Problems 16001 to 16100

Table 2.323: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

16001	$2 t + \tan (y) + (t - t^{2} \tan (y)) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	2.636

16002	$2 t - y^{2} \sin (t y) + (\cos (t y) - t y \sin (t y)) y^{'} = 0$	[_exact]	✓	41.631

16003	$- 1 + e^{t y} y + y \cos (t y) + (1 + e^{t y} t + t \cos (t y)) y^{'} = 0$	[_exact]	✓	39.674

16004	$2 t + 2 y + (2 t + 2 y) y^{'} = 0$	[_quadrature]	✓	0.881

16005	$\frac{9 t}{5} + 2 y + (2 t + 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.376

16006	$2 t + \frac{19 y}{10} + (\frac{19 t}{10} + 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.521

16007	$- \frac{y}{2} + y^{'} = \frac{t}{y}$	[_rational, _Bernoulli]	✓	1.368

16008	$y + y^{'} = t y^{2}$	[_Bernoulli]	✓	1.530

16009	$2 y^{'} t - y = 2 t y^{3} \cos (t)$	[_Bernoulli]	✓	47.981

16010	$- y + y^{'} t = t y^{3} \sin (t)$	[[_homogeneous, ‘class D‘], _Bernoulli]	✓	47.108

16011	$- 2 y + y^{'} = \frac{\cos (t)}{\sqrt{y}}$	[_Bernoulli]	✓	15.708

16012	$3 y + y^{'} = \sqrt{y} \sin (t)$	[_Bernoulli]	✓	2.061

16013	$y^{'} - \frac{y}{t} = t y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	1.794

16014	$y^{'} - \frac{y}{t} = \frac{y^{2}}{t^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	1.632

16015	$y^{'} - \frac{y}{t} = \frac{y^{2}}{t}$	[_separable]	✓	1.880

16016	$y^{'} - \frac{y}{t} = t^{2} y^{3 / 2}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	7.909

16017	$\cos (\frac{t}{t + y}) + e^{\frac{2 y}{t}} y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	29.471

16018	$y \ln (\frac{t}{y}) + \frac{t^{2} y^{'}}{t + y} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	5.400

16019	$2 \ln (t) - \ln (4 y^{2}) y^{'} = 0$	[_separable]	✓	4.116

16020	$\frac{2}{t} + \frac{1}{y} + \frac{t y^{'}}{y^{2}} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.807

16021	$\frac{\sin (2 t)}{\cos (2 y)} + \frac{\ln (y) y^{'}}{\ln (t)} = 0$	[_separable]	✓	9.080

16022	$\sqrt{t^{2} + 1} + y y^{'} = 0$	[_separable]	✓	1.961

16023	$2 t + (y - 3 t) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	10.669

16024	$2 y - 3 t + y^{'} t = 0$	[_linear]	✓	1.801

16025	$t y - y^{2} + t (t - 3 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	3.413

16026	$t^{2} + t y + y^{2} - t y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	70.471

16027	$t^{3} + y^{3} - t y^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	11.423

16028	$y^{'} = \frac{t + 4 y}{4 t + y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.754

16029	$t - y + y^{'} t = 0$	[_linear]	✓	1.339

16030	$y + (t + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.482

16031	$2 t^{2} - 7 t y + 5 y^{2} + t y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	11.393

16032	$y + 2 \sqrt{t^{2} + y^{2}} - y^{'} t = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	7.980

16033	$y^{2} = (t y - 4 t^{2}) y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	74.671

16034	$y - (3 \sqrt{t y} + t) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	59.064

16035	$(t^{2} - y^{2}) y^{'} + y^{2} + t y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.172

16036	$t y y^{'} - t^{2} e^{- \frac{y}{t}} - y^{2} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	2.784

16037	$y^{'} = \frac{1}{\frac{2 y e^{- \frac{t}{y}}}{t} + \frac{t}{y}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.451

16038	$t (\ln (t) - \ln (y)) y^{'} = y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	8.150

16039	$y^{'} + 2 y = t^{2} \sqrt{y}$ i.c.	[_Bernoulli]	✓	1.565

16040	$- 2 y + y^{'} = t^{2} \sqrt{y}$ i.c.	[_Bernoulli]	✗	2.796

16041	$y^{'} = \frac{4 y^{2} - t^{2}}{2 t y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	4.642

16042	$t + y - y^{'} t = 0$ i.c.	[_linear]	✓	1.613

16043	$y^{'} t - y - \sqrt{t^{2} + y^{2}} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	3.989

16044	$t^{3} + y^{2} \sqrt{t^{2} + y^{2}} - t y \sqrt{t^{2} + y^{2}} y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓	21.505

16045	$y^{3} - t^{3} - t y^{2} y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	82.788

16046	$t y^{3} - (t^{4} + y^{4}) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	24.891

16047	$y^{4} + (t^{4} - t y^{3}) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	7.300

16048	$1 + t - 2 y + (4 t - 3 y - 6) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.301

16049	$5 t + 2 y + 1 + (2 t + y + 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.824

16050	$3 t - y + 1 - (6 t - 2 y - 3) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.020

16051	$2 t + 3 y + 1 + (4 t + 6 y + 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.972

16052	$y^{'} - \frac{2 y}{x} = - x^{2} y$	[_separable]	✓	1.418

16053	$y^{'} + \cot (x) y = y^{4}$ i.c.	[_Bernoulli]	✓	3.172

16054	$y^{'} t - {y^{'}}^{3} = y$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.488

16055	$y^{'} t - y - 2 {(- y + y^{'} t)}^{2} = y^{'} + 1$	[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	✓	0.872

16056	$y^{'} t - y - 1 = {y^{'}}^{2} - y^{'}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.523

16057	$1 + y - y^{'} t = \ln (y^{'})$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	2.012

16058	$1 + 2 y - 2 y^{'} t = \frac{1}{{y^{'}}^{2}}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.870

16059	$y = - y^{'} t + \frac{{y^{'}}^{5}}{5}$	[_dAlembert]	✓	0.805

16060	$y = t {y^{'}}^{2} + 3 {y^{'}}^{2} - 2 {y^{'}}^{3}$	[_dAlembert]	✓	9.750

16061	$y = t (y^{'} + 1) + 2 y^{'} + 1$	[_linear]	✓	1.269

16062	$y = t (2 - y^{'}) + 2 {y^{'}}^{2} + 1$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.576

16063	$t^{1 / 3} y^{2 / 3} + t + (t^{2 / 3} y^{1 / 3} + y) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	39.020

16064	$y^{'} = \frac{y^{2} - t^{2}}{t y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	4.151

16065	$y \sin (\frac{t}{y}) - (t + t \sin (\frac{t}{y})) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓	9.321

16066	$y^{'} = \frac{2 t^{5}}{5 y^{2}}$	[_separable]	✓	2.306

16067	$\cos (4 x) - 8 y^{'} \sin (y) = 0$	[_separable]	✓	2.971

16068	$y^{'} - \frac{y}{t} = \frac{y^{2}}{t}$	[_separable]	✓	1.943

16069	$y^{'} = \frac{e^{8 y}}{t}$	[_separable]	✓	1.339

16070	$y^{'} = \frac{e^{5 t}}{y^{4}}$	[_separable]	✓	1.346

16071	$- \frac{1}{x^{5}} + \frac{1}{x^{3}} = (2 y^{4} - 6 y^{9}) y^{'}$	[_separable]	✓	2.053

16072	$y^{'} = \frac{y e^{- 2 t}}{\ln (y)}$	[_separable]	✓	1.619

16073	$y^{'} = \frac{(4 - 7 x) (2 y - 3)}{(x - 1) (2 x - 5)}$	[_separable]	✓	1.815

16074	$3 y + y^{'} = - 10 \sin (t)$	[[_linear, ‘class A‘]]	✓	1.385

16075	$3 t + (t - 4 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	3.780

16076	$y - t + (t + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.724

16077	$y - x + y^{'} = 0$	[[_linear, ‘class A‘]]	✓	0.922

16078	$y^{2} + (t^{2} + t y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	6.657

16079	$r^{'} = \frac{r^{2} + t^{2}}{r t}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	5.589

16080	$x^{'} = \frac{5 t x}{x^{2} + t^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	106.472

16081	$t^{2} - y + (y - t) y^{'} = 0$	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.245

16082	$t^{2} y + \sin (t) + (\frac{t^{3}}{3} - \cos (y)) y^{'} = 0$	[_exact]	✓	4.663

16083	$\tan (y) - t + (t \sec {(y)}^{2} + 1) y^{'} = 0$	[_exact]	✓	4.384

16084	$t \ln (y) + (\frac{t^{2}}{2 y} + 1) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.680

16085	$y + y^{'} = 5$	[_quadrature]	✓	0.683

16086	$t y + y^{'} = t$	[_separable]	✓	1.091

16087	$x^{'} + \frac{x}{y} = y^{2}$	[_linear]	✓	1.098

16088	$t r^{'} + r = t \cos (t)$	[_linear]	✓	1.326

16089	$- y + y^{'} = t y^{3}$	[_Bernoulli]	✓	2.631

16090	$y + y^{'} = \frac{e^{t}}{y^{2}}$	[[_1st_order, _with_linear_symmetries], _Bernoulli]	✓	2.534

16091	$y = y^{'} t + 3 {y^{'}}^{4}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	1.765

16092	$y - y^{'} t = 2 y^{2} \ln (t)$	[[_homogeneous, ‘class D‘], _Bernoulli]	✓	2.386

16093	$y - y^{'} t = - 2 {y^{'}}^{3}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.496

16094	$y - y^{'} t = - 4 {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.471

16095	$2 x - y - 2 + (- x + 2 y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.829

16096	$\cos (t - y) + (1 - \cos (t - y)) y^{'} = 0$ i.c.	[[_homogeneous, ‘class C‘], _exact, _dAlembert]	✓	68.053

16097	$e^{t y} y - 2 t + t e^{t y} y^{'} = 0$ i.c.	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	1.948

16098	$\sin (y) - \cos (t) y + (t \cos (y) - \sin (t)) y^{'} = 0$ i.c.	[_exact]	✓	9.271

16099	$y^{2} + (2 t y - 2 \cos (y) \sin (y)) y^{'} = 0$ i.c.	[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	2.456

16100	$\frac{y}{t} + \ln (y) + (\frac{t}{y} + \ln (t)) y^{'} = 0$ i.c.	[_exact]	✓	2.177

2.2.161 Problems 16001 to 16100