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]	✓	0.967

6302	$r^{'} + r \tan (θ) = \sec (θ)$	[_linear]	✓	1.744

6303	$y^{'} x + 2 y = \frac{1}{x^{3}}$	[_linear]	✓	1.166

6304	$t + y + 1 - y^{'} = 0$	[[_linear, ‘class A‘]]	✓	0.990

6305	$y^{'} = x^{2} e^{- 4 x} - 4 y$	[[_linear, ‘class A‘]]	✓	1.601

6306	$y x^{'} + 2 x = 5 y^{3}$	[_linear]	✓	1.401

6307	$y^{'} x + 3 y + 3 x^{2} = \frac{\sin (x)}{x}$	[_linear]	✓	1.788

6308	$(x^{2} + 1) y^{'} + x y - x = 0$	[_separable]	✓	1.541

6309	$(- x^{2} + 1) y^{'} - x^{2} y = (x + 1) \sqrt{- x^{2} + 1}$	[_linear]	✓	3.049

6310	$y^{'} - \frac{y}{x} = x e^{x}$ i.c.	[_linear]	✓	1.347

6311	$y^{'} + 4 y - e^{- x} = 0$ i.c.	[[_linear, ‘class A‘]]	✓	1.396

6312	$t^{2} x^{'} + 3 t x = t^{4} \ln (t) + 1$ i.c.	[_linear]	✓	1.647

6313	$y^{'} + \frac{3 y}{x} + 2 = 3 x$ i.c.	[_linear]	✓	1.330

6314	$\cos (x) y^{'} + y \sin (x) = 2 x \cos {(x)}^{2}$ i.c.	[_linear]	✓	3.227

6315	$y^{'} \sin (x) + \cos (x) y = x \sin (x)$ i.c.	[_linear]	✓	2.552

6316	$y^{'} + y \sqrt{1 + \sin {(x)}^{2}} = x$ i.c.	[_linear]	✗	31.607

6317	$(e^{4 y} + 2 x) y^{'} - 1 = 0$	[[_1st_order, _with_exponential_symmetries]]	✓	5.078

6318	$2 y + y^{'} = \frac{x}{y^{2}}$	[_rational, _Bernoulli]	✓	1.563

6319	$y^{'} + \frac{3 y}{x} = x^{2}$	[_linear]	✓	1.322

6320	$x^{'} = α - β \cos (\frac{π t}{12}) - k x$ i.c.	[[_linear, ‘class A‘]]	✓	2.208

6321	$u^{'} = α (1 - u) - β u$	[_quadrature]	✓	1.012

6322	$x^{2} y + x^{4} \cos (x) - x^{3} y^{'} = 0$	[_linear]	✓	1.349

6323	$x^{10 / 3} - 2 y + y^{'} x = 0$	[_linear]	✓	1.431

6324	$\sqrt{- 2 y - y^{2}} + (- x^{2} + 2 x + 3) y^{'} = 0$	[_separable]	✓	3.068

6325	$y e^{x y} + 2 x + (x e^{x y} - 2 y) y^{'} = 0$	[_exact]	✓	0.278

6326	$y^{'} + x y = 0$	[_separable]	✓	0.229

6327	$y^{2} + (2 x y + \cos (y)) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	0.306

6328	$2 x + y \cos (x y) + (x \cos (x y) - 2 y) y^{'} = 0$	[_exact]	✓	0.316

6329	$θ r^{'} + 3 r - θ - 1 = 0$	[_linear]	✓	0.211

6330	$2 x y + 3 + (x^{2} - 1) y^{'} = 0$	[_linear]	✓	0.192

6331	$(x - 2 y) y^{'} + 2 x + y = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	0.438

6332	$\cos (x) \cos (y) + 2 x - (\sin (x) \sin (y) + 2 y) y^{'} = 0$	[_exact]	✓	7.303

6333	$e^{t} (y - t) + (1 + e^{t}) y^{'} = 0$	[_linear]	✓	0.221

6334	$\frac{t y^{'}}{y} + 1 + \ln (y) = 0$	[_separable]	✓	0.294

6335	$\cos (θ) r^{'} - r \sin (θ) + e^{θ} = 0$	[_linear]	✓	0.264

6336	$y e^{x y} - \frac{1}{y} + (x e^{x y} + \frac{x}{y^{2}}) y^{'} = 0$	[_exact]	✓	0.282

6337	$\frac{1}{y} - (3 y - \frac{x}{y^{2}}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	0.227

6338	$2 x + y^{2} - \cos (x + y) + (2 x y - \cos (x + y) - e^{y}) y^{'} = 0$	[_exact]	✓	38.894

6339	$y^{'} = \frac{e^{x + y}}{- 1 + y}$	[_separable]	✓	2.437

6340	$y^{'} - 4 y = 32 x^{2}$	[[_linear, ‘class A‘]]	✓	1.084

6341	$(x^{2} - \frac{2}{y^{3}}) y^{'} + 2 x y - 3 x^{2} = 0$	[_exact, _rational]	✓	1.837

6342	$y^{'} + \frac{3 y}{x} = x^{2} - 4 x + 3$	[_linear]	✓	1.779

6343	$2 x y^{3} - (- x^{2} + 1) y^{'} = 0$	[_separable]	✓	3.256

6344	$t^{3} y^{2} + \frac{t^{4} y^{'}}{y^{6}} = 0$	[_separable]	✓	1.419

6345	$(x + 1) y^{''} - x^{2} y^{'} + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.486

6346	$x^{2} y^{''} + 3 y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.203

6347	$(x^{2} - 2) y^{''} + 2 y^{'} + y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.622

6348	$(x^{2} + x) y^{''} + 3 y^{'} - 6 x y = 0$	[[_Emden, _Fowler]]	✓	1.537

6349	$(t^{2} - t - 2) x^{''} + (1 + t) x^{'} - (t - 2) x = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.552

6350	$(x^{2} - 1) y^{''} + (1 - x) y^{'} + (x^{2} - 2 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.489

6351	$\sin (x) y^{''} + \cos (x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.660

6352	$e^{x} y^{''} - (x^{2} - 1) y^{'} + 2 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.024

6353	$\sin (x) y^{''} - y \ln (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	5.205

6354	$y^{'} + (x + 2) y = 0$	[_separable]	✓	0.342

6355	$y^{'} - y = 0$	[_quadrature]	✓	0.250

6356	$z^{'} - x^{2} z = 0$	[_separable]	✓	0.318

6357	$(x^{2} + 1) y^{''} + y = 0$	[[_Emden, _Fowler]]	✓	0.446

6358	$y^{''} + (x - 1) y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.445

6359	$y^{''} - 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.446

6360	$w^{''} - x^{2} w^{'} + w = 0$	[_Lienard]	✓	0.400

6361	$(2 x - 3) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.421

6362	$(x + 1) y^{''} - 3 y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.589

6363	$y^{''} - y^{'} x - 3 y = 0$	[_Hermite]	✓	0.506

6364	$(x^{2} + x + 1) y^{''} - 3 y = 0$	[[_Emden, _Fowler]]	✓	0.540

6365	$(x^{2} - 5 x + 6) y^{''} - 3 y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.524

6366	$y^{''} - y^{'} \tan (x) + y = 0$	[_Lienard]	✓	1.978

6367	$(x^{3} + 1) y^{''} - y^{'} x + 2 x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.742

6368	$y^{'} + 2 (x - 1) y = 0$	[_separable]	✓	0.375

6369	$y^{'} - 2 x y = 0$	[_separable]	✓	0.391

6370	$(x^{2} - 2 x) y^{''} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.490

6371	$x^{2} y^{''} - y^{'} x + 2 y = 0$	[[_Emden, _Fowler]]	✓	0.542

6372	$x^{2} y^{''} - y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.585

6373	$y^{''} + (3 x - 1) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.524

6374	$x^{'} + \sin (t) x = 0$ i.c.	[_separable]	✓	0.565

6375	$y^{'} - y e^{x} = 0$ i.c.	[_separable]	✓	0.542

6376	$(x^{2} + 1) y^{''} - e^{x} y^{'} + y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.963

6377	$y^{''} + y^{'} t + e^{t} y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.633

6378	$y^{''} - e^{2 x} y^{'} + \cos (x) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	1.128

6379	$y^{'} - x y = \sin (x)$	[_linear]	✓	0.444

6380	$w^{'} + w x = e^{x}$	[_linear]	✓	0.398

6381	$z^{''} + x z^{'} + z = x^{2} + 2 x + 1$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	0.441

6382	$y^{''} - 2 y^{'} x + 3 y = x^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.453

6383	$(x^{2} + 1) y^{''} - y^{'} x + y = \cos (x)$	[[_2nd_order, _with_linear_symmetries]]	✓	0.552

6384	$y^{''} - y^{'} x + 2 y = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.491

6385	$(- x^{2} + 1) y^{''} - y^{'} + y = \tan (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.426

6386	$y^{''} - y \sin (x) = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.614

6387	$(- x^{2} + 1) y^{''} - 2 y^{'} x + n (n + 1) y = 0$	[_Gegenbauer]	✓	0.649

6388	$x^{''} - ω^{2} x = 0$	[[_2nd_order, _missing_x]]	✓	1.617

6389	$x^{'''} - x^{''} + x^{'} - x = 0$	[[_3rd_order, _missing_x]]	✓	0.077

6390	$x^{''} + 42 x^{'} + x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.664

6391	$x^{''''} + x = 0$	[[_high_order, _missing_x]]	✓	0.091

6392	$x^{'''} - 3 x^{''} - 9 x^{'} - 5 x = 0$	[[_3rd_order, _missing_x]]	✓	0.076

6393	$x^{''} + 2 γ x^{'} + ω_{0} x = F \cos (ω t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.973

6394	$y^{''} - y^{'} - 2 y = e^{2 x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.854

6395	$y^{''} - 2 y^{'} + y = 2 \cos (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.934

6396	$y^{''} + 16 y = 16 \cos (4 x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.941

6397	$y^{''} - y = \cosh (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.970

6398	$y^{'} - y = e^{2 x}$	[[_linear, ‘class A‘]]	✓	0.999

6399	$x^{2} y^{'} + 2 x y - x + 1 = 0$ i.c.	[_linear]	✓	1.196

6400	$y^{'} + y = {(x + 1)}^{2}$ i.c.	[[_linear, ‘class A‘]]	✓	1.305

2.2.64 Problems 6301 to 6400