Problems 6801 to 6900

Table 2.139: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

6801	$y^{''} + x^{2} y = x^{2} + x + 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.337

6802	$2 (x^{3} + x^{2}) y^{''} - (- 3 x^{2} + x) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.635

6803	$4 x y^{''} + 2 (1 - x) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.638

6804	$2 x^{2} y^{''} - x y^{'} + (- x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.627

6805	$x y^{''} + y^{'} + x y = 0$	[_Lienard]	✓	0.418

6806	$x^{2} y^{''} - x y^{'} + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.509

6807	$x y^{''} - 2 y^{'} + y = 0$	[[_Emden, _Fowler]]	✓	1.198

6808	$x y^{''} + 2 y^{'} + x y = 0$	[_Lienard]	✓	0.578

6809	$x^{2} (x + 1) y^{''} + x (x + 1) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.721

6810	$2 x y^{''} + y^{'} - y = x + 1$	[[_2nd_order, _with_linear_symmetries]]	✓	0.783

6811	$2 x^{3} y^{''} + x^{2} y^{'} + y = 0$	[[_Emden, _Fowler]]	✓	0.686

6812	$x^{3} y^{''} + (x^{2} + x) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.611

6813	$z^{''} + t z^{'} + (t^{2} - \frac{1}{9}) z = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.357

6814	$x (- x^{2} + 2) y^{''} - (x^{2} + 4 x + 2) ((1 - x) y^{'} + y) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.788

6815	$x^{2} (x + 1) y^{''} - (2 x + 1) (- y + x y^{'}) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.684

6816	$x^{3} (x + 1) y^{'''} - (2 + 4 x) x^{2} y^{''} + (4 + 10 x) x y^{'} - (4 + 12 x) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.028

6817	$x^{3} (x^{2} + 1) y^{'''} - (4 x^{2} + 2) x^{2} y^{''} + (10 x^{2} + 4) x y^{'} - (12 x^{2} + 4) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.032

6818	$2 x^{2} (2 - x) y^{''} - (- x + 4) x y^{'} + (3 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.803

6819	$(1 - x) x^{2} y^{''} + (5 x - 4) x y^{'} + (6 - 9 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.477

6820	$x y^{''} + (4 x^{2} + 1) y^{'} + 4 x (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.471

6821	$x^{2} y^{''} + 4 (x + a) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.829

6822	$x y^{''} + (x^{3} + 1) y^{'} + b x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.523

6823	$(- 1 + x) (- 2 + x) y^{''} + (4 x - 6) y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.434

6824	$y^{''} - 2 x y^{'} + 8 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.324

6825	$y^{''} - 2 x y^{'} + 8 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.332

6826	$(- x^{2} + 1) y^{''} - 2 x y^{'} + 12 y = 0$ i.c.	[_Gegenbauer]	✓	0.371

6827	$y^{''} = (- 1 + x) y$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.323

6828	$x (x + 2) y^{''} + 2 (x + 1) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.560

6829	$x y^{''} + y = 0$	[[_Emden, _Fowler]]	✓	1.038

6830	$y^{''} + (- 1 + e^{x}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.444

6831	$x (1 - x) y^{''} - 3 x y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.295

6832	$2 x y^{''} - y^{'} + x^{2} y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.476

6833	$\sin (x) y^{''} - 2 \cos (x) y^{'} - y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.836

6834	$y^{''} - x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.225

6835	$x (x + 2) y^{''} + (x + 1) y^{'} - 4 y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.717

6836	$x y^{''} + (\frac{1}{2} - x) y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.656

6837	$x^{2} y^{''} + x y^{'} + (x^{2} + \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.494

6838	$x^{2} y^{''} + x y^{'} + (x^{2} + \frac{9}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.493

6839	$x^{2} y^{''} + x y^{'} + (x^{2} + \frac{25}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.496

6840	$(- 1 + x) y^{''} - x y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.313

6841	$y^{'} + x y = \cos (x)$	[_linear]	✓	0.477

6842	$y^{'} + x y = \frac{1}{x^{3}}$	[_linear]	✓	1.273

6843	$x^{3} y^{''} + y = \frac{1}{x^{4}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.074

6844	$x y^{''} - 2 y^{'} + y = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	1.335

6845	$y^{'} - \frac{y}{x} = \cos (x)$	[_linear]	✗	0.163

6846	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.454

6847	$y^{''} + 4 x y = 0$	[[_Emden, _Fowler]]	✓	0.233

6848	$y^{''} - x y = 0$	[[_Emden, _Fowler]]	✓	0.372

6849	$y^{''} + x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.246

6850	$y^{'} - x y = 0$	[_separable]	✓	0.350

6851	$(- x^{2} + 1) y^{''} - x y^{'} + p^{2} y = 0$	[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.522

6852	$(x^{2} + 1) y^{''} - 2 x y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.220

6853	$(x^{2} + 1) y^{''} + y = 0$	[[_Emden, _Fowler]]	✓	0.356

6854	$x y^{''} + y = 0$	[[_Emden, _Fowler]]	✓	0.398

6855	$y^{''} + 2 x^{3} y = 0$	[[_Emden, _Fowler]]	✓	0.246

6856	$y^{''} - x y = \frac{1}{1 - x}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.374

6857	$x^{2} y^{''} - y = 0$	[[_Emden, _Fowler]]	✓	0.490

6858	$x^{2} y^{''} + x y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.621

6859	$x^{2} y^{''} - y = 0$	[[_Emden, _Fowler]]	✓	0.483

6860	$y^{''} + \frac{y^{'}}{x} - x y = 0$	[[_Emden, _Fowler]]	✓	0.426

6861	$2 x y^{''} + y^{'} - x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.546

6862	$x^{2} y^{''} - x y^{'} - y = 0$	[[_Emden, _Fowler]]	✓	0.569

6863	$x^{2} (x^{2} + 1) y^{''} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.218

6864	$x^{2} y^{''} + y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.120

6865	$x y^{''} + x^{3} y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.265

6866	$x y^{''} + x y^{'} - y e^{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.360

6867	$x^{2} y^{''} + x^{2} y^{'} + x^{2} y = 0$	[[_2nd_order, _missing_x]]	✓	0.300

6868	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.362

6869	$x^{3} y^{''} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.088

6870	$x y^{''} + x^{5} y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.236

6871	$\sin (x) y^{''} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.342

6872	$\cos (x) y^{''} - y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.749

6873	$x^{2} y^{''} - y = 0$	[[_Emden, _Fowler]]	✓	0.484

6874	$x^{2} y^{''} + (x - \frac{3}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.230

6875	$x^{2} y^{''} - x y^{'} + y = 0$	[[_Emden, _Fowler]]	✓	0.457

6876	$(1 - x) y^{''} - 4 x y^{'} + 5 y = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	1.022

6877	$x y^{'''} - {y^{'}}^{4} + y = 0$	[NONE]	✗	0.033

6878	$t^{5} y^{''''} - t^{3} y^{''} + 6 y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.040

6879	$u^{''} + u^{'} + u = \cos (r + u)$	[NONE]	✗	0.396

6880	$y^{''} = \sqrt{1 + {y^{'}}^{2}}$	[[_2nd_order, _missing_x]]	✓	3.958

6881	$R^{''} = - \frac{k}{R^{2}}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	66.076

6882	$x^{''} - (1 - \frac{{x^{'}}^{2}}{3}) x^{'} + x = 0$	[[_2nd_order, _missing_x]]	✗	1.937

6883	$\sin (y^{'}) = x + y$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	1.645

6884	$\sin (x^{'}) + y^{3} x = \sin (y)$	[‘y=_G(x,y’)‘]	✗	25.205

6885	$y^{2} - 1 + x y^{'} = 0$	[_separable]	✓	1.862

6886	$2 y^{'} + y = 0$	[_quadrature]	✓	1.640

6887	$y^{'} + 20 y = 24$	[_quadrature]	✓	1.664

6888	$y^{''} - 6 y^{'} + 13 y = 0$	[[_2nd_order, _missing_x]]	✓	2.590

6889	$y^{''} + y = \tan (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.915

6890	$(y - x) y^{'} = y - x$	[_quadrature]	✓	1.017

6891	$y^{'} = 25 + y^{2}$	[_quadrature]	✓	9.631

6892	$y^{'} = 2 x y^{2}$	[_separable]	✓	2.152

6893	$2 y^{'} = y^{3} \cos (x)$	[_separable]	✓	2.945

6894	$x^{'} = (x - 1) (1 - 2 x)$	[_quadrature]	✓	1.827

6895	$2 x y + (x^{2} - y) y^{'} = 0$	[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.366

6896	$p^{'} = p (1 - p)$	[_quadrature]	✓	2.217

6897	$y^{'} + 4 x y = 8 x^{3}$	[_linear]	✓	1.613

6898	$y^{''} - 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.959

6899	$x^{3} y^{'''} + 2 x^{2} y^{''} - x y^{'} + y = 12 x^{2}$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓	0.299

6900	$x y^{'} - 3 x y = 1$	[[_linear, ‘class A‘]]	✓	1.143

2.2.69 Problems 6801 to 6900