Problems 9701 to 9800

Table 2.197: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

9701	$9 x^{2} y^{''} + 3 x (x^{2} + 3) y^{'} - (- 5 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.398

9702	$6 x^{2} y^{''} + x (6 x^{2} + 1) y^{'} + (9 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.445

9703	$9 x^{2} (x^{2} + 1) y^{''} + 3 x (13 x^{2} + 3) y^{'} - (- 25 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.418

9704	$4 x^{2} (x^{2} + 1) y^{''} + 4 x (6 x^{2} + 1) y^{'} - (- 25 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.376

9705	$8 x^{2} (2 x^{2} + 1) y^{''} + 2 x (34 x^{2} + 5) y^{'} - (- 30 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.510

9706	$2 x^{2} (x + 1) y^{''} - x (1 - 3 x) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.181

9707	$6 x^{2} (2 x^{2} + 1) y^{''} + x (50 x^{2} + 1) y^{'} + (30 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.196

9708	$28 x^{2} (1 - 3 x) y^{''} - 7 x (5 + 9 x) y^{'} + 7 (2 + 9 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.254

9709	$8 x^{2} (- x^{2} + 2) y^{''} + 2 x (- 21 x^{2} + 10) y^{'} - (35 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.194

9710	$4 x^{2} (x^{2} + 3 x + 1) y^{''} - 4 x (- 3 x^{2} - 3 x + 1) y^{'} + 3 (x^{2} - x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.143

9711	$3 x^{2} {(x + 1)}^{2} y^{''} - x (- 11 x^{2} - 10 x + 1) y^{'} + (5 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.189

9712	$4 x^{2} (x^{2} + 2 x + 3) y^{''} - x (- 15 x^{2} - 14 x + 3) y^{'} + (7 x^{2} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.264

9713	$x^{2} (x^{2} - 2 x + 1) y^{''} - x (x + 3) y^{'} + (4 + x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.402

9714	$2 x^{2} (x + 2) y^{''} + 5 x^{2} y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.295

9715	$x^{2} (- x^{2} + 2) y^{''} - 2 x (2 x^{2} + 1) y^{'} + (- 2 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.434

9716	$x^{2} y^{''} - x (5 - x) y^{'} + (9 - 4 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.461

9717	$4 x^{2} (x^{2} + x + 1) y^{''} + 12 x^{2} (x + 1) y^{'} + (3 x^{2} + 3 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.888

9718	$x^{2} (x^{2} + x + 1) y^{''} - x (- 2 x^{2} - 4 x + 1) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.936

9719	$9 x^{2} y^{''} + 3 x (- 2 x^{2} + 3 x + 5) y^{'} + (- 14 x^{2} + 12 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.584

9720	$x^{2} (2 x + 1) y^{''} + x (3 x^{2} + 14 x + 5) y^{'} + (12 x^{2} + 18 x + 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.640

9721	$16 x^{2} y^{''} + 4 x (2 x^{2} + x + 6) y^{'} + (18 x^{2} + 5 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.514

9722	$9 x^{2} (x + 1) y^{''} + 3 x (- x^{2} + 11 x + 5) y^{'} + (- 7 x^{2} + 16 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.454

9723	$36 x^{2} (1 - 2 x) y^{''} + 24 x (1 - 9 x) y^{'} + (1 - 70 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.408

9724	$x^{2} (x + 1) y^{''} - x (3 - x) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.319

9725	$x^{2} (1 - 2 x) y^{''} - x (5 - 4 x) y^{'} + (9 - 4 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.303

9726	$2 x^{2} (x + 2) y^{''} + x^{2} y^{'} + (1 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.233

9727	$2 x^{2} (x + 1) y^{''} - x (6 - x) y^{'} + (8 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.303

9728	$x^{2} (2 x + 1) y^{''} + x (5 + 9 x) y^{'} + (4 + 3 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.307

9729	$x^{2} (1 - 2 x) y^{''} - x (5 + 4 x) y^{'} + (9 + 4 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.352

9730	$x^{2} (1 - x) y^{''} + x (7 + x) y^{'} + (9 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.352

9731	$x^{2} y^{''} - x (- x^{2} + 1) y^{'} + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.343

9732	$x^{2} (x^{2} + 1) y^{''} - 3 x (- x^{2} + 1) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.408

9733	$4 x^{2} y^{''} + 2 x^{3} y^{'} + (3 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.345

9734	$x^{2} (x^{2} + 1) y^{''} - x (- 2 x^{2} + 1) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.340

9735	$2 x^{2} (x^{2} + 2) y^{''} + 7 x^{3} y^{'} + (3 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.423

9736	$x^{2} (x^{2} + 1) y^{''} - x (- 4 x^{2} + 1) y^{'} + (2 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.370

9737	$4 x^{2} (x^{2} + 4) y^{''} + 3 x (3 x^{2} + 8) y^{'} + (- 9 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.444

9738	$3 x^{2} (x^{2} + 3) y^{''} + x (11 x^{2} + 3) y^{'} + (5 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.416

9739	$9 x^{2} y^{''} - 3 x (- 2 x^{2} + 7) y^{'} + (2 x^{2} + 25) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.369

9740	$x^{2} y^{''} - x (- x^{2} + 1) y^{'} + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.334

9741	$x^{2} (1 - 2 x) y^{''} + 3 x y^{'} + (1 + 4 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.317

9742	$x (x + 1) y^{''} + (1 - x) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.310

9743	$x^{2} (1 - x) y^{''} - x (3 - 5 x) y^{'} + (4 - 5 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.318

9744	$x^{2} (x^{2} + 1) y^{''} - x (9 x^{2} + 1) y^{'} + (25 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.397

9745	$9 x^{2} y^{''} + 3 x (- x^{2} + 1) y^{'} + (7 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.121

9746	$x (x^{2} + 1) y^{''} + (- x^{2} + 1) y^{'} - 8 x y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.427

9747	$4 x^{2} y^{''} + 2 x (- x^{2} + 4) y^{'} + (7 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.783

9748	$4 x^{2} (x + 1) y^{''} + 8 x^{2} y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.175

9749	$9 x^{2} (x + 3) y^{''} + 3 x (3 + 7 x) y^{'} + (4 x + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.243

9750	$x^{2} (- x^{2} + 2) y^{''} - x (3 x^{2} + 2) y^{'} + (- x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.200

9751	$16 x^{2} (x^{2} + 1) y^{''} + 8 x (9 x^{2} + 1) y^{'} + (49 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.313

9752	$x^{2} (4 + 3 x) y^{''} - x (4 - 3 x) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.254

9753	$4 x^{2} (x^{2} + 3 x + 1) y^{''} + 8 x^{2} (2 x + 3) y^{'} + (9 x^{2} + 3 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.193

9754	$x^{2} {(1 - x)}^{2} y^{''} - x (- 3 x^{2} + 2 x + 1) y^{'} + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.197

9755	$9 x^{2} (x^{2} + x + 1) y^{''} + 3 x (13 x^{2} + 7 x + 1) y^{'} + (25 x^{2} + 4 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.362

9756	$2 x^{2} (x + 2) y^{''} - x (4 - 7 x) y^{'} - (5 - 3 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.326

9757	$x^{2} (1 - 2 x) y^{''} + x (8 - 9 x) y^{'} + (6 - 3 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.310

9758	$x^{2} (x^{2} + 1) y^{''} + x (10 x^{2} + 3) y^{'} - (- 14 x^{2} + 15) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.415

9759	$x^{2} (- 2 x^{2} + 1) y^{''} + x (- 13 x^{2} + 7) y^{'} - 14 x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.387

9760	$4 x^{2} (x + 1) y^{''} + 4 x (2 x + 1) y^{'} - (3 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.303

9761	$2 x^{2} (3 x + 2) y^{''} + x (4 + 21 x) y^{'} - (1 - 9 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.316

9762	$x^{2} y^{''} + x (x + 2) y^{'} - (2 - 3 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.341

9763	$4 x^{2} (x + 1) y^{''} + 4 x (3 + 8 x) y^{'} - (5 - 49 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.319

9764	$x^{2} (x + 1) y^{''} - x (3 + 10 x) y^{'} + 30 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.335

9765	$x^{2} y^{''} + x (x + 1) y^{'} - 3 (x + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.385

9766	$x^{2} (2 x + 1) y^{''} + x (9 + 13 x) y^{'} + (7 + 5 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.331

9767	$4 x^{2} (2 x + 1) y^{''} - 2 x (4 - x) y^{'} - (7 + 5 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.302

9768	$3 x^{2} (x + 3) y^{''} - x (15 + x) y^{'} - 20 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.322

9769	$x^{2} (x + 1) y^{''} + x (1 - 10 x) y^{'} - (9 - 10 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.339

9770	$x^{2} (x + 1) y^{''} + 3 x^{2} y^{'} - (6 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.304

9771	$x^{2} (2 x + 1) y^{''} - 2 x (3 + 14 x) y^{'} + (6 + 100 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.299

9772	$x^{2} (x + 1) y^{''} - x (6 + 11 x) y^{'} + (6 + 32 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.325

9773	$4 x^{2} (x + 1) y^{''} + 4 x (1 + 4 x) y^{'} - (49 + 27 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.312

9774	$x^{2} (x^{2} + 1) y^{''} - x (- 2 x^{2} + 7) y^{'} + 12 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.387

9775	$x^{2} y^{''} - x (- x^{2} + 7) y^{'} + 12 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.362

9776	$x^{2} y^{''} + x (2 x^{2} + 1) y^{'} - (- 10 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.428

9777	$x^{2} y^{''} + x (- 2 x^{2} + 1) y^{'} - 4 (2 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.359

9778	$x^{2} y^{''} + x (- 3 x^{2} + 1) y^{'} - 4 (- 3 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.674

9779	$x^{2} (x^{2} + 1) y^{''} + x (11 x^{2} + 5) y^{'} + 24 x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.444

9780	$4 x^{2} (x^{2} + 1) y^{''} + 8 x y^{'} - (- x^{2} + 35) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.423

9781	$x^{2} (x^{2} + 1) y^{''} - x (- x^{2} + 5) y^{'} - (25 x^{2} + 7) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.422

9782	$x^{2} (x^{2} + 1) y^{''} + x (2 x^{2} + 5) y^{'} - 21 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.408

9783	$4 x^{2} (x^{2} + 1) y^{''} + 4 x (x^{2} + 2) y^{'} - (x^{2} + 15) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.358

9784	$y^{''} - \frac{2 (t + 1) y^{'}}{t^{2} + 2 t - 1} + \frac{2 y}{t^{2} + 2 t - 1} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.356

9785	$y^{''} - 4 t y^{'} + (4 t^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.091

9786	$(- t^{2} + 1) y^{''} - 2 t y^{'} + 2 y = 0$	[_Gegenbauer]	✓	0.335

9787	$(t^{2} + 1) y^{''} - 2 t y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.364

9788	$(- t^{2} + 1) y^{''} - 2 t y^{'} + 6 y = 0$	[_Gegenbauer]	✓	0.352

9789	$(2 t + 1) y^{''} - 4 (t + 1) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.312

9790	$t^{2} y^{''} + t y^{'} + (t^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.173

9791	$y^{''} - \frac{2 t y^{'}}{t^{2} + 1} + \frac{2 y}{t^{2} + 1} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.361

9792	$y^{''} + (t^{2} + 2 t + 1) y^{'} - (4 + 4 t) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.356

9793	$2 t y^{''} + (1 - 2 t) y^{'} - y = 0$	[_Laguerre]	✓	0.253

9794	$2 t y^{''} + (t + 1) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.493

9795	$2 t^{2} y^{''} - t y^{'} + (t + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.255

9796	$2 t^{2} y^{''} + (t^{2} - t) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.347

9797	$t^{2} y^{''} + (- t^{2} + t) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.249

9798	$t y^{''} - (t^{2} + 2) y^{'} + t y = 0$	[_Lienard]	✓	0.362

9799	$t^{2} y^{''} + t (t + 1) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.312

9800	$t y^{''} - (4 + t) y^{'} + 2 y = 0$	[_Laguerre]	✓	0.338

2.2.98 Problems 9701 to 9800