Problems 4801 to 4900

Table 2.99: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

4801	$x y^{'} = y - x \cos {(\frac{y}{x})}^{2}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	4.195

4802	$x y^{'} = (- 2 x^{2} + 1) \cot {(y)}^{2}$	[_separable]	✓	2.151

4803	$x y^{'} = y - \cot {(y)}^{2}$	[_separable]	✓	2.558

4804	$x y^{'} + y + 2 x \sec (x y) = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	9.815

4805	$x y^{'} - y + x \sec (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	5.517

4806	$x y^{'} = y + x \sec {(\frac{y}{x})}^{2}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	8.174

4807	$x y^{'} = \sin (x - y)$	[‘y=_G(x,y’)‘]	✗	3.834

4808	$x y^{'} = y + x \sin (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	6.760

4809	$x y^{'} + \tan (y) = 0$	[_separable]	✓	2.311

4810	$x y^{'} + x + \tan (x + y) = 0$	[[_1st_order, _with_linear_symmetries]]	✓	3.142

4811	$x y^{'} = y - x \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.920

4812	$x y^{'} = (1 + y^{2}) (x^{2} + \arctan (y))$	[‘y=_G(x,y’)‘]	✓	2.588

4813	$x y^{'} = y + x e^{\frac{y}{x}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	17.282

4814	$x y^{'} = x + y + x e^{\frac{y}{x}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	10.813

4815	$x y^{'} = y \ln (y)$	[_separable]	✓	2.009

4816	$x y^{'} = (1 + \ln (x) - \ln (y)) y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	4.854

4817	$x y^{'} + (1 - \ln (x) - \ln (y)) y = 0$	[[_homogeneous, ‘class G‘]]	✓	2.700

4818	$x y^{'} = y - 2 x \tanh (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	66.346

4819	$x y^{'} + n y = f (x) g (x^{n} y)$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	3.194

4820	$x y^{'} = y f (x^{m} y^{n})$	[[_homogeneous, ‘class G‘]]	✓	1.563

4821	$(x + 1) y^{'} = x^{3} (4 + 3 x) + y$	[_linear]	✓	1.298

4822	$(x + 1) y^{'} = {(x + 1)}^{4} + 2 y$	[_linear]	✓	1.641

4823	$(x + 1) y^{'} = e^{x} {(x + 1)}^{n + 1} + n y$	[_linear]	✓	1.510

4824	$(x + 1) y^{'} = a y + b x y^{2}$	[_rational, _Bernoulli]	✓	3.094

4825	$(x + 1) y^{'} + y + {(x + 1)}^{4} y^{3} = 0$	[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]	✓	3.375

4826	$(x + 1) y^{'} = (1 - x y^{3}) y$	[_rational, _Bernoulli]	✓	1.998

4827	$(x + 1) y^{'} = 1 + y + (x + 1) \sqrt{y + 1}$	[[_1st_order, _with_linear_symmetries]]	✓	4.247

4828	$(x + a) y^{'} = b x$	[_quadrature]	✓	0.301

4829	$(x + a) y^{'} = b x + y$	[_linear]	✓	0.855

4830	$(x + a) y^{'} + b x^{2} + y = 0$	[_linear]	✓	0.826

4831	$(x + a) y^{'} = 2 {(x + a)}^{5} + 3 y$	[_linear]	✓	1.329

4832	$(x + a) y^{'} = b + c y$	[_separable]	✓	1.317

4833	$(x + a) y^{'} = b x + c y$	[_linear]	✓	1.680

4834	$(x + a) y^{'} = y (1 - a y)$	[_separable]	✓	1.526

4835	$(- x + a) y^{'} = y + (c x + b) y^{3}$	[_rational, _Bernoulli]	✓	2.671

4836	$2 x y^{'} = 2 x^{3} - y$	[_linear]	✓	7.925

4837	$2 x y^{'} + 1 = 4 i x y + y^{2}$	[_rational, _Riccati]	✓	2.319

4838	$2 x y^{'} = y (1 + y^{2})$	[_separable]	✓	4.490

4839	$2 x y^{'} + y (1 + y^{2}) = 0$	[_separable]	✓	6.030

4840	$2 x y^{'} = (1 + x - 6 y^{2}) y$	[_rational, _Bernoulli]	✓	1.490

4841	$2 x y^{'} + 4 y + a + \sqrt{a^{2} - 4 b - 4 c y} = 0$	[_separable]	✓	3.804

4842	$(1 - 2 x) y^{'} = 16 + 32 x - 6 y$	[_linear]	✓	2.083

4843	$(2 x + 1) y^{'} = 4 e^{- y} - 2$	[_separable]	✓	2.243

4844	$2 (1 - x) y^{'} = 4 x \sqrt{1 - x} + y$	[_linear]	✓	1.790

4845	$2 (x + 1) y^{'} + 2 y + {(x + 1)}^{4} y^{3} = 0$	[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]	✓	3.108

4846	$3 x y^{'} = 3 x^{2 / 3} + (1 - 3 y) y$	[_rational, _Riccati]	✓	1.504

4847	$3 x y^{'} = (2 + x y^{3}) y$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	14.767

4848	$3 x y^{'} = (1 + 3 x y^{3} \ln (x)) y$	[_Bernoulli]	✓	3.415

4849	$x^{2} y^{'} = - y + a$	[_separable]	✓	0.874

4850	$x^{2} y^{'} = a + b x + c x^{2} + x y$	[_linear]	✓	0.812

4851	$x^{2} y^{'} = a + b x + c x^{2} - x y$	[_linear]	✓	0.819

4852	$x^{2} y^{'} + (1 - 2 x) y = x^{2}$	[_linear]	✓	1.771

4853	$x^{2} y^{'} = a + b x y$	[_linear]	✓	1.086

4854	$x^{2} y^{'} = (b x + a) y$	[_separable]	✓	1.233

4855	$x^{2} y^{'} + x (x + 2) y = x (1 - e^{- 2 x}) - 2$	[_linear]	✓	1.802

4856	$x^{2} y^{'} + 2 x (1 - x) y = e^{x} (2 e^{x} - 1)$	[_linear]	✓	1.989

4857	$x^{2} y^{'} + x^{2} + x y + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	2.247

4858	$x^{2} y^{'} = {(1 + 2 x - y)}^{2}$	[[_homogeneous, ‘class C‘], _rational, _Riccati]	✓	2.908

4859	$x^{2} y^{'} = a + b y^{2}$	[_separable]	✓	2.553

4860	$x^{2} y^{'} = (x + a y) y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.387

4861	$x^{2} y^{'} = (a x + b y) y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	6.456

4862	$x^{2} y^{'} + a x^{2} + b x y + c y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	68.787

4863	$x^{2} y^{'} = a + b x^{n} + y^{2} x^{2}$	[_rational, _Riccati]	✓	2.435

4864	$x^{2} y^{'} + 2 + x y (4 + x y) = 0$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	1.928

4865	$x^{2} y^{'} + 2 + a x (1 - x y) - y^{2} x^{2} = 0$	[_rational, _Riccati]	✓	1.848

4866	$x^{2} y^{'} = a + b x^{2} y^{2}$	[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]	✓	1.912

4867	$x^{2} y^{'} = a + b x^{n} + c x^{2} y^{2}$	[_rational, _Riccati]	✓	2.526

4868	$x^{2} y^{'} = a + b x y + c x^{2} y^{2}$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	2.240

4869	$x^{2} y^{'} = a + b x y + c x^{4} y^{2}$	[_rational, _Riccati]	✓	2.947

4870	$x^{2} y^{'} + (x^{2} + y^{2} - x) y = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	2.018

4871	$x^{2} y^{'} = 2 y (x - y^{2})$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.118

4872	$x^{2} y^{'} = a x^{2} y^{2} - a y^{3}$	[_rational, _Abel]	✗	0.903

4873	$x^{2} y^{'} + a y^{2} + b x^{2} y^{3} = 0$	[_rational, _Abel]	✗	0.996

4874	$x^{2} y^{'} = (a x + b y^{3}) y$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.140

4875	$x^{2} y^{'} + x y + \sqrt{y} = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	5.151

4876	$x^{2} y^{'} = \sec (y) + 3 x \tan (y)$	[‘y=_G(x,y’)‘]	✗	7.622

4877	$(- x^{2} + 1) y^{'} = 1 - x^{2} + y$	[_linear]	✓	1.489

4878	$(- x^{2} + 1) y^{'} + 1 = x y$	[_linear]	✓	1.332

4879	$(- x^{2} + 1) y^{'} = 5 - x y$	[_linear]	✓	2.509

4880	$(x^{2} + 1) y^{'} + a + x y = 0$	[_linear]	✓	1.080

4881	$(x^{2} + 1) y^{'} + a - x y = 0$	[_linear]	✓	1.959

4882	$(- x^{2} + 1) y^{'} + a - x y = 0$	[_linear]	✓	1.106

4883	$(- x^{2} + 1) y^{'} - x + x y = 0$	[_separable]	✓	1.559

4884	$(- x^{2} + 1) y^{'} - x^{2} + x y = 0$	[_linear]	✓	1.387

4885	$(- x^{2} + 1) y^{'} + x^{2} + x y = 0$	[_linear]	✓	1.384

4886	$(x^{2} + 1) y^{'} = x (x^{2} + 1) - x y$	[_linear]	✓	3.784

4887	$(x^{2} + 1) y^{'} = x (3 x^{2} - y)$	[_linear]	✓	3.688

4888	$(- x^{2} + 1) y^{'} + 2 x y = 0$	[_separable]	✓	1.668

4889	$(x^{2} + 1) y^{'} = 2 x (x - y)$	[_linear]	✓	1.280

4890	$(x^{2} + 1) y^{'} = 2 x {(x^{2} + 1)}^{2} + 2 x y$	[_linear]	✓	1.945

4891	$(- x^{2} + 1) y^{'} + \cos (x) = 2 x y$	[_linear]	✓	2.742

4892	$(x^{2} + 1) y^{'} = \tan (x) - 2 x y$	[_linear]	✓	1.809

4893	$(- x^{2} + 1) y^{'} = a + 4 x y$	[_linear]	✓	1.104

4894	$(x^{2} + 1) y^{'} = (2 b x + a) y$	[_separable]	✓	1.386

4895	$(x^{2} + 1) y^{'} = 1 + y^{2}$	[_separable]	✓	2.265

4896	$(- x^{2} + 1) y^{'} = 1 - y^{2}$	[_separable]	✓	2.178

4897	$(- x^{2} + 1) y^{'} = 1 - (2 x - y) y$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	1.990

4898	$(- x^{2} + 1) y^{'} = n (1 - 2 x y + y^{2})$	[_rational, _Riccati]	✗	7.455

4899	$(x^{2} + 1) y^{'} + x y (1 - y) = 0$	[_separable]	✓	2.911

4900	$(- x^{2} + 1) y^{'} = x y (1 + a y)$	[_separable]	✓	2.319

2.2.49 Problems 4801 to 4900