Problems 9201 to 9300

Table 2.187: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

9201	$x^{2} y^{''} - 2 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.274

9202	$(x^{2} - 2 x) y^{''} + (- x^{2} + 2) y^{'} + (2 x - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.532

9203	$4 x^{2} y^{''} + (- 8 x^{2} + 4 x) y^{'} + (4 x^{2} - 4 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.208

9204	$y^{''} + 4 y^{'} x + (4 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.171

9205	$(2 x + 1) y^{''} - 2 y^{'} - (2 x + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.359

9206	$x y^{''} - (2 x + 2) y^{'} + (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.271

9207	$x^{2} y^{''} - 2 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.270

9208	$4 x^{2} y^{''} - 4 y^{'} x + (- 16 x^{2} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.191

9209	$4 x^{2} y^{''} - 4 y^{'} x + (4 x^{2} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.280

9210	$x^{2} y^{''} - 2 y^{'} x - (x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.191

9211	$x^{2} y^{''} - 2 x (x + 1) y^{'} + (x^{2} + 2 x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.189

9212	$x^{2} y^{''} - 2 x (x + 2) y^{'} + (x^{2} + 4 x + 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.166

9213	$x^{2} y^{''} - 4 y^{'} x + (x^{2} + 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.274

9214	$(x - 1) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.372

9215	$4 x^{2} y^{''} - 4 x (x + 1) y^{'} + (2 x + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.210

9216	$(3 x - 1) y^{''} - (3 x + 2) y^{'} - (6 x - 8) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.382

9217	$(x + 2) y^{''} + y^{'} x + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.534

9218	$x^{2} (1 - x) y^{''} + x (x + 4) y^{'} + (2 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.343

9219	$x^{2} (x + 1) y^{''} + x (2 x + 1) y^{'} - (6 x + 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.349

9220	$x^{2} (2 x^{2} + 1) y^{''} + x (2 x^{2} + 4) y^{'} + 2 (- x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.602

9221	$x^{2} (x^{2} + 2) y^{''} + 2 x (x^{2} + 5) y^{'} + 2 (- x^{2} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.661

9222	$(x^{2} + 1) y^{''} + 6 y^{'} x + 6 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.500

9223	$(x^{2} + 1) y^{''} + 2 y^{'} x - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.409

9224	$(x^{2} + 1) y^{''} - 8 y^{'} x + 20 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.468

9225	$(- x^{2} + 1) y^{''} - 8 y^{'} x - 12 y = 0$	[_Gegenbauer]	✓	0.316

9226	$(2 x^{2} + 1) y^{''} + 7 y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.611

9227	$(- x^{2} + 1) y^{''} - 5 y^{'} x - 4 y = 0$	[_Gegenbauer]	✓	0.383

9228	$(x^{2} + 1) y^{''} - 10 y^{'} x + 28 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.562

9229	$y^{''} + y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.431

9230	$(2 x^{2} + 1) y^{''} - 9 y^{'} x - 6 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.667

9231	$(2 x^{2} - 8 x + 11) y^{''} - 16 (x - 2) y^{'} + 36 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.853

9232	$y^{''} + (x - 3) y^{'} + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.476

9233	$(x^{2} - 8 x + 14) y^{''} - 8 (x - 4) y^{'} + 20 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.455

9234	$(2 x^{2} + 4 x + 5) y^{''} - 20 (x + 1) y^{'} + 60 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.764

9235	$(x^{3} + 1) y^{''} + 7 x^{2} y^{'} + 9 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.630

9236	$(2 x^{5} + 1) y^{''} + 14 x^{4} y^{'} + 10 x^{3} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.519

9237	$y^{''} + x^{6} y^{'} + 7 x^{5} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.676

9238	$(x^{8} + 1) y^{''} - 16 x^{7} y^{'} + 72 x^{6} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	220.212

9239	$y^{''} + x^{5} y^{'} + 6 y x^{4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.662

9240	$(3 x + 1) y^{''} + y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	22.473

9241	$(3 x^{2} + x + 1) y^{''} + (2 + 15 x) y^{'} + 12 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.222

9242	$(x + 2) y^{''} + (x + 1) y^{'} + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.474

9243	$(x + 4) y^{''} + (x + 2) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.467

9244	$(2 x^{2} + 3 x) y^{''} + 10 (x + 1) y^{'} + 8 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.421

9245	$x^{2} y^{''} - (6 - 7 x) y^{'} + 8 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.392

9246	$(2 x^{2} + x + 1) y^{''} + (1 + 7 x) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.379

9247	$(3 + x) y^{''} + (2 x + 1) y^{'} - (2 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.293

9248	$y^{''} + 3 y^{'} x + (2 x^{2} + 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.454

9249	$(2 + 4 x) y^{''} - 4 y^{'} - (6 + 4 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.331

9250	$y^{''} - 3 y^{'} x + (2 x^{2} + 5) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.435

9251	$2 y^{''} + 5 y^{'} x + (2 x^{2} + 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.307

9252	$y^{''} + 4 y^{'} x + (4 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.154

9253	$y^{''} + 4 y^{'} x + (4 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.145

9254	$2 x^{2} (x^{2} + x + 1) y^{''} + x (11 x^{2} + 11 x + 9) y^{'} + (7 x^{2} + 10 x + 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.449

9255	$3 x^{2} y^{''} + 2 x (- 2 x^{2} + x + 1) y^{'} + (- 8 x^{2} + 2 x) y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.583

9256	$12 x^{2} (x + 1) y^{''} + x (3 x^{2} + 35 x + 11) y^{'} - (- 5 x^{2} - 10 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.564

9257	$x^{2} (10 x^{2} + x + 5) y^{''} + x (48 x^{2} + 3 x + 4) y^{'} + (36 x^{2} + x) y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.320

9258	$18 x^{2} (x + 1) y^{''} + 3 x (x^{2} + 11 x + 5) y^{'} - (- 5 x^{2} - 2 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.544

9259	$2 x^{2} y^{''} + x (2 x + 3) y^{'} - (1 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.350

9260	$2 x^{2} y^{''} + x (5 + x) y^{'} - (2 - 3 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.485

9261	$3 x^{2} y^{''} + x (x + 1) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.598

9262	$2 x^{2} y^{''} - y^{'} x + (- 2 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.275

9263	$3 x^{2} y^{''} + x (x + 1) y^{'} - (3 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.696

9264	$2 (3 + x) x^{2} y^{''} + x (1 + 5 x) y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.462

9265	$x^{2} (x + 4) y^{''} - x (1 - 3 x) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.748

9266	$2 x^{2} y^{''} + 5 y^{'} x + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.342

9267	$6 x^{2} y^{''} + x (10 - x) y^{'} - (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.515

9268	$x^{2} (4 x + 3) y^{''} + x (11 + 4 x) y^{'} - (4 x + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.496

9269	$2 x^{2} (3 x + 2) y^{''} + x (4 + 11 x) y^{'} - (1 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.272

9270	$x^{2} (x + 2) y^{''} + 5 x (1 - x) y^{'} - (2 - 8 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.016

9271	$8 x^{2} (- x^{2} + 1) y^{''} + 2 x (- 13 x^{2} + 1) y^{'} + (- 9 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.541

9272	$x^{2} (x^{2} + 1) y^{''} - 2 x (- x^{2} + 2) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.429

9273	$x (x^{2} + 3) y^{''} + (- x^{2} + 2) y^{'} - 8 x y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.394

9274	$4 x^{2} (- x^{2} + 1) y^{''} + x (- 19 x^{2} + 7) y^{'} - (14 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.510

9275	$3 x^{2} (- x^{2} + 2) y^{''} + x (- 11 x^{2} + 1) y^{'} + (- 5 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.570

9276	$2 x^{2} (x^{2} + 2) y^{''} - x (- 7 x^{2} + 12) y^{'} + (3 x^{2} + 7) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.545

9277	$2 x^{2} (x^{2} + 2) y^{''} + x (7 x^{2} + 4) y^{'} - (- 3 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.447

9278	$2 x^{2} (2 x^{2} + 1) y^{''} + 5 x (6 x^{2} + 1) y^{'} - (- 40 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.618

9279	$x (x^{2} + 1) y^{''} + (7 x^{2} + 4) y^{'} + 8 x y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.431

9280	$2 x^{2} (x^{2} + 1) y^{''} + x (8 x^{2} + 3) y^{'} - (- 4 x^{2} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.516

9281	$9 x^{2} y^{''} + 3 x (x^{2} + 3) y^{'} - (- 5 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.471

9282	$6 x^{2} y^{''} + x (6 x^{2} + 1) y^{'} + (9 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.585

9283	$9 x^{2} (x^{2} + 1) y^{''} + 3 x (13 x^{2} + 3) y^{'} - (- 25 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.523

9284	$4 x^{2} (x^{2} + 1) y^{''} + 4 x (6 x^{2} + 1) y^{'} - (- 25 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.397

9285	$8 x^{2} (2 x^{2} + 1) y^{''} + 2 x (34 x^{2} + 5) y^{'} - (- 30 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.600

9286	$2 x^{2} (x + 1) y^{''} - x (1 - 3 x) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.254

9287	$6 x^{2} (2 x^{2} + 1) y^{''} + x (50 x^{2} + 1) y^{'} + (30 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.269

9288	$28 x^{2} (1 - 3 x) y^{''} - 7 x (5 + 9 x) y^{'} + 7 (2 + 9 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.268

9289	$8 x^{2} (- x^{2} + 2) y^{''} + 2 x (- 21 x^{2} + 10) y^{'} - (35 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.271

9290	$4 x^{2} (x^{2} + 3 x + 1) y^{''} - 4 x (- 3 x^{2} - 3 x + 1) y^{'} + 3 (x^{2} - x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.203

9291	$3 x^{2} {(x + 1)}^{2} y^{''} - x (- 11 x^{2} - 10 x + 1) y^{'} + (5 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.282

9292	$4 x^{2} (x^{2} + 2 x + 3) y^{''} - x (- 15 x^{2} - 14 x + 3) y^{'} + (7 x^{2} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.283

9293	$x^{2} (x^{2} - 2 x + 1) y^{''} - (3 + x) x y^{'} + (x + 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.490

9294	$2 x^{2} (x + 2) y^{''} + 5 x^{2} y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.313

9295	$x^{2} (- x^{2} + 2) y^{''} - 2 x (2 x^{2} + 1) y^{'} + (- 2 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.440

9296	$x^{2} y^{''} - x (5 - x) y^{'} + (9 - 4 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.549

9297	$4 x^{2} (x^{2} + x + 1) y^{''} + 12 x^{2} (x + 1) y^{'} + (3 x^{2} + 3 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.032

9298	$x^{2} (x^{2} + x + 1) y^{''} - x (- 2 x^{2} - 4 x + 1) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.177

9299	$9 x^{2} y^{''} + 3 x (- 2 x^{2} + 3 x + 5) y^{'} + (- 14 x^{2} + 12 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.660

9300	$x^{2} (2 x + 1) y^{''} + x (3 x^{2} + 14 x + 5) y^{'} + (12 x^{2} + 18 x + 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.784

2.2.93 Problems 9201 to 9300