2.3.3 Problems 201 to 300

Table 2.537: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

201

12776

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

0.034

202

12788

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

0.034

203

13116

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

0.034

204

13128

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

0.034

205

14165

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

0.034

206

18709

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

0.034

207

18712

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

0.034

208

18971

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

0.034

209

18980

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

0.034

210

6661

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

0.035

211

6713

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

0.035

212

6769

\begin{align*} -a^{2} y+12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

0.035

213

6794

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

0.035

214

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*}

0.035

215

12801

\begin{align*} x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime }-\lambda ^{2} y&=0 \\ \end{align*}

0.035

216

12828

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

0.035

217

12833

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

0.035

218

13120

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

0.035

219

16444

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

0.035

220

16468

\begin{align*} x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y&=0 \\ \end{align*}

0.035

221

18717

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

0.035

222

18967

\begin{align*} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y&=\cos \left (t \right ) \\ \end{align*}

0.035

223

20196

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

0.035

224

20534

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

0.035

225

20810

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

0.035

226

22894

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

0.035

227

23434

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

0.035

228

23469

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

0.035

229

2789

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

0.036

230

2792

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

0.036

231

2793

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

0.036

232

3702

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

0.036

233

3794

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

0.036

234

6626

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

0.036

235

6683

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

0.036

236

10047

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

0.036

237

12715

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

0.036

238

12731

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

0.036

239

12747

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

0.036

240

12755

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

0.036

241

12767

\begin{align*} -12 y+3 \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}

0.036

242

12768

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

0.036

243

12799

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

0.036

244

13043

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

0.036

245

13078

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

0.036

246

13079

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

0.036

247

13118

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

0.036

248

13119

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

0.036

249

13123

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

0.036

250

14166

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

0.036

251

14346

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

0.036

252

18402

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

0.036

253

18403

\begin{align*} x_{1}^{\prime }&={\mathrm e}^{t -x_{1}} \\ x_{2}^{\prime }&=2 \,{\mathrm e}^{x_{1}} \\ \end{align*}

0.036

254

18407

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

0.036

255

18426

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

0.036

256

18975

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

0.036

257

18981

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

0.036

258

21001

\begin{align*} w_{1}^{\prime }&=w_{2} \\ w_{2}^{\prime }&=\frac {a w_{1}}{z^{2}} \\ \end{align*}

0.036

259

22671

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

0.036

260

22673

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

0.036

261

23246

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

0.036

262

288

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

0.037

263

416

\begin{align*} x^{2} y^{\prime }+y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.037

264

608

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

0.037

265

2816

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

0.037

266

6618

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

0.037

267

6635

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

0.037

268

6658

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

0.037

269

6660

\begin{align*} -8 a x y-2 \left (-4 x^{2}-2 a +1\right ) y^{\prime }-6 y^{\prime \prime } x +y^{\prime \prime \prime }&=0 \\ \end{align*}

0.037

270

6680

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

0.037

271

8760

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime } x +4 x^{2} y^{\prime }+8 x^{3} y&=0 \\ \end{align*}

0.037

272

10381

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

0.037

273

12714

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

0.037

274

12722

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime } x +2 \left (4 x^{2}+2 a -1\right ) y^{\prime }-8 a x y&=0 \\ \end{align*}

0.037

275

12751

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

0.037

276

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*}

0.037

277

12795

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

0.037

278

12796

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

0.037

279

13047

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

0.037

280

14173

\begin{align*} x^{2} y^{\prime \prime \prime }-5 y^{\prime \prime } x +\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y&=0 \\ \end{align*}

0.037

281

16971

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

0.037

282

17540

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

0.037

283

18143

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

0.037

284

20992

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

0.037

285

22631

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

0.037

286

23472

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

0.037

287

25247

\begin{align*} t y^{\prime \prime \prime }+3 y^{\prime \prime }+t y^{\prime }+y&=0 \\ \end{align*}
Using Laplace transform method.

0.037

288

2814

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

0.038

289

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*}

0.038

290

6631

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

0.038

291

6706

\begin{align*} -2 \left (x^{2}+4\right ) y+x \left (x^{2}+8\right ) y^{\prime }-4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}

0.038

292

6723

\begin{align*} \left (a -x \right )^{3} \left (b -x \right )^{3} y^{\prime \prime \prime }&=c y \\ \end{align*}

0.038

293

12744

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

0.038

294

12822

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

0.038

295

13087

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

0.038

296

13117

\begin{align*} x^{\prime }&=x \left (a \left (p x+q y\right )+\alpha \right ) \\ y^{\prime }&=y \left (\beta +b \left (p x+q y\right )\right ) \\ \end{align*}

0.038

297

19223

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

0.038

298

20609

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

0.038

299

21238

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

0.038

300

22292

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

0.038