Problems 15201 to 15300

Table 2.307: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

15201	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.301

15202	$x y^{''} + (2 + 2 x) y^{'} + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.097

15203	$\sin {(x)}^{2} y^{''} - 2 \cos (x) \sin (x) y^{'} + (1 + \cos {(x)}^{2}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.122

15204	$x^{2} y^{''} - 2 x y^{'} + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.151

15205	$x^{2} y^{''} + x y^{'} + y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.094

15206	$x^{2} y^{''} + x y^{'} + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.166

15207	$y^{''} - 4 y^{'} + 3 y = 9 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.335

15208	$y^{''} - 6 y^{'} + 8 y = e^{4 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.441

15209	$x^{2} y^{''} + x y^{'} - y = \sqrt{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	0.175

15210	$x^{2} y^{''} - 20 y = 27 x^{5}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.177

15211	$x y^{''} + (2 + 2 x) y^{'} + 2 y = 8 e^{2 x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	0.215

15212	$(x + 1) y^{''} + x y^{'} - y = {(x + 1)}^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.213

15213	$y^{'''} - 9 y^{''} + 27 y^{'} - 27 y = 0$	[[_3rd_order, _missing_x]]	✓	0.053

15214	$y^{'''} - 9 y^{''} + 27 y^{'} - 27 y = e^{3 x} \sin (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.132

15215	$y^{''''} - 8 y^{'''} + 24 y^{''} - 32 y^{'} + 16 y = 0$	[[_high_order, _missing_x]]	✓	0.061

15216	$x^{3} y^{'''} - 4 y^{''} + 10 y^{'} - 12 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.040

15217	$y^{''} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.272

15218	$y^{''} - 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.247

15219	$y^{''} + y^{'} - 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.436

15220	$y^{''} - 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.339

15221	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.770

15222	$4 x^{2} y^{''} + 4 x y^{'} - y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.507

15223	$x^{2} y^{''} - x y^{'} + y = 0$ i.c.	[[_Emden, _Fowler]]	✓	1.876

15224	$x y^{''} - y^{'} + 4 x^{3} y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	2.154

15225	${(x + 1)}^{2} y^{''} - 2 (x + 1) y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.869

15226	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.936

15227	$x y^{''} - y^{'} + 4 x^{3} y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.197

15228	$y^{'''} + 4 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.068

15229	$y^{''''} - y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.077

15230	$y^{''} - 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.594

15231	$y^{''} + 2 y^{'} - 3 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.429

15232	$y^{''} - 10 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.439

15233	$y^{''} + 5 y^{'} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.169

15234	$y^{'''} - 9 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.048

15235	$y^{''''} - 10 y^{''} + 9 y = 0$	[[_high_order, _missing_x]]	✓	0.059

15236	$y^{''} - 7 y^{'} + 10 y = 0$	[[_2nd_order, _missing_x]]	✓	0.884

15237	$y^{''} + 2 y^{'} - 24 y = 0$	[[_2nd_order, _missing_x]]	✓	0.944

15238	$y^{''} - 25 y = 0$	[[_2nd_order, _missing_x]]	✓	2.072

15239	$y^{''} + 3 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	1.958

15240	$4 y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	2.215

15241	$3 y^{''} + 7 y^{'} - 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.911

15242	$y^{''} - 8 y^{'} + 15 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.454

15243	$y^{''} - 8 y^{'} + 15 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.473

15244	$y^{''} - 8 y^{'} + 15 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.476

15245	$y^{''} - 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.915

15246	$y^{''} - 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.300

15247	$y^{''} - 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.852

15248	$y^{''} - 10 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓	1.012

15249	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.967

15250	$4 y^{''} - 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.974

15251	$25 y^{''} - 10 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.960

15252	$16 y^{''} - 24 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.986

15253	$9 y^{''} + 12 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.994

15254	$y^{''} - 8 y^{'} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.380

15255	$y^{''} - 8 y^{'} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.313

15256	$y^{''} - 8 y^{'} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.372

15257	$4 y^{''} + 4 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.386

15258	$4 y^{''} + 4 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.388

15259	$4 y^{''} + 4 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.401

15260	$y^{''} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓	2.222

15261	$y^{''} + 2 y^{'} + 5 y = 0$	[[_2nd_order, _missing_x]]	✓	2.666

15262	$y^{''} - 2 y^{'} + 5 y = 0$	[[_2nd_order, _missing_x]]	✓	2.757

15263	$y^{''} - 4 y^{'} + 29 y = 0$	[[_2nd_order, _missing_x]]	✓	2.800

15264	$9 y^{''} + 18 y^{'} + 10 y = 0$	[[_2nd_order, _missing_x]]	✓	1.848

15265	$4 y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	2.291

15266	$y^{''} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.151

15267	$y^{''} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.292

15268	$y^{''} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.406

15269	$y^{''} - 4 y^{'} + 13 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.460

15270	$y^{''} - 4 y^{'} + 13 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.612

15271	$y^{''} - 4 y^{'} + 13 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.585

15272	$y^{''} - y^{'} + (\frac{1}{4} + 4 π^{2}) y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.134

15273	$y^{''} - y^{'} + (\frac{1}{4} + 4 π^{2}) y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.040

15274	$y^{''''} - 4 y^{'''} = 0$	[[_high_order, _missing_x]]	✓	0.053

15275	$y^{''''} + 4 y^{''} = 0$	[[_high_order, _missing_x]]	✓	0.054

15276	$y^{''''} - 34 y^{''} + 225 y = 0$	[[_high_order, _missing_x]]	✓	0.058

15277	$y^{''''} - 81 y = 0$	[[_high_order, _missing_x]]	✓	0.060

15278	$y^{''''} - 18 y^{''} + 81 y = 0$	[[_high_order, _missing_x]]	✓	0.063

15279	$y^{(5)} + 18 y^{'''} + 81 y^{'} = 0$	[[_high_order, _missing_x]]	✓	0.076

15280	$y^{'''} - y^{''} + y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.063

15281	$y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = 0$	[[_3rd_order, _missing_x]]	✓	0.070

15282	$y^{'''} - 8 y^{''} + 37 y^{'} - 50 y = 0$	[[_3rd_order, _missing_x]]	✓	0.062

15283	$y^{'''} - 9 y^{''} + 31 y^{'} - 39 y = 0$	[[_3rd_order, _missing_x]]	✓	0.063

15284	$y^{''''} + y^{'''} + 2 y^{''} + 4 y^{'} - 8 y = 0$	[[_high_order, _missing_x]]	✓	0.066

15285	$y^{''''} + 2 y^{'''} + 10 y^{''} + 18 y^{'} + 9 y = 0$	[[_high_order, _missing_x]]	✓	0.074

15286	$y^{'''} + 4 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.069

15287	$y^{'''} - 6 y^{''} + 12 y^{'} - 8 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.135

15288	$y^{''''} + 26 y^{''} + 25 y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.093

15289	$y^{''''} + y^{'''} + 9 y^{''} + 9 y^{'} = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.089

15290	$y^{'''} - 8 y = 0$	[[_3rd_order, _missing_x]]	✓	0.069

15291	$y^{'''} + 216 y = 0$	[[_3rd_order, _missing_x]]	✓	0.062

15292	$y^{''''} - 3 y^{''} - 4 y = 0$	[[_high_order, _missing_x]]	✓	0.061

15293	$y^{''''} + 13 y^{''} + 36 y = 0$	[[_high_order, _missing_x]]	✓	0.067

15294	$y^{(6)} - 3 y^{''''} + 3 y^{''} - y = 0$	[[_high_order, _missing_x]]	✓	0.071

15295	$y^{(6)} - 2 y^{'''} + y = 0$	[[_high_order, _missing_x]]	✓	0.102

15296	$16 y^{''''} - y = 0$	[[_high_order, _missing_x]]	✓	0.063

15297	$4 y^{''''} + 15 y^{''} - 4 y = 0$	[[_high_order, _missing_x]]	✓	0.069

15298	$y^{''''} - 4 y^{'''} + 16 y^{'} - 16 y = 0$	[[_high_order, _missing_x]]	✓	0.064

15299	$y^{(6)} + 16 y^{'''} + 64 y = 0$	[[_high_order, _missing_x]]	✓	0.087

15300	$x^{2} y^{''} - 5 x y^{'} + 8 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.101

2.2.153 Problems 15201 to 15300