Problems 4901 to 5000

Table 2.101: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

4901	$(x^{2} + 1) y^{'} = 1 + y^{2} - 2 x y (1 + y^{2})$	[_rational, _Abel]	✗	1.440

4902	$(x^{2} + 1) y^{'} + x \sin (y) \cos (y) = x (x^{2} + 1) \cos {(y)}^{2}$	[‘y=_G(x,y’)‘]	✗	16.212

4903	$(x^{2} + 1) y^{'} = 1 + x^{2} - y arccot (x)$	[_linear]	✓	1.901

4904	$(- x^{2} + 4) y^{'} + 4 y = (x + 2) y^{2}$	[_rational, _Bernoulli]	✓	1.635

4905	$(a^{2} + x^{2}) y^{'} = b + x y$	[_linear]	✓	1.483

4906	$(a^{2} + x^{2}) y^{'} = (b + y) (x + \sqrt{a^{2} + x^{2}})$	[_separable]	✓	3.969

4907	$(a^{2} + x^{2}) y^{'} + y (x - y) = 0$	[_rational, _Bernoulli]	✓	3.190

4908	$(a^{2} + x^{2}) y^{'} = a^{2} + 3 x y - 2 y^{2}$	[_rational, _Riccati]	✓	153.328

4909	$(a^{2} + x^{2}) y^{'} + x y + b x y^{2} = 0$	[_separable]	✓	3.493

4910	$x (1 - x) y^{'} = a + (x + 1) y$	[_linear]	✓	1.324

4911	$x (1 - x) y^{'} = 2 x y + 2$	[_linear]	✓	1.209

4912	$x (1 - x) y^{'} = 2 x y - 2$	[_linear]	✓	1.229

4913	$x (x + 1) y^{'} = (- 2 x + 1) y$	[_separable]	✓	1.343

4914	$x (1 - x) y^{'} + (2 x + 1) y = a$	[_linear]	✓	1.483

4915	$x (1 - x) y^{'} = a + 2 (2 - x) y$	[_linear]	✓	1.686

4916	$x (1 - x) y^{'} + 2 - 3 x y + y = 0$	[_linear]	✓	1.295

4917	$x (x + 1) y^{'} = (x + 1) (x^{2} - 1) + (x^{2} + x - 1) y$	[_linear]	✓	1.473

4918	$(x - 2) (x - 3) y^{'} + x^{2} - 8 y + 3 x y = 0$	[_linear]	✓	1.606

4919	$x (x + a) y^{'} = (b + c y) y$	[_separable]	✓	2.422

4920	${(x + a)}^{2} y^{'} = 2 (x + a) (b + y)$	[_separable]	✓	1.439

4921	${(x - a)}^{2} y^{'} + k {(x + y - a)}^{2} + y^{2} = 0$	[[_homogeneous, ‘class C‘], _rational, _Riccati]	✓	80.779

4922	$(x - a) (x - b) y^{'} + k y = 0$	[_separable]	✓	2.849

4923	$(x - a) (x - b) y^{'} = (x - a) (x - b) + (2 x - a - b) y$	[_linear]	✓	1.932

4924	$(x - a) (x - b) y^{'} = c y^{2}$	[_separable]	✓	2.367

4925	$(x - a) (x - b) y^{'} + k (y - a) (y - b) = 0$	[_separable]	✓	4.817

4926	$(x - a) (x - b) y^{'} + k (x + y - a) (x + y - b) + y^{2} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	3.560

4927	$2 x^{2} y^{'} = y$	[_separable]	✓	1.344

4928	$2 x^{2} y^{'} + x \cot (x) - 1 + 2 x^{2} y \cot (x) = 0$	[_linear]	✓	2.233

4929	$2 x^{2} y^{'} + 1 + 2 x y - x^{2} y^{2} = 0$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	1.663

4930	$2 x^{2} y^{'} = 2 x y + (1 - x \cot (x)) (x^{2} - y^{2})$	[[_homogeneous, ‘class D‘], _Riccati]	✓	46.270

4931	$2 (- x^{2} + 1) y^{'} = \sqrt{- x^{2} + 1} + (x + 1) y$	[_linear]	✓	3.113

4932	$x (- 2 x + 1) y^{'} + 1 + (1 - 4 x) y = 0$	[_linear]	✓	1.333

4933	$x (- 2 x + 1) y^{'} = 4 x - (1 + 4 x) y + y^{2}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	2.576

4934	$2 x (1 - x) y^{'} + x + (- 2 x + 1) y = 0$	[_linear]	✓	1.420

4935	$2 x (1 - x) y^{'} + x + (1 - x) y^{2} = 0$	[_rational, _Riccati]	✓	2.852

4936	$2 (x^{2} + x + 1) y^{'} = 1 + 8 x^{2} - (2 x + 1) y$	[_linear]	✓	4.649

4937	$4 (x^{2} + 1) y^{'} - 4 x y - x^{2} = 0$	[_linear]	✓	1.349

4938	$a x^{2} y^{'} = x^{2} + y a x + b^{2} y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	41.375

4939	$(b x^{2} + a) y^{'} = A + B y^{2}$	[_separable]	✓	4.214

4940	$(b x^{2} + a) y^{'} = c x y \ln (y)$	[_separable]	✓	2.474

4941	$x (a x + 1) y^{'} + a - y = 0$	[_separable]	✓	1.224

4942	${(b x + a)}^{2} y^{'} + c y^{2} + (b x + a) y^{3} = 0$	[_rational, _Abel]	✗	2.733

4943	$x^{3} y^{'} = a + b x^{2} y$	[_linear]	✓	1.557

4944	$x^{3} y^{'} = 3 - x^{2} + x^{2} y$	[_linear]	✓	0.996

4945	$x^{3} y^{'} = x^{4} + y^{2}$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	1.242

4946	$x^{3} y^{'} = y (y + x^{2})$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	1.784

4947	$x^{3} y^{'} = x^{2} (- 1 + y) + y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	2.374

4948	$x^{3} y^{'} = (x + 1) y^{2}$	[_separable]	✓	1.393

4949	$x^{3} y^{'} + 20 + x^{2} y (1 - x^{2} y) = 0$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	1.909

4950	$x^{3} y^{'} + 3 + (3 - 2 x) x^{2} y - y^{2} x^{6} = 0$	[_rational, _Riccati]	✓	1.953

4951	$x^{3} y^{'} = (2 x^{2} + y^{2}) y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	152.708

4952	$x^{3} y^{'} = \cos (y) (\cos (y) - 2 x^{2} \sin (y))$	[‘y=_G(x,y’)‘]	✗	40.726

4953	$x (x^{2} + 1) y^{'} = a x^{2} + y$	[_linear]	✓	1.427

4954	$x (- x^{2} + 1) y^{'} = a x^{2} + y$	[_linear]	✓	1.399

4955	$x (x^{2} + 1) y^{'} = a x^{3} + y$	[_linear]	✓	2.026

4956	$x (x^{2} + 1) y^{'} = a - x^{2} y$	[_linear]	✓	1.343

4957	$x (x^{2} + 1) y^{'} = (- x^{2} + 1) y$	[_separable]	✓	1.320

4958	$x (- x^{2} + 1) y^{'} = (x^{2} - x + 1) y$	[_separable]	✓	1.516

4959	$x (- x^{2} + 1) y^{'} = a x^{3} + (- 2 x^{2} + 1) y$	[_linear]	✓	1.344

4960	$x (- x^{2} + 1) y^{'} = x^{3} (- x^{2} + 1) + (- 2 x^{2} + 1) y$	[_linear]	✓	2.897

4961	$x (x^{2} + 1) y^{'} = 2 - 4 x^{2} y$	[_linear]	✓	1.294

4962	$x (x^{2} + 1) y^{'} = x - (5 x^{2} + 3) y$	[_linear]	✓	1.376

4963	$x (- x^{2} + 1) y^{'} + x^{2} + (- x^{2} + 1) y^{2} = 0$	[_rational, _Riccati]	✓	150.238

4964	$x^{2} (1 - x) y^{'} = x (2 - x) y - y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	2.225

4965	$2 x^{3} y^{'} = y (x^{2} - y^{2})$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	152.526

4966	$2 x^{3} y^{'} = (3 x^{2} + a y^{2}) y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	14.237

4967	$6 x^{3} y^{'} = 4 x^{2} y + (1 - 3 x) y^{4}$	[_rational, _Bernoulli]	✓	2.517

4968	$x (c x^{2} + b x + a) y^{'} + x^{2} - (c x^{2} + b x + a) y = y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	3.437

4969	$x^{4} y^{'} = (x^{3} + y) y$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	1.883

4970	$x^{4} y^{'} + a^{2} + x^{4} y^{2} = 0$	[_rational, [_Riccati, _special]]	✓	3.544

4971	$x^{4} y^{'} + x^{3} y + \csc (x y) = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	19.686

4972	$(- x^{4} + 1) y^{'} = 2 x (1 - y^{2})$	[_separable]	✓	2.859

4973	$x (- x^{3} + 1) y^{'} = 2 x - (- 4 x^{3} + 1) y$	[_linear]	✓	1.344

4974	$x (- x^{3} + 1) y^{'} = x^{2} + (1 - 2 x y) y$	[_rational, _Riccati]	✓	2.000

4975	$x^{2} (- x^{2} + 1) y^{'} = (x - 3 x^{3} y) y$	[_rational, _Bernoulli]	✓	1.581

4976	$x (- 2 x^{3} + 1) y^{'} = 2 (- x^{3} + 1) y$	[_separable]	✓	1.498

4977	${(c x^{2} + b x + a)}^{2} (y^{'} + y^{2}) + A = 0$	[_rational, _Riccati]	✓	3.482

4978	$x^{5} y^{'} = 1 - 3 y x^{4}$	[_linear]	✓	1.135

4979	$x (- x^{4} + 1) y^{'} = 2 x (x^{2} - y^{2}) + (- x^{4} + 1) y$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	2.739

4980	$x^{7} y^{'} + 5 x^{3} y^{2} + 2 (x^{2} + 1) y^{3} = 0$	[_rational, _Abel]	✗	1.417

4981	$x^{n} y^{'} = a + b x^{n - 1} y$	[_linear]	✓	1.658

4982	$x^{n} y^{'} = x^{2 n - 1} - y^{2}$	[_Riccati]	✓	2.274

4983	$x^{n} y^{'} + x^{2 n - 2} + y^{2} + (1 - n) x^{n - 1} = 0$	[_Riccati]	✗	16.893

4984	$x^{n} y^{'} = a^{2} x^{2 n - 2} + b^{2} y^{2}$	[[_homogeneous, ‘class G‘], _Riccati]	✓	4.834

4985	$x^{n} y^{'} = x^{n - 1} (a x^{2 n} + n y - b y^{2})$	[_rational, _Riccati]	✓	4.116

4986	$x^{k} y^{'} = a x^{m} + b y^{n}$	[_Chini]	✗	1.960

4987	$\sqrt{x^{2} + 1} y^{'} = 2 x - y$	[_linear]	✓	1.752

4988	$y^{'} \sqrt{- x^{2} + 1} = 1 + y^{2}$	[_separable]	✓	3.733

4989	$(x - \sqrt{x^{2} + 1}) y^{'} = y + \sqrt{1 + y^{2}}$	[_separable]	✓	2.849

4990	$y^{'} \sqrt{a^{2} + x^{2}} + x + y = \sqrt{a^{2} + x^{2}}$	[_linear]	✓	1.789

4991	$y^{'} \sqrt{b^{2} + x^{2}} = \sqrt{y^{2} + a^{2}}$	[_separable]	✓	11.584

4992	$y^{'} \sqrt{b^{2} - x^{2}} = \sqrt{a^{2} - y^{2}}$	[_separable]	✓	25.606

4993	$x y^{'} \sqrt{a^{2} + x^{2}} = y \sqrt{b^{2} + y^{2}}$	[_separable]	✓	2.484

4994	$x y^{'} \sqrt{- a^{2} + x^{2}} = y \sqrt{y^{2} - b^{2}}$	[_separable]	✓	17.505

4995	$y^{'} \sqrt{X} + \sqrt{Y} = 0$	[_quadrature]	✓	0.592

4996	$y^{'} \sqrt{X} = \sqrt{Y}$	[_quadrature]	✓	0.590

4997	$x^{3 / 2} y^{'} = a + b x^{3 / 2} y^{2}$	[_rational, [_Riccati, _special]]	✓	2.331

4998	$y^{'} \sqrt{x^{3} + 1} = \sqrt{y^{3} + 1}$	[_separable]	✓	2.366

4999	$y^{'} \sqrt{x (1 - x) (- a x + 1)} = \sqrt{y (1 - y) (1 - a y)}$	[_separable]	✓	3.316

5000	$y^{'} \sqrt{- x^{4} + 1} = \sqrt{1 - y^{4}}$	[_separable]	✓	2.941

2.2.50 Problems 4901 to 5000