Problems 5301 to 5400

Table 2.109: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

5301	$(a x^{3} + {(a x + b y)}^{3}) y y^{'} + x ({(a x + b y)}^{3} + b y^{3}) = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	19.604

5302	$(x + 2 y + 2 x^{2} y^{3} + x y^{4}) y^{'} + (1 + y^{4}) y = 0$	[_rational]	✓	100.476

5303	$2 x (x^{3} + y^{4}) y^{'} = (x^{3} + 2 y^{4}) y$	[[_homogeneous, ‘class G‘], _rational]	✓	7.046

5304	$x (1 - x^{2} y^{4}) y^{'} + y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	15.757

5305	$(x^{2} - y^{5}) y^{'} = 2 x y$	[[_homogeneous, ‘class G‘], _rational]	✓	2.184

5306	$x (x^{3} + y^{5}) y^{'} = (x^{3} - y^{5}) y$	[[_homogeneous, ‘class G‘], _rational]	✓	2.289

5307	$x^{3} (1 + 5 x^{3} y^{7}) y^{'} + (3 x^{5} y^{5} - 1) y^{3} = 0$	[_rational]	✓	1.833

5308	${(1 + a (x + y))}^{n} y^{'} + a {(x + y)}^{n} = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	4.855

5309	$x (a + x y^{n}) y^{'} + b y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	1.615

5310	$f (x) y^{m} y^{'} + g (x) y^{m + 1} + h (x) y^{n} = 0$	[_Bernoulli]	✗	4.944

5311	$y^{'} \sqrt{b^{2} + y^{2}} = \sqrt{a^{2} + x^{2}}$	[_separable]	✓	2.034

5312	$y^{'} \sqrt{b^{2} - y^{2}} = \sqrt{a^{2} - x^{2}}$	[_separable]	✓	2.270

5313	$y^{'} \sqrt{y} = \sqrt{x}$	[_separable]	✓	66.038

5314	$(1 + \sqrt{x + y}) y^{'} + 1 = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	1.569

5315	$y^{'} \sqrt{x y} + x - y = \sqrt{x y}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	33.194

5316	$(x - 2 \sqrt{x y}) y^{'} = y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	24.385

5317	$(y + \sqrt{1 + y^{2}}) {(x^{2} + 1)}^{3 / 2} y^{'} = 1 + y^{2}$	[_separable]	✓	2.950

5318	$(y + \sqrt{1 + y^{2}}) {(x^{2} + 1)}^{3 / 2} y^{'} = 1 + y^{2}$	[_separable]	✓	2.902

5319	$(x - \sqrt{x^{2} + y^{2}}) y^{'} = y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	18.819

5320	$x (1 - \sqrt{x^{2} - y^{2}}) y^{'} = y$	[‘y=_G(x,y’)‘]	✗	3.949

5321	$x (x + \sqrt{x^{2} + y^{2}}) y^{'} + y \sqrt{x^{2} + y^{2}} = 0$	[[_homogeneous, ‘class G‘], _dAlembert]	✓	193.199

5322	$x y (x + \sqrt{x^{2} - y^{2}}) y^{'} = x y^{2} - {(x^{2} - y^{2})}^{3 / 2}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	42.096

5323	$(x \sqrt{1 + x^{2} + y^{2}} - y (x^{2} + y^{2})) y^{'} = x (x^{2} + y^{2}) + y \sqrt{1 + x^{2} + y^{2}}$	[[_1st_order, _with_linear_symmetries]]	✓	3.125

5324	$y^{'} \cos (y) (\cos (y) - \sin (A) \sin (x)) + \cos (x) (\cos (x) - \sin (A) \sin (y)) = 0$	unknown	✓	39.572

5325	$(a \cos (b x + a y) - b \sin (a x + b y)) y^{'} + b \cos (b x + a y) - a \sin (a x + b y) = 0$	[_exact]	✓	37.986

5326	$(x + \cos (x) \sec (y)) y^{'} + \tan (y) - y \sin (x) \sec (y) = 0$	[NONE]	✓	43.296

5327	$(1 + (x + y) \tan (y)) y^{'} + 1 = 0$	[[_1st_order, _with_linear_symmetries]]	✓	1.942

5328	$x (x - y \tan (\frac{y}{x})) y^{'} + (x + y \tan (\frac{y}{x})) y = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	7.309

5329	$(e^{x} + x e^{y}) y^{'} + y e^{x} + e^{y} = 0$	[_exact]	✓	1.727

5330	$(1 - 2 x - \ln (y)) y^{'} + 2 y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	1.707

5331	$(\sinh (x) + x \cosh (y)) y^{'} + y \cosh (x) + \sinh (y) = 0$	[_exact]	✓	36.172

5332	$y^{'} (1 + \sinh (x)) \sinh (y) + \cosh (x) (\cosh (y) - 1) = 0$	[_separable]	✓	8.996

5333	${y^{'}}^{2} = a x^{n}$	[_quadrature]	✓	0.433

5334	${y^{'}}^{2} = y$	[_quadrature]	✓	0.358

5335	${y^{'}}^{2} = x - y$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	0.705

5336	${y^{'}}^{2} = x^{2} + y$	[[_homogeneous, ‘class G‘]]	✓	1.507

5337	${y^{'}}^{2} + x^{2} = 4 y$	[[_homogeneous, ‘class G‘]]	✓	1.570

5338	${y^{'}}^{2} + 3 x^{2} = 8 y$	[[_homogeneous, ‘class G‘]]	✓	1.592

5339	${y^{'}}^{2} + a x^{2} + b y = 0$	[[_homogeneous, ‘class G‘]]	✓	1.710

5340	${y^{'}}^{2} = 1 + y^{2}$	[_quadrature]	✓	0.862

5341	${y^{'}}^{2} = 1 - y^{2}$	[_quadrature]	✓	0.685

5342	${y^{'}}^{2} = a^{2} - y^{2}$	[_quadrature]	✓	0.843

5343	${y^{'}}^{2} = a^{2} y^{2}$	[_quadrature]	✓	0.957

5344	${y^{'}}^{2} = a + b y^{2}$	[_quadrature]	✓	1.176

5345	${y^{'}}^{2} = y^{2} x^{2}$	[_separable]	✓	2.446

5346	${y^{'}}^{2} = (y - 1) y^{2}$	[_quadrature]	✓	15.083

5347	${y^{'}}^{2} = (y - a) (y - b) (y - c)$	[_quadrature]	✓	70.980

5348	${y^{'}}^{2} = a^{2} y^{n}$	[_quadrature]	✓	0.783

5349	${y^{'}}^{2} = a^{2} (1 - \ln {(y)}^{2}) y^{2}$	[_quadrature]	✓	0.868

5350	${y^{'}}^{2} + f (x) (y - a) (y - b) = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	1.104

5351	${y^{'}}^{2} + f (x) {(y - a)}^{2} (y - b) = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	1.092

5352	${y^{'}}^{2} + f (x) (y - a) (y - b) (y - c) = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	4.507

5353	${y^{'}}^{2} + f (x) {(y - a)}^{2} (y - b) (y - c) = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	2.095

5354	${y^{'}}^{2} = f {(x)}^{2} (y - a) (y - b) {(y - c)}^{2}$	[_separable]	✓	1.577

5355	${y^{'}}^{2} = f {(x)}^{2} {(y - u (x))}^{2} (y - a) (y - b)$	[‘y=_G(x,y’)‘]	✓	12.788

5356	${y^{'}}^{2} + 2 y^{'} + x = 0$	[_quadrature]	✓	0.187

5357	${y^{'}}^{2} - 2 y^{'} + a (x - y) = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	0.444

5358	${y^{'}}^{2} - 2 y^{'} - y^{2} = 0$	[_quadrature]	✓	11.882

5359	${y^{'}}^{2} - 5 y^{'} + 6 = 0$	[_quadrature]	✓	0.352

5360	${y^{'}}^{2} - 7 y^{'} + 12 = 0$	[_quadrature]	✓	0.332

5361	${y^{'}}^{2} + a y^{'} + b = 0$	[_quadrature]	✓	0.190

5362	${y^{'}}^{2} + a y^{'} + b x = 0$	[_quadrature]	✓	0.201

5363	${y^{'}}^{2} + a y^{'} + b y = 0$	[_quadrature]	✓	0.495

5364	${y^{'}}^{2} + x y^{'} + 1 = 0$	[_quadrature]	✓	0.268

5365	${y^{'}}^{2} + x y^{'} - y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.414

5366	${y^{'}}^{2} - x y^{'} + y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.405

5367	${y^{'}}^{2} - x y^{'} - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.452

5368	${y^{'}}^{2} + x y^{'} + x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.500

5369	${y^{'}}^{2} + (1 - x) y^{'} + y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.428

5370	${y^{'}}^{2} - (x + 1) y^{'} + y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.424

5371	${y^{'}}^{2} - (2 - x) y^{'} + 1 - y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.479

5372	${y^{'}}^{2} + (x + a) y^{'} - y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.462

5373	${y^{'}}^{2} - 2 x y^{'} + 1 = 0$	[_quadrature]	✓	0.299

5374	${y^{'}}^{2} + 2 x y^{'} - 3 x^{2} = 0$	[_quadrature]	✓	0.406

5375	${y^{'}}^{2} + 2 x y^{'} - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.458

5376	${y^{'}}^{2} + 2 x y^{'} - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.447

5377	${y^{'}}^{2} - 2 x y^{'} + 2 y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.405

5378	${y^{'}}^{2} - (2 x + 1) y^{'} - x (1 - x) = 0$	[_quadrature]	✓	0.210

5379	${y^{'}}^{2} + 2 (1 - x) y^{'} - 2 x + 2 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.492

5380	${y^{'}}^{2} + 3 x y^{'} - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.502

5381	${y^{'}}^{2} - 4 (x + 1) y^{'} + 4 y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.442

5382	${y^{'}}^{2} + a x y^{'} = b c x^{2}$	[_quadrature]	✓	0.214

5383	${y^{'}}^{2} - a x y^{'} + a y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.477

5384	${y^{'}}^{2} + a x y^{'} + b x^{2} + c y = 0$	[[_homogeneous, ‘class G‘]]	✓	2.624

5385	${y^{'}}^{2} + (b x + a) y^{'} + c = b y$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.664

5386	${y^{'}}^{2} - 2 x^{2} y^{'} + 2 x y^{'} = 0$	[_quadrature]	✓	0.353

5387	${y^{'}}^{2} + a x^{3} y^{'} - 2 a x^{2} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	2.580

5388	${y^{'}}^{2} - 2 a x^{3} y^{'} + 4 a x^{2} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	2.179

5389	${y^{'}}^{2} + 4 x^{5} y^{'} - 12 x^{4} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	1.803

5390	${y^{'}}^{2} - 2 y^{'} \cosh (x) + 1 = 0$	[_quadrature]	✓	0.388

5391	${y^{'}}^{2} + y y^{'} = (x + y) x$	[_quadrature]	✓	0.502

5392	${y^{'}}^{2} - y y^{'} + e^{x} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	3.914

5393	${y^{'}}^{2} + (x + y) y^{'} + x y = 0$	[_quadrature]	✓	0.518

5394	${y^{'}}^{2} - 2 y y^{'} - 2 x = 0$	[_dAlembert]	✓	41.984

5395	${y^{'}}^{2} + (2 y + 1) y^{'} + y (y - 1) = 0$	[_quadrature]	✓	0.421

5396	${y^{'}}^{2} - 2 (x - y) y^{'} - 4 x y = 0$	[_quadrature]	✓	0.626

5397	${y^{'}}^{2} - (1 + 4 y) y^{'} + (1 + 4 y) y = 0$	[_quadrature]	✓	1.135

5398	${y^{'}}^{2} - 2 (1 - 3 y) y^{'} - (4 - 9 y) y = 0$	[_quadrature]	✓	38.253

5399	${y^{'}}^{2} + (a + 6 y) y^{'} + y (3 a + b + 9 y) = 0$	[_quadrature]	✓	39.197

5400	${y^{'}}^{2} + a y y^{'} - a x = 0$	[_dAlembert]	✓	1.809

2.2.54 Problems 5301 to 5400