Problems 9901 to 10000

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


#	ODE	CAS classiﬁcation	Solved?	time (sec)

9901	$y^{''} - 2 y^{'} x + x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.245

9902	$x (- x^{2} + 2) y^{''} - (x^{2} + 4 x + 2) ((1 - x) y^{'} + y) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.642

9903	$x^{2} (x + 1) y^{''} - (2 x + 1) (y^{'} x - y) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.376

9904	$2 x^{2} (2 - x) y^{''} - x (4 - x) y^{'} + (3 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.282

9905	$x^{2} (1 - x) y^{''} + (5 x - 4) x y^{'} + (6 - 9 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.312

9906	$x y^{''} + (4 x^{2} + 1) y^{'} + 4 x (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.256

9907	$(- x^{2} + 1) y^{''} - 2 y^{'} x + 12 y = 0$	[_Gegenbauer]	✓	0.468

9908	$x (x + 2) y^{''} + 2 (x + 1) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.310

9909	$x (x + 2) y^{''} + (x + 1) y^{'} - 4 y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.384

9910	$(x - 1) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.416

9911	$(x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.454

9912	$(x^{2} - 2 x + 10) y^{''} + y^{'} x - 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.573

9913	$(x^{2} - 2 x + 10) y^{''} + y^{'} x - 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.536

9914	$y^{''} - y^{'} x + 2 y = 0$	[_Hermite]	✓	0.387

9915	$(x + 2) y^{''} + y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.360

9916	$(x^{2} + 1) y^{''} - 6 y = 0$	[[_Emden, _Fowler]]	✓	0.345

9917	$(x^{2} + 2) y^{''} + 3 y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.585

9918	$(x - 1) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.345

9919	$x^{2} y^{''} + (\frac{5}{3} x + x^{2}) y^{'} - \frac{y}{3} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.529

9920	$2 x y^{''} - y^{'} + 2 y = 0$	[[_Emden, _Fowler]]	✓	0.366

9921	$2 x y^{''} - (2 x + 3) y^{'} + y = 0$	[_Laguerre]	✓	0.544

9922	$2 x^{2} y^{''} + 3 y^{'} x + (2 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.380

9923	$x y^{''} + 2 y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.181

9924	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.270

9925	$x y^{''} + (x - 6) y^{'} - 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.406

9926	$x^{4} y^{''} + λ y = 0$	[[_Emden, _Fowler]]	✓	0.369

9927	$4 x^{2} y^{''} + 4 y^{'} x + (4 x^{2} - 25) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.520

9928	$x^{2} y^{''} + y^{'} x + (36 x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.290

9929	$x^{2} y^{''} + (x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.418

9930	$x y^{''} + 3 y^{'} + x^{3} y = 0$	[[_Emden, _Fowler]]	✓	0.435

9931	$x^{2} y^{''} + 4 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.269

9932	$16 x^{2} y^{''} + 32 y^{'} x + (x^{4} - 12) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.401

9933	$y^{''} - x^{2} y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.511

9934	$x y^{''} - (x + 2) y^{'} + 2 y = 0$	[_Laguerre]	✓	0.401

9935	$y^{''} + y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.412

9936	$(- x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[_Gegenbauer]	✓	0.376

9937	$y^{''} - 4 y^{'} x + (4 x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.178

9938	$(- x^{2} + 1) y^{''} - 2 y^{'} x + 30 y = 0$	[_Gegenbauer]	✓	0.489

9939	$x y^{''} + 2 y^{'} + x y = 0$	[_Lienard]	✓	0.243

9940	$x y^{''} + (2 x + 1) y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.256

9941	$2 x (x - 1) y^{''} - (x + 1) y^{'} + y = 0$	[_Jacobi]	✓	0.364

9942	$x y^{''} + 2 y^{'} + 4 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.262

9943	$x y^{''} + (2 - 2 x) y^{'} + (x - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.167

9944	$x^{2} y^{''} + 6 y^{'} x + (4 x^{2} + 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.280

9945	$x y^{''} + (- 2 x + 1) y^{'} + (x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.260

9946	$x (1 - x) y^{''} + (\frac{1}{2} + 2 x) y^{'} - 2 y = 0$	[_Jacobi]	✓	0.386

9947	$4 (t^{2} - 3 t + 2) y^{''} - 2 y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.454

9948	$2 (t^{2} - 5 t + 6) y^{''} + (2 t - 3) y^{'} - 8 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.434

9949	$3 t (1 + t) y^{''} + y^{'} t - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.501

9950	$x^{2} y^{''} + \frac{(x + \frac{3}{4}) y}{4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.357

9951	$x^{2} y^{''} + y^{'} x + \frac{(x^{2} - 1) y}{4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.281

9952	$x y^{''} + (- 2 x + 1) y^{'} + (x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.274

9953	$x y^{''} - (x + 1) y^{'} + y = 0$	[_Laguerre]	✓	0.347

9954	$x y^{''} + 3 y^{'} + 4 x^{3} y = 0$	[[_Emden, _Fowler]]	✓	0.524

9955	$x^{2} (- x^{2} + 1) y^{''} + 2 x (- x^{2} + 1) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.322

9956	$2 x y^{''} + (x - 2) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.378

9957	$x y^{''} + 2 y^{'} + x y = 0$	[_Lienard]	✓	0.240

9958	$y^{''} + 2 x^{2} y^{'} + (x^{4} + 2 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.210

9959	$u^{''} + 2 u^{'} + u = 0$	[[_2nd_order, _missing_x]]	✓	0.208

9960	$u^{''} - (2 x + 1) u^{'} + (x^{2} + x - 1) u = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.197

9961	$y^{''} + 2 y^{'} + (1 + \frac{2}{{(3 x + 1)}^{2}}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.244

9962	$x^{2} y^{''} - 2 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.263

9963	$y^{''} + \frac{2 y^{'}}{x} - \frac{2 y}{{(x + 1)}^{2}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.226

9964	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.353

9965	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.353

9966	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.364

9967	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.386

9968	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.357

9969	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.357

9970	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.380

9971	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.350

9972	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.360

9973	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.410

9974	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.349

9975	$x y^{''} + 2 y^{'} + x y = 0$	[_Lienard]	✓	0.240

9976	$2 x^{2} y^{''} + 3 y^{'} x - x y = 0$	[[_Emden, _Fowler]]	✓	0.295

9977	$x^{2} y^{''} + (3 x^{2} + 2 x) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.349

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]]	✓	1.438

9979	$x y^{''} + (x + 1) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.375

9980	$x^{2} (x^{2} - 2 x + 1) y^{''} - (3 + x) x y^{'} + (x + 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.525

9981	$2 x^{2} (x + 2) y^{''} + 5 x^{2} y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.322

9982	$x^{2} y^{''} + 4 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.265

9983	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.242

9984	$x^{2} y^{''} - y^{'} x - (x^{2} + \frac{5}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.375

9985	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.261

9986	$x^{2} y^{''} + 3 y^{'} x + 4 y x^{4} = 0$	[[_Emden, _Fowler]]	✓	0.443

9987	$y^{''} = (x^{2} + 3) y$	[[_2nd_order, _with_linear_symmetries]]	✓	0.329

9988	$y^{''} + 2 y^{'} x + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.177

9989	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.278

9990	$4 x^{2} y^{''} + (- 8 x^{2} + 4 x) y^{'} + (4 x^{2} - 4 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.211

9991	$y^{''} = 0$	[[_2nd_order, _quadrature]]	✓	0.159

9992	$y^{''} = \frac{2 y}{x^{2}}$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.194

9993	$y^{''} = \frac{6 y}{x^{2}}$	[[_Emden, _Fowler]]	✓	0.201

9994	$y^{''} = (- \frac{3}{16 x^{2}} - \frac{2}{9 {(x - 1)}^{2}} + \frac{3}{16 x (x - 1)}) y$	[[_2nd_order, _with_linear_symmetries]]	✓	1.301

9995	$y^{''} = \frac{20 y}{x^{2}}$	[[_Emden, _Fowler]]	✓	0.225

9996	$y^{''} = \frac{12 y}{x^{2}}$	[[_Emden, _Fowler]]	✓	0.201

9997	$y^{''} - \frac{y}{4 x^{2}} = 0$	[[_Emden, _Fowler]]	✓	0.351

9998	$x y^{''} - (2 x + 2) y^{'} + (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.259

9999	$y^{''} + \frac{y}{x^{2}} = 0$	[[_Emden, _Fowler]]	✓	0.370

10000	$(- x^{2} + 1) y^{''} + y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.907

2.2.100 Problems 9901 to 10000