2.3.173 Problems 17201 to 17300

Table 2.919: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

17201

7686

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

2.194

17202

14703

\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y&=0 \\ \end{align*}

2.194

17203

21356

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

2.194

17204

1225

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

2.195

17205

8645

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\ y \left (\pi \right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 2 \,{\mathrm e}^{-\pi }-2 \\ \end{align*}

Using Laplace transform method.

2.195

17206

11320

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

2.195

17207

15113

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

2.195

17208

809

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

2.197

17209

4292

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

2.197

17210

16713

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

2.197

17211

19677

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

2.197

17212

4192

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

2.198

17213

14261

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

2.198

17214

22226

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

Series expansion around \(x=0\).

2.198

17215

20624

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

2.199

17216

3445

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

2.200

17217

15835

\begin{align*} v^{\prime }&=-\frac {v}{R C} \\ \end{align*}

2.200

17218

16276

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

2.200

17219

25108

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

2.200

17220

4755

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

2.201

17221

21078

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

2.201

17222

26458

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

2.201

17223

3316

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

2.202

17224

5493

\begin{align*} 16 x {y^{\prime }}^{2}+8 y y^{\prime }+y^{6}&=0 \\ \end{align*}

2.202

17225

16274

\begin{align*} y^{\prime } x +\left (2+5 x \right ) y&=\frac {20}{x} \\ \end{align*}

2.202

17226

19483

\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \\ \end{align*}

2.202

17227

16708

\begin{align*} y^{\prime \prime }+36 y&=0 \\ \end{align*}

2.203

17228

17179

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

2.203

17229

23550

\begin{align*} -3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=\frac {1}{x^{3}} \\ y \left (\frac {1}{4}\right ) &= 0 \\ y^{\prime }\left (\frac {1}{4}\right ) &= {\frac {14}{9}} \\ \end{align*}

2.203

17230

11684

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

2.204

17231

18034

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

2.204

17232

24187

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

2.204

17233

208

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

2.205

17234

26616

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

2.205

17235

21417

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

2.206

17236

1224

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

2.207

17237

17533

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

2.207

17238

19135

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

2.207

17239

15065

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

2.208

17240

748

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

2.210

17241

4637

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

2.210

17242

15395

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

2.210

17243

17521

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

2.210

17244

680

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

2.211

17245

1568

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

2.211

17246

2958

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

2.211

17247

3454

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

2.211

17248

16764

\begin{align*} y^{\prime \prime }+4 y&=3 \operatorname {Heaviside}\left (-2+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

Using Laplace transform method.

2.211

17249

21404

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

2.211

17250

22005

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

2.212

17251

26979

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

2.213

17252

20804

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

2.214

17253

25207

\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}

2.214

17254

23155

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

2.215

17255

10113

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

2.216

17256

34

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

2.217

17257

1171

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

2.217

17258

4293

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

2.217

17259

9888

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

2.217

17260

15501

\begin{align*} x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\ \end{align*}

2.217

17261

14491

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

2.218

17262

17394

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

2.218

17263

7566

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

2.220

17264

20503

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

2.220

17265

21849

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

2.220

17266

22507

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

2.220

17267

8510

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

Series expansion around \(x=0\).

2.221

17268

12866

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

2.221

17269

17968

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

2.221

17270

24196

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

2.221

17271

8879

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

2.222

17272

14274

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

2.223

17273

15407

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

2.223

17274

24913

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

2.223

17275

25498

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

2.223

17276

10117

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

2.224

17277

12865

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

2.224

17278

17662

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

2.226

17279

18549

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

2.226

17280

18880

\begin{align*} t^{2} y^{\prime \prime }+7 y^{\prime } t +5 y&=t \\ \end{align*}

2.226

17281

25672

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

2.226

17282

3779

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

2.227

17283

9628

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=\operatorname {Heaviside}\left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

2.227

17284

25448

\begin{align*} y^{\prime }-a y&=R \cos \left (\omega t -\phi \right ) \\ \end{align*}

2.227

17285

1238

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

2.228

17286

17187

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

2.228

17287

24219

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

2.228

17288

17667

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

2.229

17289

4711

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

2.230

17290

5650

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

2.230

17291

13658

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

2.231

17292

14967

\begin{align*} x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z&=0 \\ z \left (1\right ) &= 0 \\ z^{\prime }\left (1\right ) &= 5 \\ \end{align*}

2.231

17293

22001

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

2.231

17294

15604

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

2.232

17295

25810

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

2.233

17296

1612

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

2.234

17297

17469

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

2.234

17298

17973

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

2.234

17299

21345

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

2.234

17300

25208

\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5} \\ y \left (1\right ) &= -1 \\ y^{\prime }\left (1\right ) &= 3 \\ \end{align*}

2.234