Problems 4801 to 4900

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


#	ODE	CAS classiﬁcation	Solved?	time (sec)

4801	$y^{'} x = y - x \cos {(\frac{y}{x})}^{2}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.632

4802	$y^{'} x = (- 2 x^{2} + 1) \cot {(y)}^{2}$	[_separable]	✓	2.537

4803	$y^{'} x = y - \cot {(y)}^{2}$	[_separable]	✓	3.145

4804	$y^{'} x + y + 2 x \sec (x y) = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	8.443

4805	$y^{'} x - y + x \sec (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	6.283

4806	$y^{'} x = y + x \sec {(\frac{y}{x})}^{2}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	10.363

4807	$y^{'} x = \sin (x - y)$	[‘y=_G(x,y’)‘]	✗	3.425

4808	$y^{'} x = y + x \sin (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.901

4809	$y^{'} x + \tan (y) = 0$	[_separable]	✓	1.943

4810	$y^{'} x + x + \tan (x + y) = 0$	[[_1st_order, _with_linear_symmetries]]	✓	2.401

4811	$y^{'} x = y - x \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.481

4812	$y^{'} x = (1 + y^{2}) (x^{2} + \arctan (y))$	[‘y=_G(x,y’)‘]	✓	2.489

4813	$y^{'} x = e^{\frac{y}{x}} x + y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	4.913

4814	$y^{'} x = x + y + e^{\frac{y}{x}} x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	5.793

4815	$y^{'} x = y \ln (y)$	[_separable]	✓	1.685

4816	$y^{'} x = (1 + \ln (x) - \ln (y)) y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.618

4817	$y^{'} x + (1 - \ln (x) - \ln (y)) y = 0$	[[_homogeneous, ‘class G‘]]	✓	2.184

4818	$y^{'} x = y - 2 x \tanh (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	133.764

4819	$y^{'} x + n y = f (x) g (x^{n} y)$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	3.323

4820	$y^{'} x = y f (x^{m} y^{n})$	[[_homogeneous, ‘class G‘]]	✓	1.619

4821	$(x + 1) y^{'} = x^{3} (3 x + 4) + y$	[_linear]	✓	0.998

4822	$(x + 1) y^{'} = {(x + 1)}^{4} + 2 y$	[_linear]	✓	1.354

4823	$(x + 1) y^{'} = e^{x} {(x + 1)}^{n + 1} + n y$	[_linear]	✓	1.842

4824	$(x + 1) y^{'} = a y + b x y^{2}$	[_rational, _Bernoulli]	✓	3.670

4825	$(x + 1) y^{'} + y + {(x + 1)}^{4} y^{3} = 0$	[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]	✓	3.240

4826	$(x + 1) y^{'} = (1 - x y^{3}) y$	[_rational, _Bernoulli]	✓	2.009

4827	$(x + 1) y^{'} = 1 + y + (x + 1) \sqrt{1 + y}$	[[_1st_order, _with_linear_symmetries]]	✓	2.301

4828	$(x + a) y^{'} = b x$	[_quadrature]	✓	0.361

4829	$(x + a) y^{'} = b x + y$	[_linear]	✓	1.123

4830	$(x + a) y^{'} + b x^{2} + y = 0$	[_linear]	✓	1.015

4831	$(x + a) y^{'} = 2 {(x + a)}^{5} + 3 y$	[_linear]	✓	1.531

4832	$(x + a) y^{'} = b + c y$	[_separable]	✓	1.497

4833	$(x + a) y^{'} = b x + c y$	[_linear]	✓	2.234

4834	$(x + a) y^{'} = y (1 - a y)$	[_separable]	✓	1.547

4835	$(a - x) y^{'} = y + (c x + b) y^{3}$	[_rational, _Bernoulli]	✓	2.787

4836	$2 y^{'} x = 2 x^{3} - y$	[_linear]	✓	6.986

4837	$2 y^{'} x + 1 = 4 i x y + y^{2}$	[_rational, _Riccati]	✓	2.479

4838	$2 y^{'} x = y (1 + y^{2})$	[_separable]	✓	3.808

4839	$2 y^{'} x + y (1 + y^{2}) = 0$	[_separable]	✓	5.408

4840	$2 y^{'} x = (1 + x - 6 y^{2}) y$	[_rational, _Bernoulli]	✓	1.505

4841	$2 y^{'} x + 4 y + a + \sqrt{a^{2} - 4 b - 4 c y} = 0$	[_separable]	✓	4.180

4842	$(- 2 x + 1) y^{'} = 16 + 32 x - 6 y$	[_linear]	✓	1.775

4843	$(2 x + 1) y^{'} = 4 e^{- y} - 2$	[_separable]	✓	2.106

4844	$2 (1 - x) y^{'} = 4 x \sqrt{1 - x} + y$	[_linear]	✓	1.722

4845	$2 (x + 1) y^{'} + 2 y + {(x + 1)}^{4} y^{3} = 0$	[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]	✓	2.730

4846	$3 y^{'} x = 3 x^{2 / 3} + (1 - 3 y) y$	[_rational, _Riccati]	✓	1.954

4847	$3 y^{'} x = (2 + x y^{3}) y$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	23.499

4848	$3 y^{'} x = (1 + 3 x y^{3} \ln (x)) y$	[_Bernoulli]	✓	3.418

4849	$x^{2} y^{'} = - y + a$	[_separable]	✓	1.071

4850	$x^{2} y^{'} = a + b x + c x^{2} + x y$	[_linear]	✓	0.964

4851	$x^{2} y^{'} = a + b x + c x^{2} - x y$	[_linear]	✓	0.954

4852	$x^{2} y^{'} + (- 2 x + 1) y = x^{2}$	[_linear]	✓	1.600

4853	$x^{2} y^{'} = a + b x y$	[_linear]	✓	1.468

4854	$x^{2} y^{'} = (b x + a) y$	[_separable]	✓	1.385

4855	$x^{2} y^{'} + x (x + 2) y = x (1 - e^{- 2 x}) - 2$	[_linear]	✓	1.797

4856	$x^{2} y^{'} + 2 x (1 - x) y = e^{x} (2 e^{x} - 1)$	[_linear]	✓	1.974

4857	$x^{2} y^{'} + x^{2} + x y + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	1.646

4858	$x^{2} y^{'} = {(1 + 2 x - y)}^{2}$	[[_homogeneous, ‘class C‘], _rational, _Riccati]	✓	2.904

4859	$x^{2} y^{'} = a + b y^{2}$	[_separable]	✓	2.928

4860	$x^{2} y^{'} = (x + a y) y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	3.139

4861	$x^{2} y^{'} = (a x + b y) y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	38.032

4862	$x^{2} y^{'} + a x^{2} + b x y + c y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	139.107

4863	$x^{2} y^{'} = a + b x^{n} + x^{2} y^{2}$	[_rational, _Riccati]	✓	2.743

4864	$x^{2} y^{'} + 2 + x y (4 + x y) = 0$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	1.654

4865	$x^{2} y^{'} + 2 + a x (1 - x y) - x^{2} y^{2} = 0$	[_rational, _Riccati]	✓	2.263

4866	$x^{2} y^{'} = a + b x^{2} y^{2}$	[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]	✓	2.012

4867	$x^{2} y^{'} = a + b x^{n} + c x^{2} y^{2}$	[_rational, _Riccati]	✓	2.840

4868	$x^{2} y^{'} = a + b x y + c x^{2} y^{2}$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	2.262

4869	$x^{2} y^{'} = a + b x y + c x^{4} y^{2}$	[_rational, _Riccati]	✓	3.449

4870	$x^{2} y^{'} + (x^{2} + y^{2} - x) y = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	2.044

4871	$x^{2} y^{'} = 2 y (x - y^{2})$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.589

4872	$x^{2} y^{'} = a x^{2} y^{2} - a y^{3}$	[_rational, _Abel]	✗	1.212

4873	$x^{2} y^{'} + a y^{2} + b x^{2} y^{3} = 0$	[_rational, _Abel]	✗	1.529

4874	$x^{2} y^{'} = (a x + b y^{3}) y$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.859

4875	$x^{2} y^{'} + x y + \sqrt{y} = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	6.669

4876	$x^{2} y^{'} = \sec (y) + 3 x \tan (y)$	[‘y=_G(x,y’)‘]	✗	8.035

4877	$(- x^{2} + 1) y^{'} = 1 - x^{2} + y$	[_linear]	✓	1.438

4878	$(- x^{2} + 1) y^{'} + 1 = x y$	[_linear]	✓	1.261

4879	$(- x^{2} + 1) y^{'} = 5 - x y$	[_linear]	✓	1.327

4880	$(x^{2} + 1) y^{'} + a + x y = 0$	[_linear]	✓	1.213

4881	$(x^{2} + 1) y^{'} + a - x y = 0$	[_linear]	✓	2.840

4882	$(- x^{2} + 1) y^{'} + a - x y = 0$	[_linear]	✓	1.185

4883	$(- x^{2} + 1) y^{'} - x + x y = 0$	[_separable]	✓	1.242

4884	$(- x^{2} + 1) y^{'} - x^{2} + x y = 0$	[_linear]	✓	1.315

4885	$(- x^{2} + 1) y^{'} + x^{2} + x y = 0$	[_linear]	✓	1.298

4886	$(x^{2} + 1) y^{'} = x (x^{2} + 1) - x y$	[_linear]	✓	3.838

4887	$(x^{2} + 1) y^{'} = x (3 x^{2} - y)$	[_linear]	✓	3.709

4888	$(- x^{2} + 1) y^{'} + 2 x y = 0$	[_separable]	✓	1.198

4889	$(x^{2} + 1) y^{'} = 2 x (x - y)$	[_linear]	✓	1.138

4890	$(x^{2} + 1) y^{'} = 2 x {(x^{2} + 1)}^{2} + 2 x y$	[_linear]	✓	1.661

4891	$(- x^{2} + 1) y^{'} + \cos (x) = 2 x y$	[_linear]	✓	2.527

4892	$(x^{2} + 1) y^{'} = \tan (x) - 2 x y$	[_linear]	✓	1.729

4893	$(- x^{2} + 1) y^{'} = a + 4 x y$	[_linear]	✓	1.275

4894	$(x^{2} + 1) y^{'} = (2 b x + a) y$	[_separable]	✓	1.746

4895	$(x^{2} + 1) y^{'} = 1 + y^{2}$	[_separable]	✓	1.879

4896	$(- x^{2} + 1) y^{'} = 1 - y^{2}$	[_separable]	✓	1.829

4897	$(- x^{2} + 1) y^{'} = 1 - (2 x - y) y$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	1.780

4898	$(- x^{2} + 1) y^{'} = n (1 - 2 x y + y^{2})$	[_rational, _Riccati]	✗	4.256

4899	$(x^{2} + 1) y^{'} + x y (1 - y) = 0$	[_separable]	✓	3.335

4900	$(- x^{2} + 1) y^{'} = x y (1 + a y)$	[_separable]	✓	3.136

2.2.49 Problems 4801 to 4900