Problems 301 to 400

Table 2.9: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

301	$y^{'''} + 3 y^{''} + 4 y^{'} - 8 y = 0$	[[_3rd_order, _missing_x]]	✓	0.091

302	$y^{''''} + y^{'''} - 3 y^{''} - 5 y^{'} - 2 y = 0$	[[_high_order, _missing_x]]	✓	0.076

303	$y^{'''} + 3 y^{''} - 54 y = 0$	[[_3rd_order, _missing_x]]	✓	0.095

304	$3 y^{'''} - 2 y^{''} + 12 y^{'} - 8 y = 0$	[[_3rd_order, _missing_x]]	✓	0.095

305	$6 y^{''''} + 5 y^{'''} + 25 y^{''} + 20 y^{'} + 4 y = 0$	[[_high_order, _missing_x]]	✓	0.103

306	$9 y^{'''} + 11 y^{''} + 4 y^{'} - 14 y = 0$	[[_3rd_order, _missing_x]]	✓	0.098

307	$y^{''''} = y^{'''}$ i.c.	[[_high_order, _missing_x]]	✓	0.136

308	$y^{'''} - 5 y^{''} + 100 y^{'} - 500 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.119

309	$y^{''} + 2 i y^{'} + 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.380

310	$y^{''} - i y^{'} + 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.449

311	$y^{''} = (- 2 + 2 i \sqrt{3}) y$	[[_2nd_order, _missing_x]]	✓	2.117

312	$y^{'''} = y$ i.c.	[[_3rd_order, _missing_x]]	✓	0.170

313	$y^{''''} = y^{'''} + y^{''} + y^{'} + 2 y$ i.c.	[[_high_order, _missing_x]]	✓	0.114

314	$a x^{3} y^{'''} + b x^{2} y^{''} + c x y^{'} + d y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.560

315	$x^{2} y^{''} + y^{'} x + 9 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.959

316	$x^{2} y^{''} + 7 y^{'} x + 25 y = 0$	[[_Emden, _Fowler]]	✓	1.083

317	$x^{3} y^{'''} + 6 x^{2} y^{''} + 4 y^{'} x = 0$	[[_3rd_order, _missing_y]]	✓	0.151

318	$x^{3} y^{'''} - x^{2} y^{''} + y^{'} x = 0$	[[_3rd_order, _missing_y]]	✓	0.150

319	$x^{3} y^{'''} + 3 x^{2} y^{''} + y^{'} x = 0$	[[_3rd_order, _missing_y]]	✓	0.144

320	$x^{3} y^{'''} - 3 x^{2} y^{''} + y^{'} x = 0$	[[_3rd_order, _missing_y]]	✓	0.149

321	$x^{3} y^{'''} + 6 x^{2} y^{''} + 7 y^{'} x + y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	0.134

322	$y^{''} + 16 y = e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.609

323	$y^{''} - y^{'} + 2 y = 3 x + 4$	[[_2nd_order, _with_linear_symmetries]]	✓	0.723

324	$y^{''} - y^{'} - 6 y = 2 \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.596

325	$4 y^{''} + 4 y^{'} + y = 3 x e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.582

326	$y^{''} + y^{'} + y = \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.742

327	$2 y^{''} + 4 y^{'} + 7 y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.676

328	$y^{''} - 4 y = \sinh (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.775

329	$y^{''} - 4 y = \cosh (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.923

330	$y^{''} + 2 y^{'} - 3 y = 1 + x e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.616

331	$2 y^{''} + 9 y = 2 \cos (3 x) + 3 \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.934

332	$y^{'''} + 4 y^{'} = 3 x - 1$	[[_3rd_order, _missing_y]]	✓	0.143

333	$y^{'''} + y^{'} = 2 - \sin (x)$	[[_3rd_order, _missing_y]]	✓	0.506

334	$y^{''} + 2 y^{'} + 5 y = e^{x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.674

335	$y^{''''} - 2 y^{''} + y = x e^{x}$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.184

336	$y^{(5)} + 5 y^{''''} - y = 17$	[[_high_order, _missing_x]]	✓	0.161

337	$y^{''} + 9 y = 2 x^{2} e^{3 x} + 5$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.711

338	$y^{''} + y = \sin (x) + x \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.910

339	$y^{''''} - y^{''} + 4 y = e^{x} - x e^{2 x}$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.278

340	$y^{(5)} + 2 y^{'''} + 2 y^{''} = 3 x^{2} - 1$	[[_high_order, _missing_y]]	✓	0.217

341	$y^{'''} - y = e^{x} + 7$	[[_3rd_order, _with_linear_symmetries]]	✓	0.179

342	$y^{''} - 2 y^{'} + 2 y = e^{x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.663

343	$y^{(5)} - y^{'''} = e^{x} + 2 x^{2} - 5$	[[_high_order, _missing_y]]	✓	0.209

344	$y^{''} + 4 y = 3 x \cos (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.861

345	$y^{'''} - y^{''} - 12 y^{'} = x - 2 x e^{- 3 x}$	[[_3rd_order, _missing_y]]	✓	0.202

346	$y^{''} + 3 y^{'} + 2 y = x (e^{- x} - e^{- 2 x})$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.685

347	$y^{''} - 6 y^{'} + 13 y = x e^{3 x} \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.753

348	$y^{''''} + 5 y^{''} + 4 y = \sin (x) + \cos (2 x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	1.064

349	$y^{''''} + 9 y^{''} = (x^{2} + 1) \sin (3 x)$	[[_high_order, _missing_y]]	✓	0.724

350	$y^{''''} - 2 y^{''} + y = x^{2} \cos (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.227

351	$y^{''} + 4 y = 2 x$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.852

352	$y^{''} + 3 y^{'} + 2 y = e^{x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.685

353	$y^{''} + 9 y = \sin (2 x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.960

354	$y^{''} + y = \cos (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.886

355	$y^{''} - 2 y^{'} + 2 y = x + 1$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.895

356	$y^{''''} - 4 y^{''} = x^{2}$ i.c.	[[_high_order, _missing_y]]	✓	0.220

357	$y^{'''} - 2 y^{''} + y^{'} = 1 + x e^{x}$ i.c.	[[_3rd_order, _missing_y]]	✓	0.243

358	$y^{''} + 2 y^{'} + 2 y = \sin (3 x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.962

359	$y^{'''} + y^{''} = x + e^{- x}$ i.c.	[[_3rd_order, _missing_y]]	✓	0.225

360	$y^{''''} - y = 5$ i.c.	[[_high_order, _missing_x]]	✓	0.141

361	$y^{''''} - y^{'''} - y^{''} - y^{'} - 2 y = 8 x^{5}$ i.c.	[[_high_order, _linear, _nonhomogeneous]]	✓	0.173

362	$y^{''''} + 4 y = \cos {(x)}^{3}$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.226

363	$y^{''} + y^{'} + y = \sin (x) \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.005

364	$y^{''} + 9 y = \sin {(x)}^{4}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.201

365	$y^{''} + y = x \cos {(x)}^{3}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.384

366	$y^{''} + 3 y^{'} + 2 y = 4 e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.506

367	$y^{''} - 2 y^{'} - 8 y = 3 e^{- 2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.513

368	$y^{''} - 4 y^{'} + 4 y = 2 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.565

369	$y^{''} - 4 y = \sinh (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.913

370	$y^{''} + 4 y = \cos (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.698

371	$y^{''} + 9 y = \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.769

372	$y^{''} + 9 y = 2 \sec (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.101

373	$y^{''} + y = \csc {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.812

374	$y^{''} + 4 y = \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.818

375	$y^{''} - 4 y = x e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.565

376	$x^{2} y^{''} + y^{'} x - y = 72 x^{5}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.606

377	$x^{2} y^{''} - 4 y^{'} x + 6 y = x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.625

378	$x^{2} y^{''} - 3 y^{'} x + 4 y = x^{4}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.334

379	$4 x^{2} y^{''} - 4 y^{'} x + 3 y = 8 x^{4 / 3}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.647

380	$x^{2} y^{''} + y^{'} x + y = \ln (x)$	[[_2nd_order, _with_linear_symmetries]]	✓	1.545

381	$(x^{2} - 1) y^{''} - 2 y^{'} x + 2 y = x^{2} - 1$	[[_2nd_order, _with_linear_symmetries]]	✓	1.035

382	$y^{''} + y = 2 \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.674

383	$x^{''} + 9 x = 10 \cos (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.928

384	$x^{''} + 4 x = 5 \sin (3 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.038

385	$x^{''} + 100 x = 225 \cos (5 t) + 300 \sin (5 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.251

386	$x^{''} + 25 x = 90 \cos (4 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.949

387	$m x^{''} + k x = F_{0} \cos (ω t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.197

388	$x^{''} + 4 x^{'} + 4 x = 10 \cos (3 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.744

389	$x^{''} + 3 x^{'} + 5 x = - 4 \cos (5 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.777

390	$2 x^{''} + 2 x^{'} + x = 3 \sin (10 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.782

391	$x^{''} + 3 x^{'} + 3 x = 8 \cos (10 t) + 6 \sin (10 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.875

392	$x^{''} + 4 x^{'} + 5 x = 10 \cos (3 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.031

393	$x^{''} + 6 x^{'} + 13 x = 10 \sin (5 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.030

394	$x^{''} + 2 x^{'} + 26 x = 600 \cos (10 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.119

395	$x^{''} + 8 x^{'} + 25 x = 200 \cos (t) + 520 \sin (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.017

396	$x^{''} + 2 x^{'} + 2 x = 2 \cos (ω t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.684

397	$x^{''} + 4 x^{'} + 5 x = 10 \cos (ω t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.702

398	$x^{''} + 6 x^{'} + 45 x = 50 \cos (ω t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.705

399	$x^{''} + 10 x^{'} + 650 x = 100 \cos (ω t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.694

400	$y^{'} = y$	[_quadrature]	✓	0.261

2.2.4 Problems 301 to 400