Problems 9901 to 10000

Table 2.201: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

9901	$y^{''} - 2 x y^{'} + x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.184

9902	$x (- x^{2} + 2) y^{''} - (x^{2} + 4 x + 2) ((1 - x) y^{'} + y) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.588

9903	$x^{2} (x + 1) y^{''} - (2 x + 1) (- y + x y^{'}) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.237

9904	$2 (2 - x) x^{2} y^{''} - x (4 - x) y^{'} + (3 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.193

9905	$x^{2} (1 - x) y^{''} + (5 x - 4) x y^{'} + (6 - 9 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.220

9906	$x y^{''} + (4 x^{2} + 1) y^{'} + 4 x (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.189

9907	$(- x^{2} + 1) y^{''} - 2 x y^{'} + 12 y = 0$	[_Gegenbauer]	✓	0.363

9908	$x (x + 2) y^{''} + 2 (x + 1) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.309

9909	$x (x + 2) y^{''} + (x + 1) y^{'} - 4 y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.237

9910	$(- 1 + x) y^{''} - x y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.316

9911	$(x^{2} + 1) y^{''} - 2 x y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.360

9912	$(x^{2} - 2 x + 10) y^{''} + x y^{'} - 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.445

9913	$(x^{2} - 2 x + 10) y^{''} + x y^{'} - 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.437

9914	$y^{''} - x y^{'} + 2 y = 0$	[_Hermite]	✓	0.328

9915	$(x + 2) y^{''} + x y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.338

9916	$(x^{2} + 1) y^{''} - 6 y = 0$	[[_Emden, _Fowler]]	✓	0.310

9917	$(x^{2} + 2) y^{''} + 3 x y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.460

9918	$(- 1 + x) y^{''} - x y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.315

9919	$x^{2} y^{''} + (\frac{5}{3} x + x^{2}) y^{'} - \frac{y}{3} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.448

9920	$2 x y^{''} - y^{'} + 2 y = 0$	[[_Emden, _Fowler]]	✓	0.232

9921	$2 x y^{''} - (2 x + 3) y^{'} + y = 0$	[_Laguerre]	✓	0.431

9922	$2 x^{2} y^{''} + 3 x y^{'} + (2 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.300

9923	$x y^{''} + 2 y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.091

9924	$x^{2} y^{''} + x y^{'} + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.172

9925	$x y^{''} + (x - 6) y^{'} - 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.353

9926	$x^{4} y^{''} + λ y = 0$	[[_Emden, _Fowler]]	✓	0.329

9927	$4 x^{2} y^{''} + 4 x y^{'} + (4 x^{2} - 25) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.393

9928	$x^{2} y^{''} + x y^{'} + (36 x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.189

9929	$x^{2} y^{''} + (x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.359

9930	$x y^{''} + 3 y^{'} + x^{3} y = 0$	[[_Emden, _Fowler]]	✓	0.361

9931	$x^{2} y^{''} + 4 x y^{'} + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.163

9932	$16 x^{2} y^{''} + 32 x y^{'} + (x^{4} - 12) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.375

9933	$y^{''} - x^{2} y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.417

9934	$x y^{''} - (x + 2) y^{'} + 2 y = 0$	[_Laguerre]	✓	0.255

9935	$y^{''} + x y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.307

9936	$(- x^{2} + 1) y^{''} - 2 x y^{'} + 2 y = 0$	[_Gegenbauer]	✓	0.337

9937	$y^{''} - 4 x y^{'} + (4 x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.089

9938	$(- x^{2} + 1) y^{''} - 2 x y^{'} + 30 y = 0$	[_Gegenbauer]	✓	0.381

9939	$x y^{''} + 2 y^{'} + x y = 0$	[_Lienard]	✓	0.156

9940	$x y^{''} + (2 x + 1) y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.181

9941	$2 x (- 1 + x) y^{''} - (x + 1) y^{'} + y = 0$	[_Jacobi]	✓	0.217

9942	$x y^{''} + 2 y^{'} + 4 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.171

9943	$x y^{''} + (2 - 2 x) y^{'} + (- 2 + x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.097

9944	$x^{2} y^{''} + 6 x y^{'} + (4 x^{2} + 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.180

9945	$x y^{''} + (1 - 2 x) y^{'} + (- 1 + x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.179

9946	$x (1 - x) y^{''} + (\frac{1}{2} + 2 x) y^{'} - 2 y = 0$	[_Jacobi]	✓	0.352

9947	$4 (t^{2} - 3 t + 2) y^{''} - 2 y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.345

9948	$2 (t^{2} - 5 t + 6) y^{''} + (2 t - 3) y^{'} - 8 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.341

9949	$3 t (t + 1) y^{''} + t y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.363

9950	$x^{2} y^{''} + \frac{(x + \frac{3}{4}) y}{4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.226

9951	$x^{2} y^{''} + x y^{'} + \frac{(x^{2} - 1) y}{4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.191

9952	$x y^{''} + (1 - 2 x) y^{'} + (- 1 + x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.184

9953	$x y^{''} - (x + 1) y^{'} + y = 0$	[_Laguerre]	✓	0.243

9954	$x y^{''} + 3 y^{'} + 4 x^{3} y = 0$	[[_Emden, _Fowler]]	✓	0.367

9955	$x^{2} (- x^{2} + 1) y^{''} + 2 x (- x^{2} + 1) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.300

9956	$2 x y^{''} + (- 2 + x) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.247

9957	$x y^{''} + 2 y^{'} + x y = 0$	[_Lienard]	✓	0.157

9958	$y^{''} + 2 x^{2} y^{'} + (x^{4} + 2 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.126

9959	$u^{''} + 2 u^{'} + u = 0$	[[_2nd_order, _missing_x]]	✓	0.247

9960	$u^{''} - (2 x + 1) u^{'} + (x^{2} + x - 1) u = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.109

9961	$y^{''} + 2 y^{'} + (1 + \frac{2}{{(3 x + 1)}^{2}}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.163

9962	$x^{2} y^{''} - 2 x y^{'} + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.162

9963	$y^{''} + \frac{2 y^{'}}{x} - \frac{2 y}{{(x + 1)}^{2}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.148

9964	$y^{''} - x y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.322

9965	$y^{''} - x y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.318

9966	$y^{''} - x y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.325

9967	$y^{''} - x y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.260

9968	$y^{''} - x y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.321

9969	$y^{''} - x y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.317

9970	$y^{''} - x y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.325

9971	$y^{''} - x y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.317

9972	$y^{''} - x y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.317

9973	$y^{''} - x y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.323

9974	$y^{''} - x y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.324

9975	$x y^{''} + 2 y^{'} + x y = 0$	[_Lienard]	✓	0.154

9976	$2 x^{2} y^{''} + 3 x y^{'} - x y = 0$	[[_Emden, _Fowler]]	✓	0.202

9977	$x^{2} y^{''} + (3 x^{2} + 2 x) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.302

9978	$2 x^{2} (x^{2} + x + 1) y^{''} + x (11 x^{2} + 11 x + 9) y^{'} + (7 x^{2} + 10 x + 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.210

9979	$x y^{''} + (x + 1) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.348

9980	$x^{2} (x^{2} - 2 x + 1) y^{''} - x (x + 3) y^{'} + (4 + x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.392

9981	$2 x^{2} (x + 2) y^{''} + 5 x^{2} y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.233

9982	$x^{2} y^{''} + 4 x y^{'} + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.162

9983	$x^{2} y^{''} + x y^{'} + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.172

9984	$x^{2} y^{''} - x y^{'} - (x^{2} + \frac{5}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.329

9985	$x^{2} y^{''} + x y^{'} + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.172

9986	$x^{2} y^{''} + 3 x y^{'} + 4 x^{4} y = 0$	[[_Emden, _Fowler]]	✓	0.367

9987	$y^{''} = (x^{2} + 3) y$	[[_2nd_order, _with_linear_symmetries]]	✓	0.293

9988	$y^{''} + 2 x y^{'} + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.102

9989	$x^{2} y^{''} + x y^{'} + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.173

9990	$4 x^{2} y^{''} + (- 8 x^{2} + 4 x) y^{'} + (4 x^{2} - 4 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.123

9991	$y^{''} = 0$	[[_2nd_order, _quadrature]]	✓	0.209

9992	$y^{''} = \frac{2 y}{x^{2}}$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.125

9993	$y^{''} = \frac{6 y}{x^{2}}$	[[_Emden, _Fowler]]	✓	0.128

9994	$y^{''} = (- \frac{3}{16 x^{2}} - \frac{2}{9 {(- 1 + x)}^{2}} + \frac{3}{16 x (- 1 + x)}) y$	[[_2nd_order, _with_linear_symmetries]]	✓	1.132

9995	$y^{''} = \frac{20 y}{x^{2}}$	[[_Emden, _Fowler]]	✓	0.126

9996	$y^{''} = \frac{12 y}{x^{2}}$	[[_Emden, _Fowler]]	✓	0.124

9997	$y^{''} - \frac{y}{4 x^{2}} = 0$	[[_Emden, _Fowler]]	✓	0.227

9998	$x y^{''} - (2 x + 2) y^{'} + (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.158

9999	$y^{''} + \frac{y}{x^{2}} = 0$	[[_Emden, _Fowler]]	✓	0.323

10000	$(- x^{2} + 1) y^{''} + y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.769

2.2.100 Problems 9901 to 10000