Problems 2801 to 2900

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


#	ODE	CAS classiﬁcation	Solved?	time (sec)

2801	$[\begin{matrix} x^{'} = - 5 x + 3 y \\ y^{'} = y - x \end{matrix}]$	system_of_ODEs	✓	0.589

2802	$[\begin{matrix} x^{'} = x - 4 y \\ y^{'} = 4 x - 7 y \end{matrix}]$	system_of_ODEs	✓	0.439

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	✓	0.496

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	✓	0.410

2805	$[\begin{matrix} x^{'} = 2 y + z \\ y^{'} = - x - 3 y - z \\ z^{'} = x + y - z \end{matrix}]$	system_of_ODEs	✓	0.412

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	✓	0.371

2807	$[\begin{matrix} x^{'} = 2 y \\ y^{'} = - 2 x \\ z^{'} = 2 h \\ h^{'} = - 2 z \end{matrix}]$	system_of_ODEs	✓	0.541

2808	$[\begin{matrix} x^{'} = 2 y + z \\ y^{'} = - 2 x + h \\ z^{'} = 2 h \\ h^{'} = - 2 z \end{matrix}]$	system_of_ODEs	✓	0.637

2809	$x^{'} = x (1 - x)$	[_quadrature]	✓	2.268

2810	$x^{'} = - x (1 - x)$	[_quadrature]	✓	1.965

2811	$x^{'} = x^{2}$	[_quadrature]	✓	1.915

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	✗	0.033

2813	$[\begin{matrix} x_{1}^{'} = - x_{1} - x_{2} + 1 \\ x_{2}^{'} = 2 x_{1} - x_{2} + 5 \end{matrix}]$	system_of_ODEs	✓	0.956

2814	$[\begin{matrix} x^{'} = x - x^{3} - x y \\ y^{'} = 2 y - y^{5} - y x^{4} \end{matrix}]$	system_of_ODEs	✗	0.041

2815	$[\begin{matrix} x^{'} = x^{2} + y^{2} + 1 \\ y^{'} = x^{2} - y^{2} \end{matrix}]$	system_of_ODEs	✗	0.037

2816	$[\begin{matrix} x^{'} = x^{2} + y^{2} - 1 \\ y^{'} = 2 x y \end{matrix}]$	system_of_ODEs	✗	0.028

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	✗	0.035

2818	$[\begin{matrix} x^{'} = \tan (x + y) \\ y^{'} = x + x^{3} \end{matrix}]$	system_of_ODEs	✗	0.031

2819	$[\begin{matrix} x^{'} = e^{y} - x \\ y^{'} = e^{x} + y \end{matrix}]$	system_of_ODEs	✗	0.030

2820	$z^{''} + z^{3} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	4.279

2821	$z^{''} + z + z^{5} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	403.913

2822	$z^{''} + e^{z^{2}} = 1$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.466

2823	$z^{''} + \frac{z}{1 + z^{2}} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	3.232

2824	$z^{''} + z - 2 z^{3} = 0$	[[_2nd_order, _missing_x], _Duﬃng, [_2nd_order, _reducible, _mu_x_y1]]	✓	4.536

2825	$[\begin{matrix} x_{1}^{'} = - 5 x_{1} + x_{2} \\ x_{2}^{'} = x_{1} - 5 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.448

2826	$[\begin{matrix} x_{1}^{'} = - x_{2} \\ x_{2}^{'} = 8 x_{1} - 6 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.474

2827	$[\begin{matrix} x_{1}^{'} = 4 x_{1} - x_{2} \\ x_{2}^{'} = - 2 x_{1} + 5 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.474

2828	$[\begin{matrix} x_{1}^{'} = - 4 x_{1} - x_{2} \\ x_{2}^{'} = x_{1} - 6 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.437

2829	$[\begin{matrix} x_{1}^{'} = x_{1} - 4 x_{2} \\ x_{2}^{'} = - 8 x_{1} + 4 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.612

2830	$[\begin{matrix} x_{1}^{'} = 3 x_{1} - x_{2} \\ x_{2}^{'} = 5 x_{1} - 3 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.464

2831	$[\begin{matrix} x_{1}^{'} = 2 x_{2} \\ x_{2}^{'} = - 2 x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	0.796

2832	$[\begin{matrix} x_{1}^{'} = x_{1} - x_{2} \\ x_{2}^{'} = 5 x_{1} - 3 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.563

2833	$[\begin{matrix} x_{1}^{'} = 2 x_{1} + x_{2} \\ x_{2}^{'} = - 5 x_{1} - 2 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.522

2834	$[\begin{matrix} x_{1}^{'} = 4 x_{2} \\ x_{2}^{'} = - 9 x_{1} \end{matrix}]$	system_of_ODEs	✓	0.506

2835	$y^{''} + λ y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.028

2836	$y^{''} + λ y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.357

2837	$y^{''} - λ y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.681

2838	$y^{''} + λ y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.076

2839	$y^{''} - 2 y^{'} + (1 + λ) y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.716

2840	$y^{''} + λ y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.028

2841	$x y + (x^{2} + 1) y^{'} = 0$	[_separable]	✓	1.649

2842	$x y^{2} + x + (y - x^{2} y) y^{'} = 0$	[_separable]	✓	4.246

2843	$1 + y^{2} + (x^{2} + 1) y^{'} = 0$	[_separable]	✓	2.266

2844	$y + x y^{'} = 0$	[_separable]	✓	2.161

2845	$y^{'} = 2 x y$	[_separable]	✓	1.642

2846	$x y^{2} + x + (x^{2} y - y) y^{'} = 0$	[_separable]	✓	2.738

2847	$\sqrt{- x^{2} + 1} + \sqrt{1 - y^{2}} y^{'} = 0$	[_separable]	✓	2.102

2848	$(x + 1) y^{'} - 1 + y = 0$	[_separable]	✓	2.017

2849	$y^{'} \tan (x) - y = 1$	[_separable]	✓	1.847

2850	$y + 3 + \cot (x) y^{'} = 0$	[_separable]	✓	2.204

2851	$y^{'} = \frac{x}{y}$	[_separable]	✓	4.471

2852	$x^{'} = 1 - \sin (2 t)$	[_quadrature]	✓	0.603

2853	$y + x y^{'} = y^{2}$	[_separable]	✓	2.241

2854	$\sin (x) \cos {(y)}^{2} + \cos {(x)}^{2} y^{'} = 0$	[_separable]	✓	3.850

2855	$\sec (x) \cos {(y)}^{2} = \cos (x) \sin (y) y^{'}$	[_separable]	✓	7.589

2856	$y + x y^{'} = x y (y^{'} - 1)$	[_separable]	✓	1.465

2857	$x y + \sqrt{x^{2} + 1} y^{'} = 0$	[_separable]	✓	2.024

2858	$y = x y + x^{2} y^{'}$	[_separable]	✓	1.884

2859	$\tan (x) \sin {(x)}^{2} + \cos {(x)}^{2} \cot (y) y^{'} = 0$	[_separable]	✓	5.758

2860	$y^{2} + y y^{'} + x^{2} y y^{'} - 1 = 0$	[_separable]	✓	4.578

2861	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓	2.010

2862	$x y^{'} + 2 y = 0$ i.c.	[_separable]	✓	2.636

2863	$\sin (x) \cos (y) + \cos (x) \sin (y) y^{'} = 0$ i.c.	[_separable]	✓	3.429

2864	$x^{2} y^{'} + y^{2} = 0$ i.c.	[_separable]	✓	3.558

2865	$y^{'} = e^{y}$ i.c.	[_quadrature]	✓	2.233

2866	$e^{y} (y^{'} + 1) = 1$ i.c.	[_quadrature]	✓	2.632

2867	$1 + y^{2} = \frac{y^{'}}{x^{3} (- 1 + x)}$ i.c.	[_separable]	✓	3.070

2868	$x^{2} + 3 x y^{'} = y^{3} + 2 y$ i.c.	[_rational, _Abel]	✓	15.955

2869	$(x^{2} + x + 1) y^{'} = y^{2} + 2 y + 5$ i.c.	[_separable]	✓	5.608

2870	$(x^{2} - 2 x - 8) y^{'} = y^{2} + y - 2$ i.c.	[_separable]	✓	5.332

2871	$x + y = x y^{'}$	[_linear]	✓	1.526

2872	$(x + y) y^{'} + x = y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	38.231

2873	$x y^{'} - y = \sqrt{x y}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.223

2874	$y^{'} = \frac{2 x - y}{x + 4 y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.404

2875	$x y^{'} - y = \sqrt{x^{2} - y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	90.042

2876	$x + y y^{'} = 2 y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.454

2877	$x y^{'} - y + \sqrt{y^{2} - x^{2}} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	5.025

2878	$x^{2} + y^{2} = x y y^{'}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	4.886

2879	$(x y - x^{2}) y^{'} - y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	72.746

2880	$y + x y^{'} = 2 \sqrt{x y}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	13.032

2881	$x + y + (x - y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.454

2882	$y (x^{2} - x y + y^{2}) + x y^{'} (y^{2} + x y + x^{2}) = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	108.773

2883	$x y^{'} - y - x \sin (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	6.713

2884	$y^{'} = \frac{y}{x} + \cosh (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	5.157

2885	$x^{2} + y^{2} = 2 x y y^{'}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	8.003

2886	$(\frac{x}{y} + \frac{y}{x}) y^{'} + 1 = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	97.135

2887	$x e^{\frac{y}{x}} + y = x y^{'}$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓	5.127

2888	$y^{'} = \frac{x + y}{x - y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	6.162

2889	$y^{'} = \frac{y}{x} + \tan (\frac{y}{x})$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓	4.906

2890	$(3 x y - 2 x^{2}) y^{'} = 2 y^{2} - x y$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	92.096

2891	$y^{'} = \frac{y}{x - k \sqrt{x^{2} + y^{2}}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	73.005

2892	$y^{2} (y y^{'} - x) + x^{3} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	24.429

2893	$y^{'} = \frac{y}{x} + \tanh (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	53.626

2894	$x + y - (x - y + 2) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	36.931

2895	$x + (x - 2 y + 2) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	2.871

2896	$2 x - y + 1 + (x + y) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.947

2897	$x - y + 2 + (x + y - 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	36.651

2898	$x - y + (y - x + 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.789

2899	$y^{'} = \frac{x + y - 1}{x - y - 1}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	36.879

2900	$x + y + (2 x + 2 y - 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.855

2.2.29 Problems 2801 to 2900