Problems 9501 to 9600

Table 2.193: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

9501	$x y^{''} + 3 y^{'} + x^{3} y = 0$	[[_Emden, _Fowler]]	✓	0.406

9502	$x^{2} y^{''} + 4 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.250

9503	$16 x^{2} y^{''} + 32 y^{'} x + (x^{4} - 12) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.489

9504	$y^{''} - x^{2} y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.535

9505	$x y^{''} - (x + 2) y^{'} + 2 y = 0$	[_Laguerre]	✓	0.328

9506	$y^{''} + y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.322

9507	$(- x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[_Gegenbauer]	✓	0.341

9508	$y^{''} - 4 y^{'} x + (4 x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.155

9509	$(- x^{2} + 1) y^{''} - 2 y^{'} x + 30 y = 0$	[_Gegenbauer]	✓	0.457

9510	$x y^{''} + 2 y^{'} + x y = 0$	[_Lienard]	✓	0.243

9511	$x y^{''} + (2 x + 1) y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.287

9512	$2 x (x - 1) y^{''} - (x + 1) y^{'} + y = 0$	[_Jacobi]	✓	0.291

9513	$x y^{''} + 2 y^{'} + 4 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.237

9514	$x y^{''} + (2 - 2 x) y^{'} + (x - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.181

9515	$x^{2} y^{''} + 6 y^{'} x + (4 x^{2} + 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.261

9516	$x y^{''} + (- 2 x + 1) y^{'} + (x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.266

9517	$x (1 - x) y^{''} + (\frac{1}{2} + 2 x) y^{'} - 2 y = 0$	[_Jacobi]	✓	0.364

9518	$4 (t^{2} - 3 t + 2) y^{''} - 2 y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.443

9519	$2 (t^{2} - 5 t + 6) y^{''} + (2 t - 3) y^{'} - 8 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.345

9520	$3 t (1 + t) y^{''} + y^{'} t - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.475

9521	$x^{2} y^{''} + \frac{(x + \frac{3}{4}) y}{4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.337

9522	$x^{2} y^{''} + y^{'} x + \frac{(x^{2} - 1) y}{4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.268

9523	$x y^{''} + (- 2 x + 1) y^{'} + (x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.259

9524	$x y^{''} - (x + 1) y^{'} + y = 0$	[_Laguerre]	✓	0.323

9525	$x y^{''} + 3 y^{'} + 4 x^{3} y = 0$	[[_Emden, _Fowler]]	✓	0.402

9526	$x^{2} (- x^{2} + 1) y^{''} + 2 x (- x^{2} + 1) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.318

9527	$2 x y^{''} + (x - 2) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.338

9528	$x y^{''} + 2 y^{'} + x y = 0$	[_Lienard]	✓	0.244

9529	$y^{''} + 2 x^{2} y^{'} + (x^{4} + 2 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.214

9530	$u^{''} + \frac{u}{x^{2}} = 0$	[[_Emden, _Fowler]]	✓	0.351

9531	$u^{''} - (2 x + 1) u^{'} + (x^{2} + x - 1) u = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.181

9532	$y^{''} + 2 y^{'} + (1 + \frac{2}{{(3 x + 1)}^{2}}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.259

9533	$x^{2} y^{''} - 2 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.233

9534	$y^{''} + \frac{2 y^{'}}{x} - \frac{2 y}{{(x + 1)}^{2}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.221

9535	$y^{''} + \frac{y}{2 x^{4}} = 0$	[[_Emden, _Fowler]]	✓	0.415

9536	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.437

9537	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.367

9538	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.348

9539	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.336

9540	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.413

9541	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.390

9542	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.402

9543	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.354

9544	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.351

9545	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.354

9546	$y^{''} - y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.435

9547	$x y^{''} + 2 y^{'} + x y = 0$	[_Lienard]	✓	0.245

9548	$2 x^{2} y^{''} + 3 y^{'} x - x y = 0$	[[_Emden, _Fowler]]	✓	0.309

9549	$x^{2} y^{''} + (3 x^{2} + 2 x) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.322

9550	$2 x^{2} (x^{2} + x + 1) y^{''} + x (11 x^{2} + 11 x + 9) y^{'} + (7 x^{2} + 10 x + 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.371

9551	$x y^{''} + (x + 1) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.433

9552	$x^{2} (x^{2} - 2 x + 1) y^{''} - (3 + x) x y^{'} + (x + 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.485

9553	$2 x^{2} (x + 2) y^{''} + 5 x^{2} y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.309

9554	$x^{2} y^{''} + 4 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.233

9555	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.271

9556	$x^{2} y^{''} - y^{'} x - (x^{2} + \frac{5}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.371

9557	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.266

9558	$x^{2} y^{''} + 3 y^{'} x + 4 y x^{4} = 0$	[[_Emden, _Fowler]]	✓	0.489

9559	$y^{''} = (x^{2} + 3) y$	[[_2nd_order, _with_linear_symmetries]]	✓	0.347

9560	$y^{''} + 2 y^{'} x + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.160

9561	$x^{3} y^{''} + y^{'} - \frac{y}{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.320

9562	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.255

9563	$4 x^{2} y^{''} + (- 8 x^{2} + 4 x) y^{'} + (4 x^{2} - 4 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.219

9564	$y^{''} - y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.343

9565	$(x^{2} - 1) y^{''} - 2 y^{'} x + 2 y = 0$	[_Gegenbauer]	✓	0.311

9566	$x^{2} y^{''} - x (x + 2) y^{'} + (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.184

9567	$(x + 1) y^{''} - (x + 2) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.352

9568	$(- x^{2} + 1) y^{''} + 2 y^{'} x - 2 y = 0$	[_Gegenbauer]	✓	0.307

9569	$(- x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[_Gegenbauer]	✓	0.405

9570	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.254

9571	$(x^{2} - 1) y^{''} - 6 y^{'} x + 12 y = 0$	[_Gegenbauer]	✓	0.303

9572	$(x^{2} + 3) y^{''} - 7 y^{'} x + 16 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.525

9573	$(x^{2} - 1) y^{''} + 8 y^{'} x + 12 y = 0$	[_Gegenbauer]	✓	0.346

9574	$3 y^{''} + y^{'} x - 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.349

9575	$5 y^{''} - 2 y^{'} x + 10 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.436

9576	$y^{''} - x^{2} y^{'} - 3 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.402

9577	$(x^{2} + 1) y^{''} + 2 y^{'} x - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.399

9578	$y^{''} + y^{'} x - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.435

9579	$(x^{2} - 6 x + 10) y^{''} - 4 (x - 3) y^{'} + 6 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.481

9580	$(x^{2} + 6 x) y^{''} + (3 x + 9) y^{'} - 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.429

9581	$t y^{''} + (t^{2} - 1) y^{'} + t^{3} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.727

9582	$t^{2} y^{''} - t (t + 2) y^{'} + (t + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.178

9583	$(x - 1) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.355

9584	$x^{2} y^{''} - (x - \frac{3}{16}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.248

9585	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.278

9586	$t^{2} y^{''} - t (t + 2) y^{'} + (t + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.179

9587	$t y^{''} - (1 + t) y^{'} + y = 0$	[_Laguerre]	✓	0.336

9588	$(1 - t) y^{''} + y^{'} t - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.358

9589	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.256

9590	$t y^{''} - (1 + t) y^{'} + y = 0$	[_Laguerre]	✓	0.407

9591	$(1 - t) y^{''} + y^{'} t - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.367

9592	$y^{''} + y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.339

9593	$(x^{2} + 1) y^{''} - 4 y^{'} x + 6 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.437

9594	$(1 - x) y^{''} + y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.373

9595	$2 y^{''} + y^{'} x + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.373

9596	$y^{''} + y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.314

9597	$(1 - x) y^{''} + y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.354

9598	$y^{''} + y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.340

9599	$(- x^{2} + 4) y^{''} + y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.257

9600	$4 x^{2} y^{''} - 4 y^{'} x + (- 16 x^{2} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.187

2.2.96 Problems 9501 to 9600