Problems 201 to 300

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


#	ODE	CAS classiﬁcation	Solved?	time (sec)

201	$e^{y} + y \cos (x) + (x e^{y} + \sin (x)) y^{'} = 0$	[_exact]	✓	38.623

202	$9 y^{2} x^{2} + x^{3 / 2} y^{'} = y^{2}$	[_separable]	✓	2.149

203	$2 y + (x + 1) y^{'} = 3 x + 3$	[_linear]	✓	2.075

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]	✓	37.398

205	$3 y + x^{3} y^{4} + 3 x y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.949

206	$x y^{'} + y = 2 e^{2 x}$	[_linear]	✓	1.306

207	$(2 x + 1) y^{'} + y = {(2 x + 1)}^{3 / 2}$	[_linear]	✓	4.616

208	$y^{'} = \sqrt{x + y}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.865

209	$y^{'} = 3 (y + 7) x^{2}$	[_separable]	✓	1.672

210	$y^{'} = x y^{3} - x y$	[_separable]	✓	4.427

211	$y^{'} = - \frac{3 x^{2} + 2 y^{2}}{4 x y}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	75.006

212	$y^{'} = \frac{x + 3 y}{y - 3 x}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.620

213	$y^{'} = \frac{2 x y + 2 x}{x^{2} + 1}$	[_separable]	✓	1.602

214	$y^{'} = \frac{\sqrt{y} - y}{\tan (x)}$	[_separable]	✓	8.595

215	$y^{''} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.214

216	$y^{''} - 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.520

217	$y^{''} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.302

218	$y^{''} + 25 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	18.688

219	$y^{''} - 3 y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.166

220	$y^{''} + y^{'} - 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.446

221	$y^{''} + y^{'} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.574

222	$y^{''} - 3 y^{'} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.541

223	$y^{''} + 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.377

224	$y^{''} - 10 y^{'} + 25 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.358

225	$y^{''} - 2 y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.161

226	$y^{''} + 6 y^{'} + 13 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.958

227	$x^{2} y^{''} - 2 x y^{'} + 2 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.869

228	$x^{2} y^{''} + 2 x y^{'} - 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.118

229	$x^{2} y^{''} - x y^{'} + y = 0$ i.c.	[[_Emden, _Fowler]]	✓	1.763

230	$x^{2} y^{''} + x y^{'} + y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.510

231	$y^{'} + y^{2} = 0$	[_quadrature]	✓	2.038

232	$y y^{''} = 6 x^{4}$	[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]	✗	0.118

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]]	✓	1.190

234	$y^{''} - 3 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.884

235	$y^{''} + 2 y^{'} - 15 y = 0$	[[_2nd_order, _missing_x]]	✓	0.917

236	$y^{''} + 5 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	2.010

237	$2 y^{''} + 3 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	2.099

238	$2 y^{''} - y^{'} - y = 0$	[[_2nd_order, _missing_x]]	✓	0.909

239	$4 y^{''} + 8 y^{'} + 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.935

240	$4 y^{''} + 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	1.029

241	$9 y^{''} - 12 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	1.007

242	$6 y^{''} - 7 y^{'} - 20 y = 0$	[[_2nd_order, _missing_x]]	✓	0.916

243	$35 y^{''} - y^{'} - 12 y = 0$	[[_2nd_order, _missing_x]]	✓	0.889

244	$x^{2} y^{''} + x y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.262

245	$x^{2} y^{''} + 2 x y^{'} - 12 y = 0$	[[_Emden, _Fowler]]	✓	0.778

246	$4 x^{2} y^{''} + 8 x y^{'} - 3 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.803

247	$x^{2} y^{''} + x y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.556

248	$x^{2} y^{''} - 3 x y^{'} + 4 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.972

249	$y^{'''} + 2 y^{''} - y^{'} - 2 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.135

250	$y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.139

251	$y^{'''} - 3 y^{''} + 3 y^{'} - y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.129

252	$y^{'''} - 5 y^{''} + 8 y^{'} - 4 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.132

253	$y^{'''} + 9 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.075

254	$y^{'''} - 3 y^{''} + 4 y^{'} - 2 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.085

255	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 x y^{'} - 6 y = 0$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓	0.177

256	$x^{3} y^{'''} + 6 x^{2} y^{''} + 4 x y^{'} - 4 y = 0$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓	0.206

257	$y^{''} + y = 3 x$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	2.259

258	$y^{''} - 4 y = 12$ i.c.	[[_2nd_order, _missing_x]]	✓	4.151

259	$y^{''} - 2 y^{'} - 3 y = 6$ i.c.	[[_2nd_order, _missing_x]]	✓	1.584

260	$y^{''} - 2 y^{'} + 2 y = 2 x$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	3.850

261	$y^{''} + 2 y = 6 x + 4$	[[_2nd_order, _with_linear_symmetries]]	✓	3.139

262	$x^{2} y^{''} - 2 x y^{'} + 2 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.012

263	$y^{''} - 2 y^{'} - 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.607

264	$x^{2} y^{''} + x y^{'} - 9 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.084

265	$4 y^{''} - 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.257

266	$x^{2} y^{''} - x (x + 2) y^{'} + (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.102

267	$(x + 1) y^{''} - (x + 2) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.109

268	$(- x^{2} + 1) y^{''} + 2 x y^{'} - 2 y = 0$	[_Gegenbauer]	✓	0.104

269	$(- x^{2} + 1) y^{''} - 2 x y^{'} + 2 y = 0$	[_Gegenbauer]	✓	0.108

270	$x^{2} y^{''} + x y^{'} + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.147

271	$y^{''} - 4 y = 0$	[[_2nd_order, _missing_x]]	✓	2.002

272	$2 y^{''} - 3 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	1.848

273	$y^{''} + y^{'} - 10 y = 0$	[[_2nd_order, _missing_x]]	✓	1.140

274	$2 y^{''} - 7 y^{'} + 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.876

275	$y^{''} + 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.982

276	$y^{''} + 5 y^{'} + 5 y = 0$	[[_2nd_order, _missing_x]]	✓	1.142

277	$4 y^{''} - 12 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.980

278	$y^{''} - 6 y^{'} + 13 y = 0$	[[_2nd_order, _missing_x]]	✓	2.639

279	$y^{''} + 8 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓	2.755

280	$5 y^{''''} + 3 y^{'''} = 0$	[[_high_order, _missing_x]]	✓	0.054

281	$y^{''''} - 8 y^{'''} + 16 y^{''} = 0$	[[_high_order, _missing_x]]	✓	0.055

282	$y^{''''} - 3 y^{'''} + 3 y^{''} - y^{'} = 0$	[[_high_order, _missing_x]]	✓	0.056

283	$9 y^{'''} + 12 y^{''} + 4 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.052

284	$y^{''''} + 3 y^{''} - 4 y = 0$	[[_high_order, _missing_x]]	✓	0.067

285	$y^{''''} - 8 y^{''} + 16 y = 0$	[[_high_order, _missing_x]]	✓	0.060

286	$y^{''''} + 18 y^{''} + 81 y = 0$	[[_high_order, _missing_x]]	✓	0.076

287	$6 y^{''''} + 11 y^{''} + 4 y = 0$	[[_high_order, _missing_x]]	✓	0.069

288	$y^{''''} = 16 y$	[[_high_order, _missing_x]]	✓	0.058

289	$y^{'''} + y^{''} - y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.053

290	$y^{''''} + 2 y^{'''} + 3 y^{''} + 2 y^{'} + y = 0$	[[_high_order, _missing_x]]	✓	0.083

291	$y^{''} - 4 y^{'} + 3 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.419

292	$9 y^{''} + 6 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.954

293	$y^{''} - 6 y^{'} + 25 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.654

294	$2 y^{'''} - 3 y^{''} - 2 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.129

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]]	✓	0.125

297	$y^{'''} + 3 y^{''} - 4 y = 0$	[[_3rd_order, _missing_x]]	✓	0.052

298	$2 y^{'''} - y^{''} - 5 y^{'} - 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.056

299	$y^{'''} + 27 y = 0$	[[_3rd_order, _missing_x]]	✓	0.063

300	$y^{''''} - y^{'''} + y^{''} - 3 y^{'} - 6 y = 0$	[[_high_order, _missing_x]]	✓	0.074

2.2.3 Problems 201 to 300