Problems 11001 to 11100

Table 2.223: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

11001	$y^{''} + y - \sin (a x) \sin (b x) = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.248

11002	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	1.651

11003	$y^{''} - 2 y - 4 x^{2} e^{x^{2}} = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.600

11004	$y^{''} + a^{2} y - \cot (a x) = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.290

11005	$y^{''} + l y = 0$	[[_2nd_order, _missing_x]]	✓	1.769

11006	$y^{''} + (a x + b) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.222

11007	$y^{''} - (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.367

11008	$y^{''} - (x^{2} + a) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.656

11009	$y^{''} - (a^{2} x^{2} + a) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.487

11010	$y^{''} - c x^{a} y = 0$	[[_Emden, _Fowler]]	✓	0.306

11011	$y^{''} - (a^{2} x^{2 n} - 1) y = 0$	[_Titchmarsh]	✗	0.533

11012	$y^{''} + (a x^{2 c} + b x^{c - 1}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.545

11013	$y^{''} + (e^{2 x} - v^{2}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.323

11014	$y^{''} + a e^{b x} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.302

11015	$y^{''} - (4 a^{2} b^{2} x^{2} e^{2 b x^{2}} - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.608

11016	$y^{''} + (a e^{2 x} + b e^{x} + c) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.583

11017	$y^{''} + (a \cosh {(x)}^{2} + b) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.129

11018	$y^{''} + (a \cos (2 x) + b) y = 0$	[_ellipsoidal]	✗	1.001

11019	$y^{''} + (a \cos {(x)}^{2} + b) y = 0$	[_ellipsoidal]	✗	1.360

11020	$y^{''} - (1 + 2 \tan {(x)}^{2}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.137

11021	$y^{''} - (\frac{m (m - 1)}{\cos {(x)}^{2}} + \frac{n (n - 1)}{\sin {(x)}^{2}} + a) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	6.380

11022	$y^{''} - (n (n + 1) k^{2} JacobiSN {(x, k)}^{2} + b) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.534

11023	$y^{''} - (f {(x)}^{2} + f^{'} (x)) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.583

11024	$y^{''} + y^{'} + a e^{- 2 x} y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.988

11025	$y^{''} - y^{'} + e^{2 x} y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.604

11026	$y^{''} + a y^{'} + b y = 0$	[[_2nd_order, _missing_x]]	✓	1.402

11027	$y^{''} + a y^{'} + b y - f (x) = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	6.101

11028	$y^{''} + a y^{'} - (b^{2} x^{2} + c) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.931

11029	$y^{''} + 2 a y^{'} + f (x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.639

11030	$y^{''} + y^{'} x + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.766

11031	$y^{''} + y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.696

11032	$y^{''} + y^{'} x + (n + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.845

11033	$y^{''} + y^{'} x - n y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.860

11034	$y^{''} - y^{'} x + 2 y = 0$	[_Hermite]	✓	0.537

11035	$y^{''} - y^{'} x - a y = 0$	[_Hermite]	✗	0.789

11036	$y^{''} - y^{'} x + (x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.385

11037	$y^{''} - 2 y^{'} x + a y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.775

11038	$y^{''} + 4 y^{'} x + (4 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.525

11039	$y^{''} - 4 y^{'} x + (3 x^{2} + 2 n - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.847

11040	$y^{''} - 4 y^{'} x + (4 x^{2} - 1) y - e^{x} = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.810

11041	$y^{''} - 4 y^{'} x + (4 x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.448

11042	$y^{''} - 4 y^{'} x + (4 x^{2} - 3) y - e^{x^{2}} = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.734

11043	$y^{''} + a x y^{'} + b y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.874

11044	$y^{''} + 2 a x y^{'} + a^{2} x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.314

11045	$y^{''} + (a x + b) y^{'} + (c x + d) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.134

11046	$y^{''} + (a x + b) y^{'} + (a 1 x^{2} + b 1 x + c 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	2.995

11047	$y^{''} - x^{2} y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.817

11048	$y^{''} - x^{2} y^{'} - {(x + 1)}^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.647

11049	$y^{''} - x^{2} (x + 1) y^{'} + x (x^{4} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.582

11050	$y^{''} + x^{4} y^{'} - x^{3} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.928

11051	$y^{''} + a x^{q - 1} y^{'} + b x^{q - 2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.929

11052	$y^{''} + \sqrt{x} y^{'} + (\frac{1}{4 \sqrt{x}} + \frac{x}{4} - 9) y - x e^{- \frac{x^{3 / 2}}{3}} = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.959

11053	$y^{''} - \frac{y^{'}}{\sqrt{x}} + \frac{(x + \sqrt{x} - 8) y}{4 x^{2}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.544

11054	$y^{''} - (2 e^{x} + 1) y^{'} + e^{2 x} y - e^{3 x} = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.305

11055	$y^{''} + a y^{'} + \tan (x) + b y = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	37.505

11056	$y^{''} + 2 n y^{'} \cot (x) + (- a^{2} + n^{2}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	2.063

11057	$y^{''} + y^{'} \tan (x) + \cos {(x)}^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.988

11058	$y^{''} + y^{'} \tan (x) - \cos {(x)}^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.025

11059	$y^{''} + \cot (x) y^{'} + v (v + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.751

11060	$y^{''} - \cot (x) y^{'} + y \sin {(x)}^{2} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.107

11061	$y^{''} + a y^{'} \tan (x) + b y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.726

11062	$y^{''} + 2 a y^{'} \cot (a x) + (- a^{2} + b^{2}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.777

11063	$y^{''} + f (x) y^{'} + (\frac{f {(x)}^{2}}{4} + \frac{f^{'} (x)}{2} + a) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.972

11064	$y^{''} - \frac{a f^{'} (x) y^{'}}{f (x)} + b f {(x)}^{2 a} y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.122

11065	$y^{''} - (\frac{f^{'} (x)}{f (x)} + 2 a) y^{'} + (\frac{a f^{'} (x)}{f (x)} + a^{2} - b^{2} f {(x)}^{2}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.102

11066	$y^{''} - (\frac{2 f^{'} (x)}{f (x)} + \frac{g^{''} (x)}{g^{'} (x)} - \frac{g^{'} (x)}{g (x)}) y^{'} + (\frac{f^{'} (x) (\frac{2 f^{'} (x)}{f (x)} + \frac{g^{''} (x)}{g^{'} (x)} - \frac{g^{'} (x)}{g (x)})}{f (x)} - \frac{f^{''} (x)}{f (x)} - \frac{v^{2} {g^{'} (x)}^{2}}{g {(x)}^{2}} + {g^{'} (x)}^{2}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	2.034

11067	$y^{''} - (\frac{g^{''} (x)}{g^{'} (x)} + \frac{(2 v - 1) g^{'} (x)}{g (x)} + \frac{2 h^{'} (x)}{h (x)}) y^{'} + (\frac{h^{'} (x) (\frac{g^{''} (x)}{g^{'} (x)} + \frac{(2 v - 1) g^{'} (x)}{g (x)} + \frac{2 h^{'} (x)}{h (x)})}{h (x)} - \frac{h^{''} (x)}{h (x)} + {g^{'} (x)}^{2}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.999

11068	$4 y^{''} + 9 x y = 0$	[[_Emden, _Fowler]]	✓	0.312

11069	$4 y^{''} - (x^{2} + a) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.691

11070	$4 y^{''} + 4 y^{'} \tan (x) - (5 \tan {(x)}^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	2.271

11071	$a y^{''} - (a b + c + x) y^{'} + (b (x + c) + d) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.348

11072	$a^{2} y^{''} + a (a^{2} - 2 b e^{- a x}) y^{'} + b^{2} e^{- 2 a x} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.957

11073	$x (y^{''} + y) - \cos (x) = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.862

11074	$x y^{''} + (x + a) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.706

11075	$x y^{''} + y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.769

11076	$x y^{''} + y^{'} + a y = 0$	[[_Emden, _Fowler]]	✓	0.351

11077	$x y^{''} + y^{'} + l x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.540

11078	$x y^{''} + y^{'} + (x + a) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.937

11079	$x y^{''} - y^{'} + a y = 0$	[[_Emden, _Fowler]]	✓	0.354

11080	$x y^{''} - y^{'} - y a x^{3} = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.324

11081	$x y^{''} - y^{'} + x^{3} (e^{x^{2}} - v^{2}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.782

11082	$x y^{''} + 2 y^{'} - x y - e^{x} = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.232

11083	$x y^{''} + 2 y^{'} + y a x = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.863

11084	$x y^{''} + 2 y^{'} + a x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.311

11085	$x y^{''} - 2 y^{'} + a y = 0$	[[_Emden, _Fowler]]	✓	0.367

11086	$x y^{''} + v y^{'} + a y = 0$	[[_Emden, _Fowler]]	✓	0.458

11087	$x y^{''} + a y^{'} + b x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.638

11088	$x y^{''} + a y^{'} + b x^{a 1} y = 0$	[[_Emden, _Fowler]]	✓	0.390

11089	$x y^{''} + (x + b) y^{'} + a y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.179

11090	$x y^{''} + (x + a + b) y^{'} + a y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.378

11091	$x y^{''} - y^{'} x - y - x (x + 1) e^{x} = 0$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.079

11092	$x y^{''} - y^{'} x - a y = 0$	[_Laguerre]	✗	0.747

11093	$x y^{''} - (x + 1) y^{'} + y = 0$	[_Laguerre]	✓	0.607

11094	$x y^{''} - (x + 1) y^{'} - 2 (x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.513

11095	$x y^{''} + (b - x) y^{'} - a y = 0$	[_Laguerre]	✗	1.219

11096	$x y^{''} - 2 (x - 1) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.813

11097	$x y^{''} - (3 x - 2) y^{'} - (2 x - 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.971

11098	$x y^{''} + (a x + b + n) y^{'} + n a y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.466

11099	$x y^{''} - (a + b) (x + 1) y^{'} + a b x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.540

11100	$x y^{''} + ((a + b) x + m + n) y^{'} + (a b x + a n + b m) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.968

2.2.111 Problems 11001 to 11100