Problems 9401 to 9500

Table 2.191: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

9401	$6 x^{2} y^{''} + x (1 + 18 x) y^{'} + (1 + 12 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.487

9402	$3 x^{2} y^{''} - x (8 + x) y^{'} + 6 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	3.594

9403	$2 x^{2} y^{''} - x (2 x + 1) y^{'} + 2 (4 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.808

9404	$4 x^{2} y^{''} - 4 x^{2} y^{'} + (2 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.334

9405	$x^{2} y^{''} + x (3 - 2 x) y^{'} + (- 2 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.485

9406	$x^{2} y^{''} - (3 + x) x y^{'} + (4 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.466

9407	$x^{2} y^{''} + x (3 - x) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.482

9408	$x^{2} y^{''} - (2 \sqrt{5} - 1) x y^{'} + (\frac{19}{4} - 3 x^{2}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.281

9409	$x^{2} y^{''} + x (x - 3) y^{'} + (4 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.349

9410	$x^{2} y^{''} + x^{2} y^{'} - (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.319

9411	$x^{2} y^{''} + 2 x^{2} y^{'} + (x - \frac{3}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.343

9412	$x^{2} (x + 1) y^{''} + x^{2} y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.304

9413	$x^{2} y^{''} + x (x^{2} + 6) y^{'} + 6 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.496

9414	$x^{2} y^{''} + x (1 - x) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.345

9415	$x^{2} y^{''} - (3 + x) x y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.445

9416	$x^{2} y^{''} - x^{2} y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.347

9417	$x^{2} y^{''} - x^{2} y^{'} - (3 x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.453

9418	$x^{2} y^{''} + x (5 - x) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.531

9419	$4 x^{2} y^{''} + 4 x (1 - x) y^{'} + (2 x - 9) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.390

9420	$x^{2} y^{''} + 2 x (x + 2) y^{'} + 2 (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.461

9421	$x^{2} y^{''} - x (1 - x) y^{'} + (1 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.374

9422	$4 x^{2} y^{''} + 4 x (2 x + 1) y^{'} + (4 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.194

9423	$x^{2} y^{''} + x (x + 4) y^{'} + (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.441

9424	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{9}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.467

9425	$x y^{''} + 2 y^{'} + x y = 0$	[_Lienard]	✓	0.248

9426	$2 x y^{''} + 5 (- 2 x + 1) y^{'} - 5 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.593

9427	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.242

9428	$x y^{''} + (x + n) y^{'} + (n + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.573

9429	$x^{4} y^{''} + y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.535

9430	$x^{2} y^{''} + (2 x^{2} + x) y^{'} - 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.381

9431	$(4 x^{3} - 14 x^{2} - 2 x) y^{''} - (6 x^{2} - 7 x + 1) y^{'} + (6 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.559

9432	$x^{2} y^{''} + x^{2} y^{'} + (x - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.337

9433	$x^{2} y^{''} - x^{2} y^{'} + (x - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.383

9434	$x^{2} (1 - 4 x) y^{''} - \frac{y^{'} x}{2} - \frac{3 x y}{4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.508

9435	$x^{2} y^{''} + (x^{2} + x) y^{'} + (x - 9) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.362

9436	$x^{2} y^{''} + x (x + 1) y^{'} + (3 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.395

9437	$x^{2} y^{''} - (x^{2} + 4 x) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.419

9438	$2 x^{2} y^{''} - (3 x + 2) y^{'} + \frac{(2 x - 1) y}{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.601

9439	$x (1 - x) y^{''} + (\frac{3}{2} - 2 x) y^{'} - \frac{y}{4} = 0$	[_Jacobi]	✓	0.334

9440	$2 x (1 - x) y^{''} + y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.282

9441	$2 x (1 - x) y^{''} + (1 - 11 x) y^{'} - 10 y = 0$	[_Jacobi]	✓	0.326

9442	$x (1 - x) y^{''} + \frac{(- 2 x + 1) y^{'}}{3} + \frac{20 y}{9} = 0$	[_Jacobi]	✓	0.354

9443	$4 y^{''} + \frac{3 (- x^{2} + 2) y}{{(- x^{2} + 1)}^{2}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.289

9444	$u^{''} - \frac{2 u^{'}}{x} - a^{2} u = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.489

9445	$u^{''} + \frac{2 u^{'}}{x} - a^{2} u = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.200

9446	$u^{''} + \frac{2 u^{'}}{x} + a^{2} u = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.225

9447	$u^{''} + \frac{4 u^{'}}{x} - a^{2} u = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.407

9448	$u^{''} + \frac{4 u^{'}}{x} + a^{2} u = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.489

9449	$y^{''} - a^{2} y = \frac{6 y}{x^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.420

9450	$y^{''} + n^{2} y = \frac{6 y}{x^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.536

9451	$x^{2} y^{''} + y^{'} x - (x^{2} + \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.180

9452	$x^{2} y^{''} + y^{'} x + \frac{(- 9 a^{2} + 4 x^{2}) y}{4 a^{2}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.488

9453	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{25}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.496

9454	$y^{''} + q y^{'} = \frac{2 y}{x^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.462

9455	$x y^{''} + 3 y^{'} + 4 x^{3} y = 0$	[[_Emden, _Fowler]]	✓	0.458

9456	$(x^{2} + 2 x) y^{''} - 2 (x + 1) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.335

9457	$(x^{2} + 2 x) y^{''} - 2 (x + 1) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.321

9458	$(x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.377

9459	$(x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.402

9460	$y^{''} - 4 y^{'} x + (4 x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.149

9461	$y^{''} - 4 y^{'} x + (4 x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.136

9462	$(2 x - 3) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.542

9463	$y^{''} - y^{'} x - 3 y = 0$	[_Hermite]	✓	0.412

9464	$(x^{2} + 1) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.401

9465	$y^{''} - y^{'} x + 2 y = 0$	[_Hermite]	✓	0.365

9466	$(- x^{2} + 1) y^{''} - y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.930

9467	$x {(x + 1)}^{2} y^{''} + (- x^{2} + 1) y^{'} + (x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.281

9468	$2 x y^{''} - y^{'} + 2 y = 0$	[[_Emden, _Fowler]]	✓	0.333

9469	$x y^{''} + y^{'} x - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.338

9470	$x {(x - 1)}^{2} y^{''} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.256

9471	$y^{''} - 2 y^{'} x + x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.280

9472	$x (- x^{2} + 2) y^{''} - (x^{2} + 4 x + 2) ((1 - x) y^{'} + y) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.615

9473	$x^{2} (x + 1) y^{''} - (2 x + 1) (y^{'} x - y) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.328

9474	$2 x^{2} (2 - x) y^{''} - x (4 - x) y^{'} + (3 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.264

9475	$x^{2} (1 - x) y^{''} + (5 x - 4) x y^{'} + (6 - 9 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.302

9476	$x y^{''} + (4 x^{2} + 1) y^{'} + 4 x (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.277

9477	$y^{''} - 2 y^{'} x + 8 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.341

9478	$(- x^{2} + 1) y^{''} - 2 y^{'} x + 12 y = 0$	[_Gegenbauer]	✓	0.408

9479	$x (x + 2) y^{''} + 2 (x + 1) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.325

9480	$x (x + 2) y^{''} + (x + 1) y^{'} - 4 y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.304

9481	$(x - 1) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.361

9482	$(x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.458

9483	$(x^{2} - 2 x + 10) y^{''} + y^{'} x - 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.515

9484	$(x^{2} - 2 x + 10) y^{''} + y^{'} x - 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.548

9485	$y^{''} - y^{'} x + 2 y = 0$	[_Hermite]	✓	0.368

9486	$(x + 2) y^{''} + y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.415

9487	$(x^{2} + 1) y^{''} - 6 y = 0$	[[_Emden, _Fowler]]	✓	0.344

9488	$(x^{2} + 2) y^{''} + 3 y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.604

9489	$(x - 1) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.324

9490	$x^{2} y^{''} + (\frac{5}{3} x + x^{2}) y^{'} - \frac{y}{3} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.526

9491	$2 x y^{''} - y^{'} + 2 y = 0$	[[_Emden, _Fowler]]	✓	0.326

9492	$2 x y^{''} - (2 x + 3) y^{'} + y = 0$	[_Laguerre]	✓	0.567

9493	$2 x^{2} y^{''} + 3 y^{'} x + (2 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.334

9494	$x y^{''} + 2 y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.155

9495	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.273

9496	$x y^{''} + (x - 6) y^{'} - 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.433

9497	$x^{4} y^{''} + λ y = 0$	[[_Emden, _Fowler]]	✓	0.414

9498	$4 x^{2} y^{''} + 4 y^{'} x + (4 x^{2} - 25) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.634

9499	$x^{2} y^{''} + y^{'} x + (36 x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.279

9500	$x^{2} y^{''} + (x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.432

2.2.95 Problems 9401 to 9500