Problems 201 to 300

Table 2.7: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

201	$e^{y} + \cos (x) y + (x e^{y} + \sin (x)) y^{'} = 0$	[_exact]	✓	40.201

202	$9 x^{2} y^{2} + x^{3 / 2} y^{'} = y^{2}$	[_separable]	✓	1.764

203	$2 y + (x + 1) y^{'} = 3 x + 3$	[_linear]	✓	1.487

204	$9 \sqrt{x} y^{4 / 3} - 12 x^{1 / 5} y^{3 / 2} + (8 x^{3 / 2} y^{1 / 3} - 15 x^{6 / 5} \sqrt{y}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _exact, _rational]	✓	36.710

205	$3 y + y^{4} x^{3} + 3 y^{'} x = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.255

206	$y^{'} x + y = 2 e^{2 x}$	[_linear]	✓	1.117

207	$(2 x + 1) y^{'} + y = {(2 x + 1)}^{3 / 2}$	[_linear]	✓	3.937

208	$y^{'} = \sqrt{x + y}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.986

209	$y^{'} = 3 (y + 7) x^{2}$	[_separable]	✓	1.111

210	$y^{'} = x y^{3} - x y$	[_separable]	✓	3.738

211	$y^{'} = - \frac{3 x^{2} + 2 y^{2}}{4 x y}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	79.629

212	$y^{'} = \frac{x + 3 y}{y - 3 x}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.202

213	$y^{'} = \frac{2 x y + 2 x}{x^{2} + 1}$	[_separable]	✓	1.249

214	$y^{'} = \frac{\sqrt{y} - y}{\tan (x)}$	[_separable]	✓	9.981

215	$y^{''} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.582

216	$y^{''} - 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.564

217	$y^{''} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.863

218	$y^{''} + 25 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	20.122

219	$y^{''} - 3 y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.538

220	$y^{''} + y^{'} - 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.587

221	$y^{''} + y^{'} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.558

222	$y^{''} - 3 y^{'} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.795

223	$y^{''} + 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.658

224	$y^{''} - 10 y^{'} + 25 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.668

225	$y^{''} - 2 y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.665

226	$y^{''} + 6 y^{'} + 13 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.821

227	$x^{2} y^{''} - 2 y^{'} x + 2 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.776

228	$x^{2} y^{''} + 2 y^{'} x - 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.010

229	$x^{2} y^{''} - y^{'} x + y = 0$ i.c.	[[_Emden, _Fowler]]	✓	1.531

230	$x^{2} y^{''} + y^{'} x + y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.347

231	$y^{'} + y^{2} = 0$	[_quadrature]	✓	1.441

232	$y y^{''} = 6 x^{4}$	[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]	✗	0.246

233	$y y^{''} + {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	1.191

234	$y^{''} - 3 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.330

235	$y^{''} + 2 y^{'} - 15 y = 0$	[[_2nd_order, _missing_x]]	✓	0.339

236	$y^{''} + 5 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	1.062

237	$2 y^{''} + 3 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	1.203

238	$2 y^{''} - y^{'} - y = 0$	[[_2nd_order, _missing_x]]	✓	0.356

239	$4 y^{''} + 8 y^{'} + 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.340

240	$4 y^{''} + 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.467

241	$9 y^{''} - 12 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.391

242	$6 y^{''} - 7 y^{'} - 20 y = 0$	[[_2nd_order, _missing_x]]	✓	0.377

243	$35 y^{''} - y^{'} - 12 y = 0$	[[_2nd_order, _missing_x]]	✓	0.361

244	$x^{2} y^{''} + y^{'} x - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.120

245	$x^{2} y^{''} + 2 y^{'} x - 12 y = 0$	[[_Emden, _Fowler]]	✓	0.689

246	$4 x^{2} y^{''} + 8 y^{'} x - 3 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.828

247	$x^{2} y^{''} + y^{'} x = 0$	[[_2nd_order, _missing_y]]	✓	0.562

248	$x^{2} y^{''} - 3 y^{'} x + 4 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.965

249	$y^{'''} + 2 y^{''} - y^{'} - 2 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.132

250	$y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.141

251	$y^{'''} - 3 y^{''} + 3 y^{'} - y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.136

252	$y^{'''} - 5 y^{''} + 8 y^{'} - 4 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.143

253	$y^{'''} + 9 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.102

254	$y^{'''} - 3 y^{''} + 4 y^{'} - 2 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.112

255	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 y^{'} x - 6 y = 0$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓	0.192

256	$x^{3} y^{'''} + 6 x^{2} y^{''} + 4 y^{'} x - 4 y = 0$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓	0.250

257	$y^{''} + y = 3 x$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.749

258	$y^{''} - 4 y = 12$ i.c.	[[_2nd_order, _missing_x]]	✓	2.602

259	$y^{''} - 2 y^{'} - 3 y = 6$ i.c.	[[_2nd_order, _missing_x]]	✓	0.653

260	$y^{''} - 2 y^{'} + 2 y = 2 x$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.900

261	$y^{''} + 2 y = 6 x + 4$	[[_2nd_order, _with_linear_symmetries]]	✓	0.622

262	$x^{2} y^{''} - 2 y^{'} x + 2 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.017

263	$y^{''} - 2 y^{'} - 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.680

264	$x^{2} y^{''} + y^{'} x - 9 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.135

265	$4 y^{''} - 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.178

266	$x^{2} y^{''} - x (x + 2) y^{'} + (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.164

267	$(x + 1) y^{''} - (x + 2) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.152

268	$(- x^{2} + 1) y^{''} + 2 y^{'} x - 2 y = 0$	[_Gegenbauer]	✓	0.160

269	$(- x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[_Gegenbauer]	✓	0.172

270	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.139

271	$y^{''} - 4 y = 0$	[[_2nd_order, _missing_x]]	✓	1.469

272	$2 y^{''} - 3 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	1.012

273	$y^{''} + y^{'} - 10 y = 0$	[[_2nd_order, _missing_x]]	✓	0.391

274	$2 y^{''} - 7 y^{'} + 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.347

275	$y^{''} + 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.352

276	$y^{''} + 5 y^{'} + 5 y = 0$	[[_2nd_order, _missing_x]]	✓	0.410

277	$4 y^{''} - 12 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.417

278	$y^{''} - 6 y^{'} + 13 y = 0$	[[_2nd_order, _missing_x]]	✓	0.511

279	$y^{''} + 8 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓	0.473

280	$5 y^{''''} + 3 y^{'''} = 0$	[[_high_order, _missing_x]]	✓	0.075

281	$y^{''''} - 8 y^{'''} + 16 y^{''} = 0$	[[_high_order, _missing_x]]	✓	0.083

282	$y^{''''} - 3 y^{'''} + 3 y^{''} - y^{'} = 0$	[[_high_order, _missing_x]]	✓	0.078

283	$9 y^{'''} + 12 y^{''} + 4 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.082

284	$y^{''''} + 3 y^{''} - 4 y = 0$	[[_high_order, _missing_x]]	✓	0.088

285	$y^{''''} - 8 y^{''} + 16 y = 0$	[[_high_order, _missing_x]]	✓	0.092

286	$y^{''''} + 18 y^{''} + 81 y = 0$	[[_high_order, _missing_x]]	✓	0.103

287	$6 y^{''''} + 11 y^{''} + 4 y = 0$	[[_high_order, _missing_x]]	✓	0.096

288	$y^{''''} = 16 y$	[[_high_order, _missing_x]]	✓	0.095

289	$y^{'''} + y^{''} - y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.074

290	$y^{''''} + 2 y^{'''} + 3 y^{''} + 2 y^{'} + y = 0$	[[_high_order, _missing_x]]	✓	0.110

291	$y^{''} - 4 y^{'} + 3 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.538

292	$9 y^{''} + 6 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.873

293	$y^{''} - 6 y^{'} + 25 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.731

294	$2 y^{'''} - 3 y^{''} - 2 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.146

295	$3 y^{'''} + 2 y^{''} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.125

296	$y^{'''} + 10 y^{''} + 25 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.146

297	$y^{'''} + 3 y^{''} - 4 y = 0$	[[_3rd_order, _missing_x]]	✓	0.081

298	$2 y^{'''} - y^{''} - 5 y^{'} - 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.085

299	$y^{'''} + 27 y = 0$	[[_3rd_order, _missing_x]]	✓	0.097

300	$y^{''''} - y^{'''} + y^{''} - 3 y^{'} - 6 y = 0$	[[_high_order, _missing_x]]	✓	0.094

2.2.3 Problems 201 to 300