Problems 16101 to 16200

Table 2.325: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

16101	$y^{'} = - x + y^{2}$ i.c.	[[_Riccati, _special]]	✓	18.714

16102	$y^{'} = \sqrt{x - y}$ i.c.	[[_homogeneous, ‘class C‘], _dAlembert]	✓	4.342

16103	$y^{'} = t y^{3}$ i.c.	[_separable]	✓	2.373

16104	$y^{'} = \frac{t}{y^{3}}$ i.c.	[_separable]	✓	3.454

16105	$y^{'} = - \frac{y}{t - 2}$ i.c.	[_separable]	✓	1.662

16106	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	1.468

16107	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.377

16108	$2 t^{2} y^{''} - 3 y^{'} t - 3 y = 0$	[[_Emden, _Fowler]]	✓	0.717

16109	$y^{''} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	1.421

16110	$y^{''} - y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.554

16111	$y^{''} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.826

16112	$3 t^{2} y^{''} - 5 y^{'} t - 3 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	1.343

16113	$t^{2} y^{''} + 7 y^{'} t - 7 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	1.525

16114	$y^{''} + y = 2 \cos (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.971

16115	$y^{''} + 10 y^{'} + 24 y = 0$	[[_2nd_order, _missing_x]]	✓	0.296

16116	$y^{''} + 16 y = 0$	[[_2nd_order, _missing_x]]	✓	1.456

16117	$y^{''} + 6 y^{'} + 18 y = 0$	[[_2nd_order, _missing_x]]	✓	0.517

16118	$t^{2} y^{''} + y^{'} t - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.148

16119	$y^{''} - 5 y^{'} + 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.198

16120	$y^{''} + 6 y^{'} + 8 y = 0$	[[_2nd_order, _missing_x]]	✓	0.205

16121	$y^{''} - 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.267

16122	$y^{''} + 10 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓	0.189

16123	$y^{''} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.236

16124	$y^{''} + 49 y = 0$	[[_2nd_order, _missing_x]]	✓	0.154

16125	$t^{2} y^{''} + 4 y^{'} t - 4 y = 0$	[[_Emden, _Fowler]]	✓	0.137

16126	$t^{2} y^{''} + 6 y^{'} t + 6 y = 0$	[[_Emden, _Fowler]]	✓	0.149

16127	$t^{2} y^{''} + y^{'} t + (t^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.125

16128	$t^{2} y^{''} + 3 y^{'} t + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.121

16129	$a y^{''} + b y^{'} + c y = 0$	[[_2nd_order, _missing_x]]	✓	1.513

16130	$t^{2} y^{''} + a t y^{'} + b y = 0$	[[_Emden, _Fowler]]	✓	1.556

16131	$4 t^{2} y^{''} + 4 y^{'} t + (36 t^{2} - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.137

16132	$t y^{''} + 2 y^{'} + 16 t y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.137

16133	$y^{''} + b (t) y^{'} + c (t) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.158

16134	$y^{''} + b y^{'} + c y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.207

16135	$y^{''} = 0$	[[_2nd_order, _quadrature]]	✓	0.720

16136	$y^{''} - 4 y^{'} - 12 y = 0$	[[_2nd_order, _missing_x]]	✓	0.320

16137	$y^{''} + y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	0.942

16138	$y^{''} + 3 y^{'} - 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.337

16139	$y^{''} + 8 y^{'} + 12 y = 0$	[[_2nd_order, _missing_x]]	✓	0.369

16140	$y^{''} + 5 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.422

16141	$8 y^{''} + 6 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.343

16142	$4 y^{''} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	1.429

16143	$y^{''} + 16 y = 0$	[[_2nd_order, _missing_x]]	✓	1.349

16144	$y^{''} + 8 y = 0$	[[_2nd_order, _missing_x]]	✓	1.520

16145	$y^{''} + 7 y = 0$	[[_2nd_order, _missing_x]]	✓	1.656

16146	$4 y^{''} + 21 y^{'} + 5 y = 0$	[[_2nd_order, _missing_x]]	✓	0.390

16147	$7 y^{''} + 4 y^{'} - 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.338

16148	$4 y^{''} + 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.437

16149	$y^{''} - 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.381

16150	$y^{''} - y^{'} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.104

16151	$3 y^{''} - y^{'} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.476

16152	$y^{''} + y^{'} - 12 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.579

16153	$y^{''} - 7 y^{'} + 12 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.582

16154	$2 y^{''} - 7 y^{'} - 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.556

16155	$y^{''} - 7 y^{'} + 10 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.487

16156	$y^{''} + 36 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	17.864

16157	$y^{''} + 100 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.900

16158	$y^{''} - 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.634

16159	$y^{''} + 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.673

16160	$y^{''} + 2 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.709

16161	$y^{''} + 4 y^{'} + 20 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.749

16162	$y^{''} + y^{'} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.662

16163	$y^{''} + y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.810

16164	$y^{''} - y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.733

16165	$y^{''} - y^{'} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.683

16166	$6 y^{''} + 5 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.353

16167	$9 y^{''} + 6 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.435

16168	$y^{''} + 4 y^{'} + 20 y = 0$	[[_2nd_order, _missing_x]]	✓	0.420

16169	$3 t^{2} y^{''} - 2 y^{'} t + 2 y = 0$	[[_Emden, _Fowler]]	✓	1.006

16170	$t^{2} y^{''} - y^{'} t + y = 0$	[[_Emden, _Fowler]]	✓	0.940

16171	$a y^{''} + 2 b y^{'} + c y = 0$	[[_2nd_order, _missing_x]]	✓	1.551

16172	$y^{''} + 6 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.480

16173	$y^{''} - 5 y^{'} + 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.311

16174	$y^{''} - 6 y^{'} - 16 y = 0$	[[_2nd_order, _missing_x]]	✓	0.326

16175	$y^{''} - 16 y = 0$	[[_2nd_order, _missing_x]]	✓	1.410

16176	$y^{''} + 2 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.526

16177	${y^{''}}^{2} - 5 y^{''} y^{'} + 4 y^{2} = 0$	[[_2nd_order, _missing_x]]	✗	0.101

16178	${y^{''}}^{2} - 2 y^{''} y^{'} + y^{2} = 0$	[[_2nd_order, _missing_x]]	✗	0.090

16179	$y^{''} + 4 y^{'} + 3 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.468

16180	$y^{''} + y = 8 e^{2 t}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.612

16181	$y^{''} - 4 y^{'} + 3 y = - e^{- 9 t}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.444

16182	$y^{''} - 4 y^{'} + 3 y = 2 e^{3 t}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.568

16183	$y^{''} - y = 2 t - 4$	[[_2nd_order, _with_linear_symmetries]]	✓	0.441

16184	$y^{''} - 2 y^{'} + y = t^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.555

16185	$y^{''} + 2 y^{'} = 3 - 4 t$	[[_2nd_order, _missing_y]]	✓	1.145

16186	$y^{''} + y = \cos (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.662

16187	$y^{''} + 4 y = 4 \cos (t) - \sin (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.910

16188	$y^{''} + 4 y = \cos (2 t) + t$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.841

16189	$y^{''} + 4 y = 3 t e^{- t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.720

16190	$y^{''} = 3 t^{4} - 2 t$	[[_2nd_order, _quadrature]]	✓	0.884

16191	$y^{''} - 4 y^{'} + 13 y = 2 t e^{- 2 t} \sin (3 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.865

16192	$y^{''} + y^{'} - 2 y = - 1$	[[_2nd_order, _missing_x]]	✓	0.411

16193	$5 y^{''} + y^{'} - 4 y = - 3$	[[_2nd_order, _missing_x]]	✓	0.430

16194	$y^{''} - 2 y^{'} - 8 y = 32 t$	[[_2nd_order, _with_linear_symmetries]]	✓	0.415

16195	$16 y^{''} - 8 y^{'} - 15 y = 75 t$	[[_2nd_order, _with_linear_symmetries]]	✓	0.501

16196	$y^{''} + 2 y^{'} + 26 y = - 338 t$	[[_2nd_order, _with_linear_symmetries]]	✓	0.630

16197	$y^{''} + 3 y^{'} - 4 y = - 32 t^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.516

16198	$8 y^{''} + 6 y^{'} + y = 5 t^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.473

16199	$y^{''} - 6 y^{'} + 8 y = - 256 t^{3}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.443

16200	$y^{''} - 2 y^{'} = 52 \sin (3 t)$	[[_2nd_order, _missing_y]]	✓	1.455

2.2.162 Problems 16101 to 16200