Problems 15901 to 16000

Table 2.321: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

15901	$y^{'} x + y = x e^{x}$	[_linear]	✓	1.075

15902	$y^{'} x + y = e^{- x}$	[_linear]	✓	1.127

15903	$y^{'} - \frac{2 t y}{t^{2} + 1} = 2$	[_linear]	✓	1.434

15904	$y^{'} - \frac{4 t y}{4 t^{2} + 1} = 4 t$	[_linear]	✓	1.866

15905	$y^{'} = 2 x + \frac{x y}{x^{2} - 1}$	[_linear]	✓	3.628

15906	$y^{'} + \cot (t) y = \cos (t)$	[_linear]	✓	1.958

15907	$y^{'} - \frac{3 t y}{t^{2} - 4} = t$	[_linear]	✓	1.868

15908	$y^{'} - \frac{4 t y}{4 t^{2} - 9} = t$	[_linear]	✓	4.909

15909	$y^{'} - \frac{9 x y}{9 x^{2} + 49} = x$	[_linear]	✓	3.925

15910	$y^{'} + 2 \cot (x) y = \cos (x)$	[_linear]	✓	1.751

15911	$y^{'} + x y = x^{3}$	[_linear]	✓	1.328

15912	$y^{'} - x y = x$	[_separable]	✓	1.137

15913	$y^{'} = \frac{1}{x + y^{2}}$	[[_1st_order, _with_exponential_symmetries]]	✓	0.994

15914	$y^{'} - x = y$	[[_linear, ‘class A‘]]	✓	0.925

15915	$y - (x + 3 y^{2}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.017

15916	$x^{'} = \frac{3 x t^{2}}{- t^{3} + 1}$	[_separable]	✓	1.228

15917	$p^{'} = t^{3} + \frac{p}{t}$	[_linear]	✓	1.157

15918	$v^{'} + v = e^{- s}$	[[_linear, ‘class A‘]]	✓	0.921

15919	$- y + y^{'} = 4 e^{t}$ i.c.	[[_linear, ‘class A‘]]	✓	1.294

15920	$y + y^{'} = e^{- t}$ i.c.	[[_linear, ‘class A‘]]	✓	1.186

15921	$y^{'} + 3 t^{2} y = e^{- t^{3}}$ i.c.	[_linear]	✓	2.353

15922	$2 t y + y^{'} = 2 t$ i.c.	[_separable]	✓	1.429

15923	$y^{'} t + y = \cos (t)$ i.c.	[_linear]	✓	1.470

15924	$y^{'} t + y = 2 e^{t} t$ i.c.	[_linear]	✓	1.402

15925	$(1 + e^{t}) y^{'} + e^{t} y = t$ i.c.	[_linear]	✓	2.059

15926	$(t^{2} + 4) y^{'} + 2 t y = 2 t$ i.c.	[_separable]	✓	1.576

15927	$x^{'} = x + t + 1$ i.c.	[[_linear, ‘class A‘]]	✓	1.266

15928	$y^{'} = 2 y + e^{2 t}$ i.c.	[[_linear, ‘class A‘]]	✓	1.231

15929	$y^{'} - \frac{y}{t} = \ln (t)$	[_linear]	✓	0.968

15930	$y^{''} - \frac{y^{'}}{t} + \frac{y}{t^{2}} = \frac{1}{t}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.462

15931	$y + y^{'} = {\begin{array}{cc} 4 & 0 \leq t < 2 \\ 0 & 2 \leq t \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	0.960

15932	$y + y^{'} = {\begin{array}{cc} t & 0 \leq t < 1 \\ 0 & 1 \leq t \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	0.894

15933	$- y + y^{'} = \sin (2 t)$	[[_linear, ‘class A‘]]	✓	1.397

15934	$y + y^{'} = 5 e^{2 t}$	[[_linear, ‘class A‘]]	✓	1.131

15935	$y + y^{'} = e^{- t}$	[[_linear, ‘class A‘]]	✓	0.896

15936	$y + y^{'} = 2 - e^{2 t}$	[[_linear, ‘class A‘]]	✓	1.081

15937	$y^{'} - 5 y = t$	[[_linear, ‘class A‘]]	✓	0.973

15938	$3 y + y^{'} = 27 t^{2} + 9$	[[_linear, ‘class A‘]]	✓	1.023

15939	$- \frac{y}{2} + y^{'} = 5 \cos (t) + 2 e^{t}$	[[_linear, ‘class A‘]]	✓	1.961

15940	$y^{'} + 4 y = 8 \cos (4 t)$	[[_linear, ‘class A‘]]	✓	1.574

15941	$y^{'} + 10 y = 2 e^{t}$	[[_linear, ‘class A‘]]	✓	1.160

15942	$y^{'} - 3 y = 27 t^{2}$	[[_linear, ‘class A‘]]	✓	1.070

15943	$- y + y^{'} = 2 e^{t}$	[[_linear, ‘class A‘]]	✓	0.970

15944	$y + y^{'} = 4 + 3 e^{t}$	[[_linear, ‘class A‘]]	✓	1.066

15945	$y + y^{'} = 2 \cos (t) + t$	[[_linear, ‘class A‘]]	✓	1.681

15946	$\frac{y}{2} + y^{'} = \sin (t)$ i.c.	[[_linear, ‘class A‘]]	✓	1.634

15947	$- \frac{y}{2} + y^{'} = \sin (t)$ i.c.	[[_linear, ‘class A‘]]	✓	1.524

15948	$y^{'} t + y = t \cos (t)$	[_linear]	✓	1.233

15949	$y + y^{'} = t$ i.c.	[[_linear, ‘class A‘]]	✓	1.215

15950	$y + y^{'} = \sin (t)$ i.c.	[[_linear, ‘class A‘]]	✓	1.572

15951	$y + y^{'} = \cos (t)$ i.c.	[[_linear, ‘class A‘]]	✓	1.465

15952	$y + y^{'} = e^{t}$ i.c.	[[_linear, ‘class A‘]]	✓	1.319

15953	$y^{2} - \frac{y}{2 \sqrt{t}} + (2 t y - \sqrt{t} + 1) y^{'} = 0$	[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	91.976

15954	$\frac{t}{\sqrt{t^{2} + y^{2}}} + \frac{y y^{'}}{\sqrt{t^{2} + y^{2}}} = 0$	[_separable]	✓	3.392

15955	$y \cos (t y) + t \cos (t y) y^{'} = 0$	[_separable]	✓	1.759

15956	$\sec {(t)}^{2} y + 2 t + \tan (t) y^{'} = 0$	[_linear]	✓	12.898

15957	$3 t y^{2} + y^{3} y^{'} = 0$	[_separable]	✓	3.527

15958	$t - \sin (t) y + (y^{6} + \cos (t)) y^{'} = 0$	[_exact]	✓	3.106

15959	$\sin (2 t) y + (\sqrt{y} + \cos (2 t)) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	6.167

15960	$\ln (t y) + \frac{t y^{'}}{y} = 0$	[[_homogeneous, ‘class G‘], _exact]	✓	2.172

15961	$e^{t y} + \frac{t e^{t y} y^{'}}{y} = 0$	[_separable]	✓	1.709

15962	$3 t^{2} - y^{'} = 0$	[_quadrature]	✓	0.302

15963	$- 1 + 3 y^{2} y^{'} = 0$	[_quadrature]	✓	1.078

15964	$y^{2} + 2 t y y^{'} = 0$	[_separable]	✓	1.841

15965	$\frac{3 t^{2}}{y} - \frac{t^{3} y^{'}}{y^{2}} = 0$	[_separable]	✓	1.814

15966	$2 t + y^{3} + (3 t y^{2} + 4) y^{'} = 0$	[_exact, _rational]	✓	1.344

15967	$- \frac{1}{y} + (\frac{t}{y^{2}} + 3 y^{2}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _exact, _rational]	✓	1.591

15968	$2 t y + (t^{2} + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	3.175

15969	$2 t y^{3} + (1 + 3 t^{2} y^{2}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _exact, _rational]	✓	1.812

15970	$\sin {(y)}^{2} + t \sin (2 y) y^{'} = 0$	[_separable]	✓	6.091

15971	$3 t^{2} + 3 y^{2} + 6 t y y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	✓	3.624

15972	$e^{t} \sin (y) + (1 + e^{t} \cos (y)) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	2.205

15973	$3 t^{2} y + 3 y^{2} - 1 + (t^{3} + 6 t y) y^{'} = 0$	[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.731

15974	$- 2 t y^{2} \sin (t^{2}) + 2 y \cos (t^{2}) y^{'} = 0$	[_separable]	✓	3.290

15975	$2 t - y^{2} \sin (t y) + (\cos (t y) - t y \sin (t y)) y^{'} = 0$	[_exact]	✓	41.275

15976	$1 - y^{2} \cos (t y) + (t y \cos (t y) + \sin (t y)) y^{'} = 0$	[‘y=_G(x,y’)‘]	✗	62.290

15977	$2 t \sin (y) - 2 t y \sin (t^{2}) + (t^{2} \cos (y) + \cos (t^{2})) y^{'} = 0$	[_exact]	✓	38.152

15978	$(t + 3) \cos (t + y) + \sin (t + y) + (t + 3) \cos (t + y) y^{'} = 0$	[[_1st_order, _with_linear_symmetries], _exact]	✓	22.855

15979	$\frac{2 t^{2} y \cos (t^{2}) - y \sin (t^{2})}{t^{2}} + \frac{(2 t y + \sin (t^{2})) y^{'}}{t} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	✓	9.367

15980	$- \frac{y^{2} e^{\frac{y}{t}}}{t^{2}} + 1 + e^{\frac{y}{t}} (1 + \frac{y}{t}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _dAlembert]	✓	4.526

15981	$2 t \sin (\frac{y}{t}) - y \cos (\frac{y}{t}) + t \cos (\frac{y}{t}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _dAlembert]	✓	4.593

15982	$2 t y^{2} + 2 t^{2} y y^{'} = 0$ i.c.	[_separable]	✓	1.990

15983	$1 + \frac{y}{t^{2}} - \frac{y^{'}}{t} = 0$ i.c.	[_linear]	✓	1.374

15984	$2 t y + 3 t^{2} + (t^{2} - 1) y^{'} = 0$ i.c.	[_linear]	✓	1.462

15985	$1 + 5 t - y - (t + 2 y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.323

15986	$e^{y} - 2 t y + (t e^{y} - t^{2}) y^{'} = 0$ i.c.	[_exact]	✓	2.118

15987	$2 t y e^{t^{2}} + 2 t e^{- y} + (e^{t^{2}} - t^{2} e^{- y} + 1) y^{'} = 0$ i.c.	[_exact]	✓	37.780

15988	$y^{2} - 2 \sin (2 t) + (1 + 2 t y) y^{'} = 0$ i.c.	[_exact, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	36.629

15989	$\cos {(t)}^{2} - \sin {(t)}^{2} + y + (\sec (y) \tan (y) + t) y^{'} = 0$ i.c.	[_exact]	✓	41.635

15990	$\frac{1}{t^{2} + 1} - y^{2} - 2 t y y^{'} = 0$ i.c.	[_exact, _rational, _Bernoulli]	✓	2.163

15991	$\frac{2 t}{t^{2} + 1} + y + (e^{y} + t) y^{'} = 0$ i.c.	[_exact]	✓	3.067

15992	$- 2 x - y \cos (x y) + (2 y - x \cos (x y)) y^{'} = 0$ i.c.	[_exact]	✓	11.780

15993	$- 4 x^{3} + 6 y \sin (6 x y) + (4 y^{3} + 6 x \sin (6 x y)) y^{'} = 0$ i.c.	[_exact]	✓	50.225

15994	$t^{2} y + t^{3} y^{'} = 0$	[_separable]	✓	1.436

15995	$y (2 e^{t} + 4 t) + 3 (e^{t} + t^{2}) y^{'} = 0$	[_separable]	✓	1.862

15996	$y + (2 t - y e^{y}) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.370

15997	$2 t y + y^{2} - t^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.186

15998	$y + 2 t^{2} + (t^{2} y - t) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.503

15999	$5 t y + 4 y^{2} + 1 + (t^{2} + 2 t y) y^{'} = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.635

16000	$5 t y^{2} + y + (2 t^{3} - t) y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	3.425

2.2.160 Problems 15901 to 16000