1.229

13265

9356

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

1.230

13266

11719

\begin{align*} \left (\operatorname {a2} x +\operatorname {c2} \right ) {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {a0} x +\operatorname {b0} y+\operatorname {c0}&=0 \\ \end{align*}

1.230

13267

21564

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

1.230

13268

22217

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

Series expansion around \(x=0\).

1.230

13269

2864

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

1.231

13270

6597

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

1.231

13271

12424

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

1.231

13272

20890

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

Series expansion around \(x=0\).

1.231

13273

11892

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

1.232

13274

18881

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

1.232

13275

1512

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

Using Laplace transform method.

1.233

13276

2640

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

Series expansion around \(t=0\).

1.233

13277

6340

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

1.233

13278

8182

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

1.233

13279

22711

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

1.233

13280

25087

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

1.233

13281

2373

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

1.234

13282

5821

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

1.234

13283

9544

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

Series expansion around \(x=0\).

1.234

13284

18786

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

1.234

13285

19424

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

1.234

13286

23619

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

1.234

13287

1354

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

1.235

13288

4376

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

1.235

13289

21023

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

1.235

13290

21678

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

Series expansion around \(x=0\).

1.235

13291

21265

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

1.236

13292

21522

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

1.236

13293

4010

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

Series expansion around \(x=0\).

1.237

13294

8773

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

1.237

13295

19889

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

1.237

13296

24798

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

1.237

13297

25530

\begin{align*} y^{\prime \prime }&={\mathrm e}^{i \omega t} \\ \end{align*}

1.237

13298

26669

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

1.237

13299

10273

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

1.238

13300

20605

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

1.238