Problems 15801 to 15900

Table 2.319: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

15801	$y^{'} = \sqrt{y^{2} - 1}$ i.c.	[_quadrature]	✗	4.387

15802	$y^{'} = \sqrt{y^{2} - 1}$ i.c.	[_quadrature]	✓	7.808

15803	$y^{'} = \sqrt{y^{2} - 1}$ i.c.	[_quadrature]	✓	6.115

15804	$y^{'} = \sqrt{y^{2} - 1}$ i.c.	[_quadrature]	✓	6.259

15805	$y^{'} = \sqrt{25 - y^{2}}$ i.c.	[_quadrature]	✓	216.110

15806	$y^{'} = \sqrt{25 - y^{2}}$ i.c.	[_quadrature]	✓	4.912

15807	$y^{'} = \sqrt{25 - y^{2}}$ i.c.	[_quadrature]	✓	81.468

15808	$y^{'} = \sqrt{25 - y^{2}}$ i.c.	[_quadrature]	✓	39.548

15809	$y^{'} t + y = t^{3}$ i.c.	[_linear]	✓	1.511

15810	$t^{3} y^{'} + t^{4} y = 2 t^{3}$ i.c.	[_linear]	✓	1.261

15811	$2 y^{'} + t y = \ln (t)$ i.c.	[_linear]	✓	1.801

15812	$y^{'} + y \sec (t) = t$ i.c.	[_linear]	✓	2.514

15813	$y^{'} + \frac{y}{- 3 + t} = \frac{1}{t - 1}$ i.c.	[_linear]	✓	1.753

15814	$(t - 2) y^{'} + (t^{2} - 4) y = \frac{1}{t + 2}$ i.c.	[_linear]	✓	1.798

15815	$y^{'} + \frac{y}{\sqrt{- t^{2} + 4}} = t$ i.c.	[_linear]	✓	2.411

15816	$y^{'} + \frac{y}{\sqrt{- t^{2} + 4}} = t$ i.c.	[_linear]	✓	2.990

15817	$y^{'} t + y = t \sin (t)$ i.c.	[_linear]	✓	1.573

15818	$\tan (t) y + y^{'} = \sin (t)$ i.c.	[_linear]	✓	2.294

15819	$y^{'} = y^{2}$ i.c.	[_quadrature]	✓	1.422

15820	$y^{'} = t y^{2}$ i.c.	[_separable]	✓	1.875

15821	$y^{'} = - \frac{t}{y}$ i.c.	[_separable]	✓	7.292

15822	$y^{'} = - y^{3}$ i.c.	[_quadrature]	✓	2.004

15823	$y^{'} = \frac{x}{y^{2}}$	[_separable]	✓	2.263

15824	$\frac{1}{2 \sqrt{t}} + y^{2} y^{'} = 0$	[_separable]	✓	2.471

15825	$y^{'} = \frac{\sqrt{y}}{x^{2}}$	[_separable]	✓	3.681

15826	$y^{'} = \frac{1 + y^{2}}{y}$	[_quadrature]	✓	1.268

15827	$6 + 4 t^{3} + (5 + \frac{9}{y^{8}}) y^{'} = 0$	[_separable]	✓	2.125

15828	$\frac{6}{t^{9}} - \frac{6}{t^{3}} + t^{7} + (9 + \frac{1}{s^{2}} - 4 s^{8}) s^{'} = 0$	[_separable]	✓	2.071

15829	$4 \sinh (4 y) y^{'} = 6 \cosh (3 x)$	[_separable]	✓	2.753

15830	$y^{'} = \frac{1 + y}{1 + t}$	[_separable]	✓	1.485

15831	$y^{'} = \frac{y + 2}{2 t + 1}$	[_separable]	✓	2.157

15832	$\frac{3}{t^{2}} = (\frac{1}{\sqrt{y}} + \sqrt{y}) y^{'}$	[_separable]	✓	1.807

15833	$3 \sin (x) - 4 y^{'} \cos (y) = 0$	[_separable]	✓	2.096

15834	$\cos (y) y^{'} = 8 \sin (8 t)$	[_separable]	✓	3.475

15835	$y^{'} + k y = 0$	[_quadrature]	✓	0.726

15836	$(5 x^{5} - 4 \cos (x)) x^{'} + 2 \cos (9 t) + 2 \sin (7 t) = 0$	[_separable]	✓	42.805

15837	$\cosh (6 t) + 5 \sinh (4 t) + 20 \sinh (y) y^{'} = 0$	[_separable]	✓	9.160

15838	$y^{'} = e^{2 y + 10 t}$	[_separable]	✓	2.262

15839	$y^{'} = e^{3 y + 2 t}$	[_separable]	✓	2.269

15840	$\sin {(t)}^{2} = \cos {(y)}^{2} y^{'}$	[_separable]	✓	2.700

15841	$3 \sin (t) - \sin (3 t) = (\cos (4 y) - 4 \cos (y)) y^{'}$	[_separable]	✓	37.862

15842	$x^{'} = \frac{\sec {(t)}^{2}}{\sec (x) \tan (x)}$	[_separable]	✓	39.939

15843	$(2 - \frac{5}{y^{2}}) y^{'} + 4 \cos {(x)}^{2} = 0$	[_separable]	✓	2.248

15844	$y^{'} = \frac{t^{3}}{y \sqrt{(1 - y^{2}) (t^{4} + 9)}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	2.918

15845	$\tan (y) \sec {(y)}^{2} y^{'} + \cos {(2 x)}^{3} \sin (2 x) = 0$	[_separable]	✓	43.098

15846	$y^{'} = \frac{(1 + 2 e^{y}) e^{- y}}{t \ln (t)}$	[_separable]	✓	2.431

15847	$x \sin (x^{2}) = \frac{\cos (\sqrt{y}) y^{'}}{\sqrt{y}}$	[_separable]	✓	7.344

15848	$\frac{x - 2}{x^{2} - 4 x + 3} = \frac{{(1 - \frac{1}{y})}^{2} y^{'}}{y^{2}}$	[_separable]	✓	2.067

15849	$\frac{\cos (y) y^{'}}{{(1 - \sin (y))}^{2}} = \sin {(x)}^{3} \cos (x)$	[_separable]	✓	41.811

15850	$y^{'} = \frac{{(5 - 2 \cos (x))}^{3} \sin (x) \cos {(y)}^{4}}{\sin (y)}$	[_separable]	✓	46.668

15851	$\frac{\sqrt{\ln (x)}}{x} = \frac{e^{\frac{3}{y}} y^{'}}{y}$	[_separable]	✓	1.626

15852	$y^{'} = \frac{5^{- t}}{y^{2}}$	[_separable]	✓	3.634

15853	$y^{'} = t^{2} y^{2} + y^{2} - t^{2} - 1$	[_separable]	✓	2.496

15854	$y^{'} = y^{2} - 3 y + 2$	[_quadrature]	✓	0.863

15855	$4 {(x - 1)}^{2} y^{'} - 3 {(3 + y)}^{2} = 0$	[_separable]	✓	2.245

15856	$y^{'} = \sin (t - y) + \sin (t + y)$	[_separable]	✓	3.570

15857	$y^{'} = y^{3} + 1$	[_quadrature]	✓	241.072

15858	$y^{'} = y^{3} - 1$	[_quadrature]	✓	110.803

15859	$y^{'} = y^{3} + y$	[_quadrature]	✓	4.941

15860	$y^{'} = y^{3} - y^{2}$	[_quadrature]	✓	85.668

15861	$y^{'} = y^{3} - y$	[_quadrature]	✓	1.684

15862	$y^{'} = y^{3} + y$	[_quadrature]	✓	4.805

15863	$y^{'} = x^{3}$ i.c.	[_quadrature]	✓	0.511

15864	$y^{'} = \cos (t)$ i.c.	[_quadrature]	✓	0.600

15865	$1 = y^{'} \cos (y)$ i.c.	[_quadrature]	✓	3.220

15866	$\sin {(y)}^{2} = x^{'}$ i.c.	[_quadrature]	✓	0.763

15867	$y^{'} = \frac{\sqrt{t}}{y}$ i.c.	[_separable]	✓	9.909

15868	$y^{'} = \sqrt{\frac{y}{t}}$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓	9.311

15869	$y^{'} = \frac{e^{t}}{1 + y}$ i.c.	[_separable]	✓	1.604

15870	$y^{'} = e^{t - y}$ i.c.	[_separable]	✓	3.834

15871	$y^{'} = \frac{y}{\ln (y)}$ i.c.	[_quadrature]	✓	0.954

15872	$y^{'} = t \sin (t^{2})$ i.c.	[_quadrature]	✓	0.687

15873	$y^{'} = \frac{1}{x^{2} + 1}$ i.c.	[_quadrature]	✓	0.566

15874	$y^{'} = \frac{\sin (x)}{\cos (y) + 1}$ i.c.	[_separable]	✓	2.779

15875	$y^{'} = \frac{3 + y}{3 x + 1}$ i.c.	[_separable]	✓	1.897

15876	$y^{'} = e^{x - y}$ i.c.	[_separable]	✓	2.334

15877	$y^{'} = e^{2 x - y}$ i.c.	[_separable]	✓	2.692

15878	$y^{'} = \frac{3 y + 1}{3 + x}$ i.c.	[_separable]	✓	1.870

15879	$y^{'} = \cos (t) y$ i.c.	[_separable]	✓	2.513

15880	$y^{'} = y^{2} \cos (t)$ i.c.	[_separable]	✓	1.866

15881	$y^{'} = \sqrt{y} \cos (t)$ i.c.	[_separable]	✓	2.694

15882	$y^{'} + y f (t) = 0$ i.c.	[_separable]	✓	1.466

15883	$y^{'} = - \frac{- 2 + y}{x - 2}$ i.c.	[_separable]	✓	1.666

15884	$y^{'} = \frac{x + y + 3}{3 x + 3 y + 1}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.021

15885	$y^{'} = \frac{x - y + 2}{2 x - 2 y - 1}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.996

15886	$y^{'} = {(x + y - 4)}^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	5.728

15887	$y^{'} = {(3 y + 1)}^{4}$	[_quadrature]	✓	1.436

15888	$y^{'} = 3 y$	[_quadrature]	✓	0.819

15889	$y^{'} = - y$	[_quadrature]	✓	0.746

15890	$y^{'} = y^{2} - y$	[_quadrature]	✓	0.989

15891	$y^{'} = 16 y - 8 y^{2}$	[_quadrature]	✓	1.093

15892	$y^{'} = 12 + 4 y - y^{2}$	[_quadrature]	✓	0.980

15893	$y^{'} = y f (t)$ i.c.	[_separable]	✓	1.358

15894	$- y + y^{'} = 10$	[_quadrature]	✓	0.557

15895	$- y + y^{'} = 2 e^{- t}$	[[_linear, ‘class A‘]]	✓	1.109

15896	$- y + y^{'} = 2 \cos (t)$	[[_linear, ‘class A‘]]	✓	1.345

15897	$- y + y^{'} = t^{2} - 2 t$	[[_linear, ‘class A‘]]	✓	1.035

15898	$- y + y^{'} = 4 t e^{- t}$	[[_linear, ‘class A‘]]	✓	1.300

15899	$y^{'} t + y = t^{2}$	[_linear]	✓	1.167

15900	$y^{'} t + y = t$	[_linear]	✓	2.269

2.2.159 Problems 15801 to 15900