Problems 11201 to 11300

Table 2.227: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

11201	$x^{2} y^{''} + 2 x^{2} f (x) y^{'} + (x^{2} (f^{'} (x) + f {(x)}^{2} + a) - v (v - 1)) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.437

11202	$x^{2} y^{''} + (x - 2 x^{2} f (x)) y^{'} + (x^{2} (1 + f {(x)}^{2} - f^{'} (x)) - f (x) x - v^{2}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.451

11203	$(x^{2} + 1) y^{''} + y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.028

11204	$(x^{2} + 1) y^{''} + y^{'} x - 9 y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.966

11205	$(x^{2} + 1) y^{''} + y^{'} x + a y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.528

11206	$(x^{2} + 1) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.914

11207	$(x^{2} + 1) y^{''} + 2 y^{'} x - v (v - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.363

11208	$(x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.924

11209	$(x^{2} + 1) y^{''} + 3 y^{'} x + a y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.755

11210	$(x^{2} + 1) y^{''} + 4 y^{'} x + 2 y - 2 \cos (x) + 2 x = 0$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.109

11211	$(x^{2} + 1) y^{''} + a x y^{'} + (a - 2) y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.232

11212	$(x^{2} - 1) y^{''} - v (v + 1) y = 0$	[_Gegenbauer]	✗	0.769

11213	$(x^{2} - 1) y^{''} - n (n + 1) y + \frac{d}{d x} LegendreP (n, x) = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.999

11214	$(x^{2} - 1) y^{''} + y^{'} x + 2 = 0$	[[_2nd_order, _missing_y]]	✓	1.006

11215	$(x^{2} - 1) y^{''} + y^{'} x + a y = 0$	[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.818

11216	$(x^{2} - 1) y^{''} + y^{'} x + f (x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.047

11217	$(x^{2} - 1) y^{''} + 2 y^{'} x = 0$	[[_2nd_order, _missing_y]]	✓	0.891

11218	$(x^{2} - 1) y^{''} + 2 y^{'} x - a = 0$	[[_2nd_order, _missing_y]]	✓	1.416

11219	$(x^{2} - 1) y^{''} + 2 y^{'} x - l y = 0$	[_Gegenbauer]	✗	1.205

11220	$(x^{2} - 1) y^{''} + 2 y^{'} x - v (v + 1) y = 0$	[_Gegenbauer]	✗	1.229

11221	$(x^{2} - 1) y^{''} - 2 y^{'} x - (v + 2) (v - 1) y = 0$	[_Gegenbauer]	✗	650.271

11222	$(x^{2} - 1) y^{''} - (3 x + 1) y^{'} - (x^{2} - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.686

11223	$(x^{2} - 1) y^{''} + 4 y^{'} x + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.731

11224	$(x^{2} - 1) y^{''} + 2 (n + 1) x y^{'} - (v + n + 1) (v - n) y = 0$	[_Gegenbauer]	✗	1.776

11225	$(x^{2} - 1) y^{''} - 2 (n - 1) x y^{'} - (v - n + 1) (v + n) y = 0$	[_Gegenbauer]	✗	1.826

11226	$(x^{2} - 1) y^{''} - 2 (v - 1) x y^{'} - 2 v y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.326

11227	$(x^{2} - 1) y^{''} + 2 a x y^{'} + a (a - 1) y = 0$	[_Gegenbauer]	✓	0.933

11228	$(x^{2} - 1) y^{''} + a x y^{'} + (b x^{2} + c x + d) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.653

11229	$(x^{2} - 1) y^{''} + (a x + b) y^{'} + c y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.781

11230	$(- a^{2} + x^{2}) y^{''} + 8 y^{'} x + 12 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.566

11231	$x (x + 1) y^{''} - (x - 1) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.664

11232	$x (x + 1) y^{''} + (a x + b) y^{'} + c y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.607

11233	$x (x + 1) y^{''} + (3 x + 2) y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.933

11234	$(x^{2} + x - 2) y^{''} + (x^{2} - x) y^{'} - (6 x^{2} + 7 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.700

11235	$x (x - 1) y^{''} + a y^{'} - 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.287

11236	$x (x - 1) y^{''} + (2 x - 1) y^{'} - v (v + 1) y = 0$	[_Jacobi]	✗	1.260

11237	$x (x - 1) y^{''} + ((a + 1) x + b) y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	1.170

11238	$x (x - 1) y^{''} + (a x + b) y^{'} + c y = 0$	[_Jacobi]	✗	1.832

11239	$x (x - 1) y^{''} + ((a + 1) x + b) y^{'} - l y = 0$	[_Jacobi]	✗	1.806

11240	$x (x - 1) y^{''} + ((a 1 + b 1 + 1) x - d 1) y^{'} + a 1 b 1 d 1 = 0$	[[_2nd_order, _missing_y]]	✓	1.075

11241	$x (x + 2) y^{''} + 2 (n + 1 + (n + 1 - 2 l) x - l x^{2}) y^{'} + (2 l (p - n - 1) x + 2 p l + m) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	2.141

11242	${(x + 1)}^{2} y^{''} + (x^{2} + x - 1) y^{'} - (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.860

11243	$x (3 + x) y^{''} + (3 x - 1) y^{'} + y - (20 x + 30) {(x^{2} + 3 x)}^{7 / 3} = 0$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	2.583

11244	$(x^{2} + 3 x + 4) y^{''} + (x^{2} + x + 1) y^{'} - (2 x + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.747

11245	$(x - 1) (x - 2) y^{''} - (2 x - 3) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	329.436

11246	${(x - 2)}^{2} y^{''} - (x - 2) y^{'} - 3 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.797

11247	$2 x^{2} y^{''} - (2 x^{2} + l - 5 x) y^{'} - (4 x - 1) y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.352

11248	$2 x (x - 1) y^{''} + (2 x - 1) y^{'} + (a x + b) y = 0$	[_Jacobi]	✗	0.940

11249	$2 x (x - 1) y^{''} + ((2 v + 5) x - 2 v - 3) y^{'} + (v + 1) y = 0$	[_Jacobi]	✗	1.479

11250	$(2 x^{2} + 6 x + 4) y^{''} + (10 x^{2} + 21 x + 8) y^{'} + (12 x^{2} + 17 x + 8) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.830

11251	$4 x^{2} y^{''} + y = 0$	[[_Emden, _Fowler]]	✓	0.347

11252	$4 x^{2} y^{''} + (4 a^{2} x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.536

11253	$4 x^{2} y^{''} - (- 4 k x + 4 m^{2} + x^{2} - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.966

11254	$4 x^{2} y^{''} + 4 y^{'} x + (- v^{2} + x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.466

11255	$4 x^{2} y^{''} + 4 y^{'} x + (- x^{2} + 2 (1 - m + 2 l) x - m^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.203

11256	$4 x^{2} y^{''} + 4 y^{'} x - (4 x^{2} + 1) y - 4 \sqrt{x^{3}} e^{x} = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.094

11257	$4 x^{2} y^{''} + 4 y^{'} x - (a x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.027

11258	$4 x^{2} y^{''} + 4 y^{'} x + f (x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.800

11259	$4 x^{2} y^{''} + 5 y^{'} x - y - \ln (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.748

11260	$4 x^{2} y^{''} + 8 y^{'} x - (4 x^{2} + 12 x + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.550

11261	$4 x^{2} y^{''} - 4 x (2 x - 1) y^{'} + (4 x^{2} - 4 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.540

11262	$4 x^{2} y^{''} + 4 x^{3} y^{'} + (x^{2} + 6) (x^{2} - 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.496

11263	$4 x^{2} y^{''} + 4 x^{2} \ln (x) y^{'} + (x^{2} \ln {(x)}^{2} + 2 x - 8) y - 4 x^{2} \sqrt{e^{x} x^{- x}} = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.800

11264	${(2 x + 1)}^{2} y^{''} - 2 (2 x + 1) y^{'} - 12 y - 3 x - 1 = 0$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.159

11265	$x (4 x - 1) y^{''} + ((4 a + 2) x - a) y^{'} + a (a - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.618

11266	${(3 x - 1)}^{2} y^{''} + 3 (3 x - 1) y^{'} - 9 y - \ln {(3 x - 1)}^{2} = 0$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	2.699

11267	$9 x (x - 1) y^{''} + 3 (2 x - 1) y^{'} - 20 y = 0$	[_Jacobi]	✓	0.674

11268	$16 x^{2} y^{''} + (4 x + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.518

11269	$16 x^{2} y^{''} + 32 y^{'} x - (5 + 4 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.654

11270	$(27 x^{2} + 4) y^{''} + 27 y^{'} x - 3 y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.032

11271	$48 x (x - 1) y^{''} + (152 x - 40) y^{'} + 53 y = 0$	[_Jacobi]	✗	1.757

11272	$50 x (x - 1) y^{''} + 25 (2 x - 1) y^{'} - 2 y = 0$	[_Jacobi, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.427

11273	$144 x (x - 1) y^{''} + (120 x - 48) y^{'} + y = 0$	[_Jacobi]	✗	1.598

11274	$144 x (x - 1) y^{''} + (168 x - 96) y^{'} + y = 0$	[_Jacobi]	✗	1.341

11275	$a x^{2} y^{''} + b x y^{'} + (c x^{2} + d x + f) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.358

11276	$a 2 x^{2} y^{''} + (a 1 x^{2} + b 1 x) y^{'} + (a 0 x^{2} + b 0 x + c 0) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	3.299

11277	$(a x^{2} + 1) y^{''} + a x y^{'} + b y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	169.711

11278	$(a^{2} x^{2} - 1) y^{''} + 2 a^{2} x y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	1.173

11279	$(a^{2} x^{2} - 1) y^{''} + 2 a^{2} x y^{'} - 2 a^{2} y = 0$	[_Gegenbauer]	✓	1.108

11280	$(a x^{2} + b x) y^{''} + 2 b y^{'} - 2 a y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.999

11281	$A 2 {(a x + b)}^{2} y^{''} + A 1 (a x + b) y^{'} + A 0 (a x + b) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.028

11282	$(a x^{2} + b x + c) y^{''} + (d x + f) y^{'} + g y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	3.731

11283	$x^{3} y^{''} + y^{'} x - (2 x + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.521

11284	$x^{3} y^{''} + 2 y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.844

11285	$x^{3} y^{''} + x^{2} y^{'} + (a x^{2} + b x + a) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.753

11286	$x^{3} y^{''} + x (x + 1) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.584

11287	$x^{3} y^{''} - x^{2} y^{'} + x y - \ln {(x)}^{3} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.388

11288	$x^{3} y^{''} - (x^{2} - 1) y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.962

11289	$x^{3} y^{''} + 3 x^{2} y^{'} + x y - 1 = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.356

11290	$x (x^{2} + 1) y^{''} + (2 x^{2} + 1) y^{'} - v (v + 1) x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.574

11291	$x (x^{2} + 1) y^{''} + 2 (x^{2} - 1) y^{'} - 2 x y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.795

11292	$x (x^{2} + 1) y^{''} + (2 (n + 1) x^{2} + 2 n + 1) y^{'} - (v - n) (v + n + 1) x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.879

11293	$x (x^{2} + 1) y^{''} - (2 (n - 1) x^{2} + 2 n - 1) y^{'} + (v + n) (- v + n - 1) x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.831

11294	$x (x^{2} - 1) y^{''} + y^{'} + y a x^{3} = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.729

11295	$x (x^{2} - 1) y^{''} + (x^{2} - 1) y^{'} - x y = 0$	[[_elliptic, _class_II]]	✗	147.497

11296	$x (x^{2} - 1) y^{''} + (3 x^{2} - 1) y^{'} + x y = 0$	[[_elliptic, _class_I]]	✗	1.289

11297	$x (x^{2} - 1) y^{''} + (a x^{2} + b) y^{'} + c x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	2.081

11298	$x (x^{2} + 2) y^{''} - y^{'} - 6 x y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.180

11299	$x (x^{2} - 2) y^{''} - (x^{3} + 3 x^{2} - 2 x - 2) y^{'} + (x^{2} + 4 x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.795

11300	$x^{2} (x + 1) y^{''} - x (2 x + 1) y^{'} + (2 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.662

2.2.113 Problems 11201 to 11300