2.3.3 Problems 201 to 300

Table 2.579: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

201

14171

\begin{align*} 2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 {y^{\prime }}^{2} x^{2}+36 x y y^{\prime }+6 y^{2}&=0 \\ \end{align*}

0.044

202

16932

\begin{align*} x^{\prime } t +2 x&=15 y \\ t y^{\prime }&=x \\ \end{align*}

0.044

203

18631

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

0.044

204

21316

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

0.044

205

22907

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

With initial conditions

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

0.044

206

22908

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

With initial conditions

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

0.044

207

23469

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

0.044

208

25144

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

0.044

209

26107

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

0.044

210

949

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

0.045

211

3071

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

0.045

212

7054

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\ \end{align*}

0.045

213

8153

\begin{align*} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\ \end{align*}

0.045

214

12755

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

0.045

215

12789

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

0.045

216

13046

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

0.045

217

13100

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

0.045

218

13133

\begin{align*} x^{\prime }&=\frac {x^{2}}{2}-\frac {y}{24} \\ y^{\prime }&=2 x y-3 z \\ z^{\prime }&=3 x z-\frac {y^{2}}{6} \\ \end{align*}

0.045

219

13135

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

0.045

220

15739

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

With initial conditions

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

0.045

221

19175

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

0.045

222

26771

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

0.045

223

938

\begin{align*} 9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime }&=0 \\ \end{align*}

0.046

224

3090

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

0.046

225

7053

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

0.046

226

7057

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

0.046

227

9486

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

With initial conditions

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

0.046

228

12717

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

0.046

229

12729

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

0.046

230

12749

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

0.046

231

12753

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

0.046

232

12757

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

0.046

233

13084

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

0.046

234

13086

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

0.046

235

13130

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

0.046

236

17540

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

0.046

237

18439

\begin{align*} x^{\prime }&=-4 x-2 y+\frac {2}{{\mathrm e}^{t}-1} \\ y^{\prime }&=6 x+3 y-\frac {3}{{\mathrm e}^{t}-1} \\ \end{align*}

0.046

238

21250

\begin{align*} x^{\prime }&=2 x-7 x y-a x \\ y^{\prime }&=-y+4 x y-a y \\ \end{align*}

0.046

239

21252

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

0.046

240

23275

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

0.046

241

23365

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

With initial conditions

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

0.046

242

23566

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

0.046

243

25387

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

With initial conditions

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

0.046

244

25392

\begin{align*} y_{1}^{\prime }&=\frac {y_{1}}{t}+1 \\ y_{2}^{\prime }&=\frac {y_{2}}{t}+t \\ \end{align*}

With initial conditions

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

0.046

245

26136

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

0.046

246

26794

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

0.046

247

951

\begin{align*} y^{\prime \prime \prime }+27 y&=0 \\ \end{align*}

0.047

248

1058

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

Series expansion around \(x=0\).

0.047

249

2795

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

0.047

250

3072

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}

0.047

251

3078

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

0.047

252

7046

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

0.047

253

7271

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

0.047

254

8054

\begin{align*} \left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y&=8 \\ \end{align*}

0.047

255

12774

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

0.047

256

13099

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

0.047

257

20155

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

0.047

258

21237

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

0.047

259

22911

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

With initial conditions

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

0.047

260

23309

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

0.047

261

23436

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

Series expansion around \(x=0\).

0.047

262

3073

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }-17 y^{\prime }+60 y&=0 \\ \end{align*}

0.048

263

3074

\begin{align*} y^{\prime \prime \prime }-9 y^{\prime \prime }+23 y^{\prime }-15 y&=0 \\ \end{align*}

0.048

264

12725

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

0.048

265

12770

\begin{align*} x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (4 x +2\right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-4 \left (1+3 x \right ) y&=0 \\ \end{align*}

0.048

266

12833

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

0.048

267

13032

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

0.048

268

13112

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

0.048

269

13113

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

0.048

270

15114

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

0.048

271

19170

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

0.048

272

21235

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

0.048

273

22078

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

0.048

274

23557

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

With initial conditions

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

0.048

275

23818

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

0.048

276

25649

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

0.048

277

297

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

0.049

278

604

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

0.049

279

936

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

0.049

280

943

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

0.049

281

1464

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

0.049

282

1471

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

0.049

283

2121

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

0.049

284

3067

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

0.049

285

3068

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y&=0 \\ \end{align*}

0.049

286

3089

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

0.049

287

3093

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

0.049

288

3823

\begin{align*} x_{1}^{\prime }&=-\tan \left (t \right ) x_{1}+3 \cos \left (t \right )^{2} \\ x_{2}^{\prime }&=x_{1}+\tan \left (t \right ) x_{2}+2 \sin \left (t \right ) \\ \end{align*}

With initial conditions

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

0.049

289

7067

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

0.049

290

12711

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

0.049

291

12716

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

0.049

292

12718

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

0.049

293

12739

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

0.049

294

12748

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

0.049

295

12772

\begin{align*} x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-4 \left (3 x^{2}+1\right ) y&=0 \\ \end{align*}

0.049

296

12796

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

0.049

297

15734

\begin{align*} y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\ y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \\ \end{align*}

With initial conditions

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

0.049

298

15737

\begin{align*} y_{1}^{\prime }&=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\ y_{2}^{\prime }&=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \\ \end{align*}

With initial conditions

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

0.049

299

18423

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

0.049

300

19181

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

0.049