Problems 16201 to 16300

Table 2.327: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

16201	$y^{''} - 6 y^{'} + 13 y = 25 \sin (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.687

16202	$y^{''} - 9 y = 54 t \sin (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.814

16203	$y^{''} - 5 y^{'} + 6 y = - 78 \cos (3 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.616

16204	$y^{''} + 4 y^{'} + 4 y = - 32 t^{2} \cos (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.162

16205	$y^{''} - y^{'} - 20 y = - 2 e^{t}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.455

16206	$y^{''} - 4 y^{'} - 5 y = - 648 t^{2} e^{5 t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.635

16207	$y^{''} - 7 y^{'} + 12 y = - 2 t^{3} e^{4 t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.553

16208	$y^{''} + 4 y^{'} = 8 e^{4 t} - 4 e^{- 4 t}$	[[_2nd_order, _missing_y]]	✓	1.344

16209	$y^{''} - 3 y^{'} = t^{2} - e^{3 t}$	[[_2nd_order, _missing_y]]	✓	1.294

16210	$y^{''} + 4 y^{'} = - 24 t - 6 - 4 t e^{- 4 t} + e^{- 4 t}$	[[_2nd_order, _missing_y]]	✓	1.320

16211	$y^{''} - 3 y^{'} = t^{2} - e^{3 t}$	[[_2nd_order, _missing_y]]	✓	1.283

16212	$y^{''} = t^{2} + e^{t} + \sin (t)$	[[_2nd_order, _quadrature]]	✓	1.185

16213	$y^{''} + 3 y^{'} = 18$ i.c.	[[_2nd_order, _missing_x]]	✓	1.549

16214	$y^{''} - y = 4$ i.c.	[[_2nd_order, _missing_x]]	✓	1.339

16215	$y^{''} - 4 y = 32 t$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.672

16216	$y^{''} + 2 y^{'} - 3 y = - 2$ i.c.	[[_2nd_order, _missing_x]]	✓	0.633

16217	$y^{''} + y^{'} - 6 y = 3 t$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.671

16218	$y^{''} + 8 y^{'} + 16 y = 4$ i.c.	[[_2nd_order, _missing_x]]	✓	0.797

16219	$y^{''} + 7 y^{'} + 10 y = t e^{- t}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.699

16220	$y^{''} + 6 y^{'} + 25 y = - 1$ i.c.	[[_2nd_order, _missing_x]]	✓	0.859

16221	$y^{''} - 3 y^{'} = - e^{3 t} - 2 t$ i.c.	[[_2nd_order, _missing_y]]	✓	1.644

16222	$y^{''} - y^{'} = - 3 t - 4 e^{2 t} t^{2}$ i.c.	[[_2nd_order, _missing_y]]	✓	1.555

16223	$y^{''} - 2 y^{'} = 2 t^{2}$ i.c.	[[_2nd_order, _missing_y]]	✓	1.403

16224	$y^{''} + 4 y^{'} = - 24 t - 6 - 4 t e^{- 4 t} + e^{- 4 t}$ i.c.	[[_2nd_order, _missing_y]]	✓	1.690

16225	$y^{''} - 3 y^{'} = e^{- 3 t} - e^{3 t}$ i.c.	[[_2nd_order, _missing_y]]	✓	2.022

16226	$y^{''} + 9 y = {\begin{array}{cc} 2 t & 0 \leq t < π \\ 0 & π \leq t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.080

16227	$y^{''} + 9 π^{2} y = {\begin{array}{cc} 2 t & 0 \leq t < π \\ 2 t - 2 π & π \leq t < 2 π \\ 0 & 2 π \leq t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	8.693

16228	$y^{''} + 4 y = {\begin{array}{cc} 0 & 0 \leq t < π \\ 10 & π \leq t < 2 π \\ 0 & 2 π \leq t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.590

16229	$y^{'} - 4 y = t^{2}$	[[_linear, ‘class A‘]]	✓	1.000

16230	$y + y^{'} = \cos (2 t)$ i.c.	[[_linear, ‘class A‘]]	✓	1.521

16231	$- y + y^{'} = e^{4 t}$ i.c.	[[_linear, ‘class A‘]]	✓	1.298

16232	$y^{'} + 4 y = e^{- 4 t}$ i.c.	[[_linear, ‘class A‘]]	✓	1.258

16233	$y^{'} + 4 y = t e^{- 4 t}$	[[_linear, ‘class A‘]]	✓	1.563

16234	$y^{''} + y^{'} - 2 y = f (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.664

16235	$x^{''} + 9 x = \sin (3 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.953

16236	$4 y^{''} + 4 y^{'} + 37 y = \cos (3 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.873

16237	$y^{''} + 4 y = 1$	[[_2nd_order, _missing_x]]	✓	1.651

16238	$y^{''} + 16 y^{'} = t$	[[_2nd_order, _missing_y]]	✓	1.109

16239	$y^{''} - 7 y^{'} + 10 y = e^{3 t}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.501

16240	$y^{''} + 16 y = 2 \cos (4 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.736

16241	$y^{''} + 4 y^{'} + 20 y = 2 t e^{- 2 t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.662

16242	$y^{''} + \frac{y}{4} = \sec (\frac{t}{2}) + \csc (\frac{t}{2})$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.195

16243	$y^{''} + 16 y = \csc (4 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.378

16244	$y^{''} + 16 y = \cot (4 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.696

16245	$y^{''} + 2 y^{'} + 50 y = e^{- t} \csc (7 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.854

16246	$y^{''} + 6 y^{'} + 25 y = e^{- 3 t} (\sec (4 t) + \csc (4 t))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.028

16247	$y^{''} - 2 y^{'} + 26 y = e^{t} (\sec (5 t) + \csc (5 t))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.936

16248	$y^{''} + 12 y^{'} + 37 y = e^{- 6 t} \csc (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.739

16249	$y^{''} - 6 y^{'} + 34 y = e^{3 t} \tan (5 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.901

16250	$y^{''} - 10 y^{'} + 34 y = e^{5 t} \cot (3 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.891

16251	$y^{''} - 12 y^{'} + 37 y = e^{6 t} \sec (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.724

16252	$y^{''} - 8 y^{'} + 17 y = e^{4 t} \sec (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.749

16253	$y^{''} - 9 y = \frac{1}{1 + e^{3 t}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.632

16254	$y^{''} - 25 y = \frac{1}{1 - e^{5 t}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.811

16255	$y^{''} - y = 2 \sinh (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.752

16256	$y^{''} - 2 y^{'} + y = \frac{e^{t}}{t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.579

16257	$y^{''} - 4 y^{'} + 4 y = \frac{e^{2 t}}{t^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.697

16258	$y^{''} + 8 y^{'} + 16 y = \frac{e^{- 4 t}}{t^{4}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.622

16259	$y^{''} + 6 y^{'} + 9 y = \frac{e^{- 3 t}}{t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.673

16260	$y^{''} + 6 y^{'} + 9 y = e^{- 3 t} \ln (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.655

16261	$y^{''} + 3 y^{'} + 2 y = \cos (e^{t})$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.711

16262	$y^{''} + 4 y^{'} + 4 y = e^{- 2 t} \sqrt{- t^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.748

16263	$y^{''} - 2 y^{'} + y = e^{t} \sqrt{- t^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.706

16264	$y^{''} - 10 y^{'} + 25 y = e^{5 t} \ln (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.766

16265	$y^{''} - 4 y^{'} + 4 y = e^{2 t} \arctan (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.759

16266	$y^{''} + 8 y^{'} + 16 y = \frac{e^{- 4 t}}{t^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.657

16267	$y^{''} + y = \sec (\frac{t}{2}) + \csc (\frac{t}{2})$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.264

16268	$y^{''} + 9 y = \tan {(3 t)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.335

16269	$y^{''} + 9 y = \sec (3 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.064

16270	$y^{''} + 9 y = \tan (3 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.152

16271	$y^{''} + 4 y = \tan (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.071

16272	$y^{''} + 16 y = \tan (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.965

16273	$y^{''} + 4 y = \tan (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.891

16274	$y^{''} + 9 y = \sec (3 t) \tan (3 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.450

16275	$y^{''} + 4 y = \sec (2 t) \tan (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.443

16276	$y^{''} + 9 y = \frac{\csc (3 t)}{2}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.109

16277	$y^{''} + 4 y = \sec {(2 t)}^{2}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.890

16278	$y^{''} - 16 y = 16 t e^{- 4 t}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.738

16279	$y^{''} + y = \tan {(t)}^{2}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.382

16280	$y^{''} + 4 y = \sec (2 t) + \tan (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.629

16281	$y^{''} + 9 y = \csc (3 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.097

16282	$y^{''} + 4 y^{'} + 3 y = 65 \cos (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.611

16283	$t^{2} y^{''} + 3 y^{'} t + y = \ln (t)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.633

16284	$t^{2} y^{''} + y^{'} t + 4 y = t$	[[_2nd_order, _with_linear_symmetries]]	✓	1.585

16285	$t^{2} y^{''} - 4 y^{'} t - 6 y = 2 \ln (t)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.364

16286	$4 y^{''} + 4 y^{'} + y = e^{- \frac{t}{2}}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.678

16287	$y^{''} + 4 y = f (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.845

16288	$t^{2} y^{''} - 4 y^{'} t + (t^{2} + 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.127

16289	$t^{2} y^{''} - 4 y^{'} t + (t^{2} + 6) y = t^{3} + 2 t$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	1.094

16290	$t y^{''} + 2 y^{'} + t y = 0$	[_Lienard]	✓	0.138

16291	$t y^{''} + 2 y^{'} + t y = - t$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	1.069

16292	$4 t^{2} y^{''} + 4 y^{'} t + (16 t^{2} - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.124

16293	$4 t^{2} y^{''} + 4 y^{'} t + (16 t^{2} - 1) y = 16 t^{3 / 2}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.277

16294	$t^{2} (\ln (t) - 1) y^{''} - y^{'} t + y = - \frac{3 (1 + \ln (t))}{4 \sqrt{t}}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	1.433

16295	$(\sin (t) - t \cos (t)) y^{''} - t \sin (t) y^{'} + \sin (t) y = t$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	2.404

16296	$y^{'''} = 0$	[[_3rd_order, _quadrature]]	✓	0.075

16297	$y^{'''} - 10 y^{''} + 25 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.083

16298	$8 y^{'''} + y^{''} = 0$	[[_3rd_order, _missing_x]]	✓	0.081

16299	$y^{''''} + 16 y^{''} = 0$	[[_high_order, _missing_x]]	✓	0.083

16300	$y^{'''} - 2 y^{''} - y^{'} + 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.079

2.2.163 Problems 16201 to 16300