Problems 6301 to 6400

Table 2.129: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

6301	$y^{'} = \frac{y}{x} + 2 x + 1$	[_linear]	✓	1.354

6302	$r^{'} + r \tan (θ) = \sec (θ)$	[_linear]	✓	1.745

6303	$x y^{'} + 2 y = \frac{1}{x^{3}}$	[_linear]	✓	1.522

6304	$t + y + 1 - y^{'} = 0$	[[_linear, ‘class A‘]]	✓	1.272

6305	$y^{'} = x^{2} e^{- 4 x} - 4 y$	[[_linear, ‘class A‘]]	✓	1.791

6306	$y x^{'} + 2 x = 5 y^{3}$	[_linear]	✓	1.627

6307	$x y^{'} + 3 x^{2} + 3 y = \frac{\sin (x)}{x}$	[_linear]	✓	1.894

6308	$(x^{2} + 1) y^{'} + x y - x = 0$	[_separable]	✓	1.846

6309	$(- x^{2} + 1) y^{'} - x^{2} y = (x + 1) \sqrt{- x^{2} + 1}$	[_linear]	✓	3.398

6310	$y^{'} - \frac{y}{x} = x e^{x}$ i.c.	[_linear]	✓	1.749

6311	$y^{'} + 4 y - e^{- x} = 0$ i.c.	[[_linear, ‘class A‘]]	✓	1.725

6312	$t^{2} x^{'} + 3 t x = t^{4} \ln (t) + 1$ i.c.	[_linear]	✓	1.718

6313	$y^{'} + \frac{3 y}{x} + 2 = 3 x$ i.c.	[_linear]	✓	1.817

6314	$\cos (x) y^{'} + y \sin (x) = 2 x \cos {(x)}^{2}$ i.c.	[_linear]	✓	3.490

6315	$\sin (x) y^{'} + y \cos (x) = x \sin (x)$ i.c.	[_linear]	✓	2.852

6316	$y^{'} + y \sqrt{1 + \sin {(x)}^{2}} = x$ i.c.	[_linear]	✗	741.593

6317	$(e^{4 y} + 2 x) y^{'} - 1 = 0$	[[_1st_order, _with_exponential_symmetries]]	✓	4.872

6318	$y^{'} + 2 y = \frac{x}{y^{2}}$	[_rational, _Bernoulli]	✓	1.644

6319	$y^{'} + \frac{3 y}{x} = x^{2}$	[_linear]	✓	1.738

6320	$x^{'} = α - β \cos (\frac{π t}{12}) - k x$ i.c.	[[_linear, ‘class A‘]]	✓	2.082

6321	$u^{'} = α (1 - u) - β u$	[_quadrature]	✓	1.149

6322	$x^{2} y + x^{4} \cos (x) - x^{3} y^{'} = 0$	[_linear]	✓	1.659

6323	$x^{10 / 3} - 2 y + x y^{'} = 0$	[_linear]	✓	1.664

6324	$\sqrt{- 2 y - y^{2}} + (- x^{2} + 2 x + 3) y^{'} = 0$	[_separable]	✓	13.676

6325	$y e^{x y} + 2 x + (x e^{x y} - 2 y) y^{'} = 0$	[_exact]	✓	0.384

6326	$y^{'} + x y = 0$	[_separable]	✓	0.283

6327	$y^{2} + (2 x y + \cos (y)) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	0.330

6328	$2 x + y \cos (x y) + (x \cos (x y) - 2 y) y^{'} = 0$	[_exact]	✓	0.451

6329	$θ r^{'} + 3 r - θ - 1 = 0$	[_linear]	✓	0.280

6330	$2 x y + 3 + (x^{2} - 1) y^{'} = 0$	[_linear]	✓	0.269

6331	$2 x + y + (x - 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	0.496

6332	$\cos (x) \cos (y) + 2 x - (\sin (x) \sin (y) + 2 y) y^{'} = 0$	[_exact]	✓	7.833

6333	$e^{t} (- t + y) + (1 + e^{t}) y^{'} = 0$	[_linear]	✓	0.288

6334	$\frac{t y^{'}}{y} + 1 + \ln (y) = 0$	[_separable]	✓	0.329

6335	$\cos (θ) r^{'} - r \sin (θ) + e^{θ} = 0$	[_linear]	✓	0.303

6336	$y e^{x y} - \frac{1}{y} + (x e^{x y} + \frac{x}{y^{2}}) y^{'} = 0$	[_exact]	✓	0.350

6337	$\frac{1}{y} - (3 y - \frac{x}{y^{2}}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	0.292

6338	$2 x + y^{2} - \cos (x + y) + (2 x y - \cos (x + y) - e^{y}) y^{'} = 0$	[_exact]	✓	38.029

6339	$y^{'} = \frac{e^{x + y}}{y - 1}$	[_separable]	✓	2.539

6340	$y^{'} - 4 y = 32 x^{2}$	[[_linear, ‘class A‘]]	✓	1.323

6341	$(x^{2} - \frac{2}{y^{3}}) y^{'} + 2 x y - 3 x^{2} = 0$	[_exact, _rational]	✓	2.050

6342	$y^{'} + \frac{3 y}{x} = x^{2} - 4 x + 3$	[_linear]	✓	1.971

6343	$2 x y^{3} - (- x^{2} + 1) y^{'} = 0$	[_separable]	✓	3.459

6344	$t^{3} y^{2} + \frac{t^{4} y^{'}}{y^{6}} = 0$	[_separable]	✓	1.692

6345	$(x + 1) y^{''} - x^{2} y^{'} + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.414

6346	$x^{2} y^{''} + 3 y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.145

6347	$(x^{2} - 2) y^{''} + 2 y^{'} + y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.738

6348	$(x^{2} + x) y^{''} + 3 y^{'} - 6 x y = 0$	[[_Emden, _Fowler]]	✓	1.370

6349	$(t^{2} - t - 2) x^{''} + (t + 1) x^{'} - (t - 2) x = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.546

6350	$(x^{2} - 1) y^{''} + (1 - x) y^{'} + (x^{2} - 2 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.440

6351	$\sin (x) y^{''} + y \cos (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.575

6352	$e^{x} y^{''} - (x^{2} - 1) y^{'} + 2 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.805

6353	$\sin (x) y^{''} - y \ln (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	6.130

6354	$y^{'} + (x + 2) y = 0$	[_separable]	✓	0.462

6355	$y^{'} - y = 0$	[_quadrature]	✓	0.323

6356	$z^{'} - x^{2} z = 0$	[_separable]	✓	0.415

6357	$(x^{2} + 1) y^{''} + y = 0$	[[_Emden, _Fowler]]	✓	0.361

6358	$y^{''} + (- 1 + x) y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.380

6359	$y^{''} - 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.519

6360	$w^{''} - x^{2} w^{'} + w = 0$	[_Lienard]	✓	0.393

6361	$(2 x - 3) y^{''} - x y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.391

6362	$(x + 1) y^{''} - 3 x y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.498

6363	$y^{''} - x y^{'} - 3 y = 0$	[_Hermite]	✓	0.429

6364	$(x^{2} + x + 1) y^{''} - 3 y = 0$	[[_Emden, _Fowler]]	✓	0.477

6365	$(x^{2} - 5 x + 6) y^{''} - 3 x y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.467

6366	$y^{''} - \tan (x) y^{'} + y = 0$	[_Lienard]	✓	1.833

6367	$(x^{3} + 1) y^{''} - x y^{'} + 2 x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.662

6368	$y^{'} + 2 (- 1 + x) y = 0$	[_separable]	✓	0.462

6369	$y^{'} - 2 x y = 0$	[_separable]	✓	0.485

6370	$(x^{2} - 2 x) y^{''} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.416

6371	$x^{2} y^{''} - x y^{'} + 2 y = 0$	[[_Emden, _Fowler]]	✓	0.457

6372	$x^{2} y^{''} - y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.493

6373	$y^{''} + (3 x - 1) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.434

6374	$x^{'} + \sin (t) x = 0$ i.c.	[_separable]	✓	0.563

6375	$y^{'} - y e^{x} = 0$ i.c.	[_separable]	✓	0.571

6376	$(x^{2} + 1) y^{''} - e^{x} y^{'} + y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.747

6377	$y^{''} + t y^{'} + e^{t} y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.521

6378	$y^{''} - e^{2 x} y^{'} + y \cos (x) = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	1.038

6379	$y^{'} - x y = \sin (x)$	[_linear]	✓	0.510

6380	$w^{'} + w x = e^{x}$	[_linear]	✓	0.485

6381	$z^{''} + x z^{'} + z = x^{2} + 2 x + 1$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	0.391

6382	$y^{''} - 2 x y^{'} + 3 y = x^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.362

6383	$(x^{2} + 1) y^{''} - x y^{'} + y = \cos (x)$	[[_2nd_order, _with_linear_symmetries]]	✓	0.542

6384	$y^{''} - x y^{'} + 2 y = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.397

6385	$(- x^{2} + 1) y^{''} - y^{'} + y = \tan (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.490

6386	$y^{''} - y \sin (x) = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.590

6387	$(- x^{2} + 1) y^{''} - 2 x y^{'} + n (n + 1) y = 0$	[_Gegenbauer]	✓	0.588

6388	$x^{''} - ω^{2} x = 0$	[[_2nd_order, _missing_x]]	✓	1.649

6389	$x^{'''} - x^{''} + x^{'} - x = 0$	[[_3rd_order, _missing_x]]	✓	0.054

6390	$x^{''} + 42 x^{'} + x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.285

6391	$x^{''''} + x = 0$	[[_high_order, _missing_x]]	✓	0.069

6392	$x^{'''} - 3 x^{''} - 9 x^{'} - 5 x = 0$	[[_3rd_order, _missing_x]]	✓	0.056

6393	$x^{''} + 2 γ x^{'} + ω_{0} x = F \cos (ω t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	83.747

6394	$y^{''} - y^{'} - 2 y = e^{2 x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	1.770

6395	$y^{''} - 2 y^{'} + y = 2 \cos (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.876

6396	$y^{''} + 16 y = 16 \cos (4 x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.226

6397	$y^{''} - y = \cosh (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.538

6398	$y^{'} - y = e^{2 x}$	[[_linear, ‘class A‘]]	✓	1.345

6399	$x^{2} y^{'} + 2 x y - x + 1 = 0$ i.c.	[_linear]	✓	1.714

6400	$y^{'} + y = {(x + 1)}^{2}$ i.c.	[[_linear, ‘class A‘]]	✓	1.612

2.2.64 Problems 6301 to 6400