Problems 15201 to 15300

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


#	ODE	CAS classiﬁcation	Solved?	time (sec)

15201	$y^{''} - 5 y^{'} + 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.208

15202	$y^{''} - 10 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓	0.184

15203	$x^{2} y^{''} - 6 y^{'} x + 12 y = 0$	[[_Emden, _Fowler]]	✓	0.146

15204	$2 x^{2} y^{''} - y^{'} x + y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.162

15205	$4 x^{2} y^{''} + y = 0$	[[_Emden, _Fowler]]	✓	0.177

15206	$y^{''} - (4 + \frac{2}{x}) y^{'} + (4 + \frac{4}{x}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.171

15207	$(x + 1) y^{''} + y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.161

15208	$y^{''} - \frac{y^{'}}{x} - 4 x^{2} y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.133

15209	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.188

15210	$x y^{''} + (2 x + 2) y^{'} + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.163

15211	$\sin {(x)}^{2} y^{''} - 2 \cos (x) \sin (x) y^{'} + (\cos {(x)}^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.221

15212	$x^{2} y^{''} - 2 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.158

15213	$x^{2} y^{''} + y^{'} x + y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.135

15214	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.142

15215	$y^{''} - 4 y^{'} + 3 y = 9 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.321

15216	$y^{''} - 6 y^{'} + 8 y = e^{4 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.380

15217	$x^{2} y^{''} + y^{'} x - y = \sqrt{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	0.256

15218	$x^{2} y^{''} - 20 y = 27 x^{5}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.212

15219	$x y^{''} + (2 x + 2) y^{'} + 2 y = 8 e^{2 x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	0.591

15220	$(x + 1) y^{''} + y^{'} x - y = {(x + 1)}^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.324

15221	$y^{'''} - 9 y^{''} + 27 y^{'} - 27 y = 0$	[[_3rd_order, _missing_x]]	✓	0.082

15222	$y^{'''} - 9 y^{''} + 27 y^{'} - 27 y = e^{3 x} \sin (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.198

15223	$y^{''''} - 8 y^{'''} + 24 y^{''} - 32 y^{'} + 16 y = 0$	[[_high_order, _missing_x]]	✓	0.083

15224	$x^{3} y^{'''} - 4 y^{''} + 10 y^{'} - 12 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.066

15225	$y^{''} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.909

15226	$y^{''} - 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.411

15227	$y^{''} + y^{'} - 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.581

15228	$y^{''} - 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.637

15229	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.648

15230	$4 x^{2} y^{''} + 4 y^{'} x - y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.443

15231	$x^{2} y^{''} - y^{'} x + y = 0$ i.c.	[[_Emden, _Fowler]]	✓	1.677

15232	$x y^{''} - y^{'} + 4 x^{3} y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.582

15233	${(x + 1)}^{2} y^{''} - 2 (x + 1) y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.680

15234	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.920

15235	$x y^{''} - y^{'} + 4 x^{3} y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.858

15236	$y^{'''} + 4 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.102

15237	$y^{''''} - y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.107

15238	$y^{''} - 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.630

15239	$y^{''} + 2 y^{'} - 3 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.608

15240	$y^{''} - 10 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.534

15241	$y^{''} + 5 y^{'} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.132

15242	$y^{'''} - 9 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.089

15243	$y^{''''} - 10 y^{''} + 9 y = 0$	[[_high_order, _missing_x]]	✓	0.086

15244	$y^{''} - 7 y^{'} + 10 y = 0$	[[_2nd_order, _missing_x]]	✓	0.342

15245	$y^{''} + 2 y^{'} - 24 y = 0$	[[_2nd_order, _missing_x]]	✓	0.354

15246	$y^{''} - 25 y = 0$	[[_2nd_order, _missing_x]]	✓	1.684

15247	$y^{''} + 3 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	1.103

15248	$4 y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	1.638

15249	$3 y^{''} + 7 y^{'} - 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.402

15250	$y^{''} - 8 y^{'} + 15 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.618

15251	$y^{''} - 8 y^{'} + 15 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.613

15252	$y^{''} - 8 y^{'} + 15 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.574

15253	$y^{''} - 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.920

15254	$y^{''} - 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.548

15255	$y^{''} - 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.755

15256	$y^{''} - 10 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓	0.388

15257	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.362

15258	$4 y^{''} - 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.391

15259	$25 y^{''} - 10 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.476

15260	$16 y^{''} - 24 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.467

15261	$9 y^{''} + 12 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.473

15262	$y^{''} - 8 y^{'} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.670

15263	$y^{''} - 8 y^{'} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.689

15264	$y^{''} - 8 y^{'} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.664

15265	$4 y^{''} + 4 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.698

15266	$4 y^{''} + 4 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.691

15267	$4 y^{''} + 4 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.678

15268	$y^{''} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓	1.481

15269	$y^{''} + 2 y^{'} + 5 y = 0$	[[_2nd_order, _missing_x]]	✓	0.534

15270	$y^{''} - 2 y^{'} + 5 y = 0$	[[_2nd_order, _missing_x]]	✓	0.475

15271	$y^{''} - 4 y^{'} + 29 y = 0$	[[_2nd_order, _missing_x]]	✓	0.560

15272	$9 y^{''} + 18 y^{'} + 10 y = 0$	[[_2nd_order, _missing_x]]	✓	0.520

15273	$4 y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	1.488

15274	$y^{''} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.885

15275	$y^{''} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.365

15276	$y^{''} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.960

15277	$y^{''} - 4 y^{'} + 13 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.765

15278	$y^{''} - 4 y^{'} + 13 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.739

15279	$y^{''} - 4 y^{'} + 13 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.786

15280	$y^{''} - y^{'} + (\frac{1}{4} + 4 π^{2}) y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.728

15281	$y^{''} - y^{'} + (\frac{1}{4} + 4 π^{2}) y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.795

15282	$y^{''''} - 4 y^{'''} = 0$	[[_high_order, _missing_x]]	✓	0.079

15283	$y^{''''} + 4 y^{''} = 0$	[[_high_order, _missing_x]]	✓	0.087

15284	$y^{''''} - 34 y^{''} + 225 y = 0$	[[_high_order, _missing_x]]	✓	0.093

15285	$y^{''''} - 81 y = 0$	[[_high_order, _missing_x]]	✓	0.088

15286	$y^{''''} - 18 y^{''} + 81 y = 0$	[[_high_order, _missing_x]]	✓	0.087

15287	$y^{(5)} + 18 y^{'''} + 81 y^{'} = 0$	[[_high_order, _missing_x]]	✓	0.111

15288	$y^{'''} - y^{''} + y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.095

15289	$y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = 0$	[[_3rd_order, _missing_x]]	✓	0.083

15290	$y^{'''} - 8 y^{''} + 37 y^{'} - 50 y = 0$	[[_3rd_order, _missing_x]]	✓	0.091

15291	$y^{'''} - 9 y^{''} + 31 y^{'} - 39 y = 0$	[[_3rd_order, _missing_x]]	✓	0.085

15292	$y^{''''} + y^{'''} + 2 y^{''} + 4 y^{'} - 8 y = 0$	[[_high_order, _missing_x]]	✓	0.092

15293	$y^{''''} + 2 y^{'''} + 10 y^{''} + 18 y^{'} + 9 y = 0$	[[_high_order, _missing_x]]	✓	0.097

15294	$y^{'''} + 4 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.095

15295	$y^{'''} - 6 y^{''} + 12 y^{'} - 8 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.138

15296	$y^{''''} + 26 y^{''} + 25 y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.104

15297	$y^{''''} + y^{'''} + 9 y^{''} + 9 y^{'} = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.120

15298	$y^{'''} - 8 y = 0$	[[_3rd_order, _missing_x]]	✓	0.086

15299	$y^{'''} + 216 y = 0$	[[_3rd_order, _missing_x]]	✓	0.085

15300	$y^{''''} - 3 y^{''} - 4 y = 0$	[[_high_order, _missing_x]]	✓	0.082

2.2.153 Problems 15201 to 15300