Problems 2801 to 2900

Table 2.59: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

2801	$[\begin{matrix} x^{'} = - 5 x + 3 y \\ y^{'} = - x + y \end{matrix}]$	system_of_ODEs	✓	0.567

2802	$[\begin{matrix} x^{'} = x - 4 y \\ y^{'} = 4 x - 7 y \end{matrix}]$	system_of_ODEs	✓	0.320

2803	$[\begin{matrix} x^{'} = - 7 x + y - 6 z \\ y^{'} = 10 x - 4 y + 12 z \\ z^{'} = 2 x - y + z \end{matrix}]$	system_of_ODEs	✓	0.609

2804	$[\begin{matrix} x^{'} = 3 x + 2 y + 4 z \\ y^{'} = 2 x + 2 z \\ z^{'} = 4 x + 2 y + 3 z \end{matrix}]$	system_of_ODEs	✓	0.473

2805	$[\begin{matrix} x^{'} = 2 y + z \\ y^{'} = - x - 3 y - z \\ z^{'} = x + y - z \end{matrix}]$	system_of_ODEs	✓	0.510

2806	$[\begin{matrix} x^{'} = - 2 x + y + z \\ y^{'} = - 3 x + 2 y + 3 z \\ z^{'} = x - y - 2 z \end{matrix}]$	system_of_ODEs	✓	0.409

2807	$[\begin{matrix} x^{'} = 2 y \\ y^{'} = - 2 x \\ z^{'} = 2 h \\ h^{'} = - 2 z \end{matrix}]$	system_of_ODEs	✓	0.580

2808	$[\begin{matrix} x^{'} = 2 y + z \\ y^{'} = - 2 x + h \\ z^{'} = 2 h \\ h^{'} = - 2 z \end{matrix}]$	system_of_ODEs	✓	0.644

2809	$x^{'} = x (1 - x)$	[_quadrature]	✓	1.020

2810	$x^{'} = - x (1 - x)$	[_quadrature]	✓	0.957

2811	$x^{'} = x^{2}$	[_quadrature]	✓	1.430

2812	$[\begin{matrix} x_{1}^{'} = x_{2} \\ x_{2}^{'} = - \frac{(x_{1}^{2} + \sqrt{x_{1}^{2} + 4 x_{2}^{2}}) x_{1}}{2} \end{matrix}]$	system_of_ODEs	✓	0.058

2813	$[\begin{matrix} x_{1}^{'} = - x_{1} - x_{2} + 1 \\ x_{2}^{'} = 2 x_{1} - x_{2} + 5 \end{matrix}]$	system_of_ODEs	✓	0.899

2814	$[\begin{matrix} x^{'} = x - x^{3} - x y \\ y^{'} = 2 y - y^{5} - y x^{4} \end{matrix}]$	system_of_ODEs	✓	0.062

2815	$[\begin{matrix} x^{'} = x^{2} + y^{2} + 1 \\ y^{'} = x^{2} - y^{2} \end{matrix}]$	system_of_ODEs	✓	0.050

2816	$[\begin{matrix} x^{'} = x^{2} + y^{2} - 1 \\ y^{'} = 2 x y \end{matrix}]$	system_of_ODEs	✓	0.057

2817	$[\begin{matrix} x^{'} = 6 x - 6 x^{2} - 2 x y \\ y^{'} = 4 y - 4 y^{2} - 2 x y \end{matrix}]$	system_of_ODEs	✓	0.055

2818	$[\begin{matrix} x^{'} = \tan (x + y) \\ y^{'} = x + x^{3} \end{matrix}]$	system_of_ODEs	✓	0.050

2819	$[\begin{matrix} x^{'} = e^{y} - x \\ y^{'} = e^{x} + y \end{matrix}]$	system_of_ODEs	✓	0.053

2820	$z^{''} + z^{3} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	4.395

2821	$z^{''} + z + z^{5} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	708.952

2822	$z^{''} + e^{z^{2}} = 1$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.682

2823	$z^{''} + \frac{z}{1 + z^{2}} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	3.195

2824	$z^{''} + z - 2 z^{3} = 0$	[[_2nd_order, _missing_x], _Duﬃng, [_2nd_order, _reducible, _mu_x_y1]]	✓	5.505

2825	$[\begin{matrix} x_{1}^{'} = - 5 x_{1} + x_{2} \\ x_{2}^{'} = x_{1} - 5 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.365

2826	$[\begin{matrix} x_{1}^{'} = - x_{2} \\ x_{2}^{'} = 8 x_{1} - 6 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.420

2827	$[\begin{matrix} x_{1}^{'} = 4 x_{1} - x_{2} \\ x_{2}^{'} = - 2 x_{1} + 5 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.408

2828	$[\begin{matrix} x_{1}^{'} = - 4 x_{1} - x_{2} \\ x_{2}^{'} = x_{1} - 6 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.313

2829	$[\begin{matrix} x_{1}^{'} = x_{1} - 4 x_{2} \\ x_{2}^{'} = - 8 x_{1} + 4 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.610

2830	$[\begin{matrix} x_{1}^{'} = 3 x_{1} - x_{2} \\ x_{2}^{'} = 5 x_{1} - 3 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.420

2831	$[\begin{matrix} x_{1}^{'} = 2 x_{2} \\ x_{2}^{'} = - 2 x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	0.732

2832	$[\begin{matrix} x_{1}^{'} = x_{1} - x_{2} \\ x_{2}^{'} = 5 x_{1} - 3 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.506

2833	$[\begin{matrix} x_{1}^{'} = 2 x_{1} + x_{2} \\ x_{2}^{'} = - 5 x_{1} - 2 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.427

2834	$[\begin{matrix} x_{1}^{'} = 4 x_{2} \\ x_{2}^{'} = - 9 x_{1} \end{matrix}]$	system_of_ODEs	✓	0.405

2835	$y^{''} + λ y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.298

2836	$y^{''} + λ y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.397

2837	$y^{''} - λ y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.897

2838	$y^{''} + λ y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.310

2839	$y^{''} - 2 y^{'} + (1 + λ) y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.623

2840	$y^{''} + λ y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.385

2841	$(x^{2} + 1) y^{'} + x y = 0$	[_separable]	✓	1.191

2842	$x y^{2} + x + (y - x^{2} y) y^{'} = 0$	[_separable]	✓	3.762

2843	$1 + y^{2} + (x^{2} + 1) y^{'} = 0$	[_separable]	✓	1.825

2844	$y^{'} x + y = 0$	[_separable]	✓	1.442

2845	$y^{'} = 2 x y$	[_separable]	✓	1.123

2846	$x y^{2} + x + (x^{2} y - y) y^{'} = 0$	[_separable]	✓	2.621

2847	$\sqrt{- x^{2} + 1} + \sqrt{1 - y^{2}} y^{'} = 0$	[_separable]	✓	2.238

2848	$(x + 1) y^{'} - 1 + y = 0$	[_separable]	✓	1.415

2849	$y^{'} \tan (x) - y = 1$	[_separable]	✓	1.525

2850	$y + 3 + \cot (x) y^{'} = 0$	[_separable]	✓	2.049

2851	$y^{'} = \frac{x}{y}$	[_separable]	✓	3.480

2852	$x^{'} = 1 - \sin (2 t)$	[_quadrature]	✓	0.400

2853	$y^{'} x + y = y^{2}$	[_separable]	✓	1.527

2854	$\sin (x) \cos {(y)}^{2} + \cos {(x)}^{2} y^{'} = 0$	[_separable]	✓	3.567

2855	$\sec (x) \cos {(y)}^{2} = \cos (x) \sin (y) y^{'}$	[_separable]	✓	7.840

2856	$y^{'} x + y = x y (y^{'} - 1)$	[_separable]	✓	1.477

2857	$x y + \sqrt{x^{2} + 1} y^{'} = 0$	[_separable]	✓	1.589

2858	$y = x y + x^{2} y^{'}$	[_separable]	✓	1.514

2859	$\tan (x) \sin {(x)}^{2} + \cos {(x)}^{2} \cot (y) y^{'} = 0$	[_separable]	✓	6.332

2860	$y^{2} + y y^{'} + x^{2} y y^{'} - 1 = 0$	[_separable]	✓	4.025

2861	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓	1.532

2862	$y^{'} x + 2 y = 0$ i.c.	[_separable]	✓	1.776

2863	$\sin (x) \cos (y) + \cos (x) \sin (y) y^{'} = 0$ i.c.	[_separable]	✓	3.174

2864	$x^{2} y^{'} + y^{2} = 0$ i.c.	[_separable]	✓	2.666

2865	$y^{'} = e^{y}$ i.c.	[_quadrature]	✓	1.259

2866	$e^{y} (y^{'} + 1) = 1$ i.c.	[_quadrature]	✓	1.484

2867	$1 + y^{2} = \frac{y^{'}}{x^{3} (x - 1)}$ i.c.	[_separable]	✓	3.281

2868	$x^{2} + 3 y^{'} x = y^{3} + 2 y$ i.c.	[_rational, _Abel]	✓	17.620

2869	$(x^{2} + x + 1) y^{'} = y^{2} + 2 y + 5$ i.c.	[_separable]	✓	4.462

2870	$(x^{2} - 2 x - 8) y^{'} = y^{2} + y - 2$ i.c.	[_separable]	✓	3.885

2871	$x + y = y^{'} x$	[_linear]	✓	1.291

2872	$(x + y) y^{'} + x = y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.431

2873	$y^{'} x - y = \sqrt{x y}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	6.287

2874	$y^{'} = \frac{2 x - y}{x + 4 y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.678

2875	$y^{'} x - y = \sqrt{x^{2} - y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	119.919

2876	$y y^{'} + x = 2 y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.209

2877	$y^{'} x - y + \sqrt{y^{2} - x^{2}} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	4.366

2878	$x^{2} + y^{2} = x y^{'} y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	5.244

2879	$(x y - x^{2}) y^{'} - y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	77.657

2880	$y^{'} x + y = 2 \sqrt{x y}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	21.532

2881	$x + y + (x - y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.974

2882	$y (x^{2} - x y + y^{2}) + x y^{'} (x^{2} + x y + y^{2}) = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	173.829

2883	$y^{'} x - y - x \sin (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.745

2884	$y^{'} = \frac{y}{x} + \cosh (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	6.864

2885	$x^{2} + y^{2} = 2 x y^{'} y$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	6.083

2886	$(\frac{x}{y} + \frac{y}{x}) y^{'} + 1 = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	4.426

2887	$e^{\frac{y}{x}} x + y = y^{'} x$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.414

2888	$y^{'} = \frac{x + y}{x - y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	5.523

2889	$y^{'} = \frac{y}{x} + \tan (\frac{y}{x})$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓	4.595

2890	$(3 x y - 2 x^{2}) y^{'} = 2 y^{2} - x y$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	9.353

2891	$y^{'} = \frac{y}{x - k \sqrt{x^{2} + y^{2}}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	140.811

2892	$y^{2} (y y^{'} - x) + x^{3} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	27.041

2893	$y^{'} = \frac{y}{x} + \tanh (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	106.757

2894	$x + y - (x - y + 2) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.428

2895	$x + (x - 2 y + 2) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	2.829

2896	$2 x - y + 1 + (x + y) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.775

2897	$x - y + 2 + (x + y - 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.557

2898	$x - y + (y - x + 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.562

2899	$y^{'} = \frac{x + y - 1}{x - y - 1}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.411

2900	$x + y + (2 x + 2 y - 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.977

2.2.29 Problems 2801 to 2900