Problems 18201 to 18300

Table 2.367: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

18201	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.171

18202	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	0.177

18203	$x y^{''} + 3 y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.131

18204	$x^{2} y^{''} + y^{'} x - 4 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.149

18205	$(- x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[_Gegenbauer]	✓	0.146

18206	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.134

18207	$y^{''} - \frac{x y^{'}}{x - 1} + \frac{y}{x - 1} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.148

18208	$x^{2} y^{''} + 2 y^{'} x - 2 y = 0$	[[_Emden, _Fowler]]	✓	0.142

18209	$x^{2} y^{''} - x (x + 2) y^{'} + (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.154

18210	$y^{''} - x f (x) y^{'} + f (x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.829

18211	$x y^{''} - (2 x + 1) y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.171

18212	$x y^{''} - (x + n) y^{'} + n y = 0$	[_Laguerre]	✗	1.311

18213	$x y^{''} - (x + 1) y^{'} + y = 0$	[_Laguerre]	✓	0.621

18214	$x y^{''} - (x + 2) y^{'} + 2 y = 0$	[_Laguerre]	✓	0.488

18215	$x y^{''} - (3 + x) y^{'} + 3 y = 0$	[_Laguerre]	✓	0.501

18216	$y^{''} - f (x) y^{'} + (f (x) - 1) y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✗	0.620

18217	$y^{''} + y^{'} - 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.325

18218	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.361

18219	$y^{''} + 8 y = 0$	[[_2nd_order, _missing_x]]	✓	1.649

18220	$2 y^{''} - 4 y^{'} + 8 y = 0$	[[_2nd_order, _missing_x]]	✓	0.556

18221	$y^{''} - 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.450

18222	$y^{''} - 9 y^{'} + 20 y = 0$	[[_2nd_order, _missing_x]]	✓	0.326

18223	$2 y^{''} + 2 y^{'} + 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.551

18224	$4 y^{''} - 12 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.444

18225	$y^{''} + y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	0.981

18226	$y^{''} - 6 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓	0.534

18227	$4 y^{''} + 20 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓	0.398

18228	$y^{''} + 2 y^{'} + 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.562

18229	$y^{''} = 4 y$	[[_2nd_order, _missing_x]]	✓	1.537

18230	$4 y^{''} - 8 y^{'} + 7 y = 0$	[[_2nd_order, _missing_x]]	✓	0.562

18231	$2 y^{''} + y^{'} - y = 0$	[[_2nd_order, _missing_x]]	✓	0.331

18232	$16 y^{''} - 8 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.354

18233	$y^{''} + 4 y^{'} + 5 y = 0$	[[_2nd_order, _missing_x]]	✓	0.468

18234	$y^{''} + 4 y^{'} - 5 y = 0$	[[_2nd_order, _missing_x]]	✓	0.329

18235	$y^{''} - 5 y^{'} + 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.572

18236	$y^{''} - 6 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.555

18237	$y^{''} - 6 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.629

18238	$y^{''} + 4 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.774

18239	$y^{''} + 4 y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.667

18240	$y^{''} + 8 y^{'} - 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.583

18241	$x^{2} y^{''} + 3 y^{'} x + 10 y = 0$	[[_Emden, _Fowler]]	✓	1.036

18242	$2 x^{2} y^{''} + 10 y^{'} x + 8 y = 0$	[[_Emden, _Fowler]]	✓	0.948

18243	$x^{2} y^{''} + 2 y^{'} x - 12 y = 0$	[[_Emden, _Fowler]]	✓	0.745

18244	$4 x^{2} y^{''} - 3 y = 0$	[[_Emden, _Fowler]]	✓	0.410

18245	$x^{2} y^{''} - 3 y^{'} x + 4 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.910

18246	$x^{2} y^{''} + 2 y^{'} x - 6 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.700

18247	$x^{2} y^{''} + 2 y^{'} x + 3 y = 0$	[[_Emden, _Fowler]]	✓	1.156

18248	$x^{2} y^{''} + y^{'} x - 2 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.975

18249	$x^{2} y^{''} + y^{'} x - 16 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.840

18250	$x y^{''} + (x^{2} - 1) y^{'} + x^{3} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.332

18251	$y^{''} + 3 y^{'} x + x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.854

18252	$y^{''} + 3 y^{'} - 10 y = 6 e^{4 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.441

18253	$y^{''} + 4 y = 3 \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.734

18254	$y^{''} + 10 y^{'} + 25 y = 14 e^{- 5 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.552

18255	$y^{''} - 2 y^{'} + 5 y = 25 x^{2} + 12$	[[_2nd_order, _with_linear_symmetries]]	✓	0.622

18256	$y^{''} - y^{'} - 6 y = 20 e^{- 2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.448

18257	$y^{''} - 3 y^{'} + 2 y = 14 \sin (2 x) - 18 \cos (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.608

18258	$y^{''} + y = 2 \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.674

18259	$y^{''} - 2 y^{'} = 12 x - 10$	[[_2nd_order, _missing_y]]	✓	1.063

18260	$y^{''} - 2 y^{'} + y = 6 e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.490

18261	$y^{''} - 2 y^{'} + 2 y = e^{x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.648

18262	$y^{''} + y^{'} = 10 x^{4} + 2$	[[_2nd_order, _missing_y]]	✓	1.065

18263	$y^{''} + k^{2} y = \sin (b x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.697

18264	$y^{''} + 4 y = 4 \cos (2 x) + 6 \cos (x) + 8 x^{2} - 4 x$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.255

18265	$y^{''} + 9 y = 2 \sin (3 x) + 4 \sin (x) - 26 e^{- 2 x} + 27 x^{3}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.290

18266	$y^{''} - 2 y^{'} + y = 2 x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.536

18267	$y^{''} - y^{'} - 6 y = e^{- x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.428

18268	$y^{''} + 4 y = \tan (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.054

18269	$y^{''} + 2 y^{'} + y = e^{- x} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.654

18270	$y^{''} - 2 y^{'} - 3 y = 64 x e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.513

18271	$y^{''} + 2 y^{'} + 5 y = e^{- x} \sec (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.797

18272	$2 y^{''} + 3 y^{'} + y = e^{- 3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.466

18273	$y^{''} - 3 y^{'} + 2 y = \frac{1}{1 + e^{- x}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.601

18274	$y^{''} + y = \sec (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.696

18275	$y^{''} + y = \cot {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.930

18276	$y^{''} + y = \cot (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.314

18277	$y^{''} + y = x \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.736

18278	$y^{''} + y = \tan (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.721

18279	$y^{''} + y = \sec (x) \tan (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.860

18280	$y^{''} + y = \sec (x) \csc (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.059

18281	$(x^{2} - 1) y^{''} - 2 y^{'} x + 2 y = {(x^{2} - 1)}^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.193

18282	$(x^{2} + x) y^{''} + (- x^{2} + 2) y^{'} - (x + 2) y = x {(x + 1)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.966

18283	$(1 - x) y^{''} + y^{'} x - y = {(1 - x)}^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.985

18284	$x y^{''} - (x + 1) y^{'} + y = x^{2} e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.720

18285	$x^{2} y^{''} - 2 y^{'} x + 2 y = x e^{- x}$	[[_2nd_order, _with_linear_symmetries]]	✓	2.062

18286	$y^{'''} - 3 y^{''} + 2 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.070

18287	$y^{'''} - 3 y^{''} + 4 y^{'} - 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.086

18288	$y^{'''} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.081

18289	$y^{'''} + y = 0$	[[_3rd_order, _missing_x]]	✓	0.088

18290	$y^{'''} + 3 y^{''} + 3 y^{'} + y = 0$	[[_3rd_order, _missing_x]]	✓	0.084

18291	$y^{''''} + 4 y^{'''} + 6 y^{''} + 4 y^{'} + y = 0$	[[_high_order, _missing_x]]	✓	0.081

18292	$y^{''''} - y = 0$	[[_high_order, _missing_x]]	✓	0.080

18293	$y^{''''} + 5 y^{''} + 4 y = 0$	[[_high_order, _missing_x]]	✓	0.089

18294	$y^{''''} + 2 a^{2} y^{''} + a^{4} y = 0$	[[_high_order, _missing_x]]	✓	0.106

18295	$y^{''''} + 2 a^{2} y^{''} + a^{4} y = 0$	[[_high_order, _missing_x]]	✓	0.113

18296	$y^{''''} + 2 y^{'''} + 2 y^{''} + 2 y^{'} + y = 0$	[[_high_order, _missing_x]]	✓	0.097

18297	$y^{''''} + 2 y^{'''} - 2 y^{''} - 6 y^{'} + 5 y = 0$	[[_high_order, _missing_x]]	✓	0.086

18298	$y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = 0$	[[_3rd_order, _missing_x]]	✓	0.079

18299	$y^{''''} + y^{'''} - 3 y^{''} - 5 y^{'} - 2 y = 0$	[[_high_order, _missing_x]]	✓	0.088

18300	$y^{(5)} - 6 y^{''''} - 8 y^{'''} + 48 y^{''} + 16 y^{'} - 96 y = 0$	[[_high_order, _missing_x]]	✓	0.084

2.2.183 Problems 18201 to 18300