Problems 11901 to 12000

Table 2.241: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

11901	$[\begin{array}{cc} - 1 & 4 \\ - 1 & 3 \end{array}]$	Eigenvectors	✓	0.081

11902	$[\begin{array}{cc} 3 & - 1 \\ 1 & 1 \end{array}]$	Eigenvectors	✓	0.079

11903	$[\begin{array}{cc} 5 & 1 \\ - 9 & - 1 \end{array}]$	Eigenvectors	✓	0.086

11904	$[\begin{array}{cc} 11 & 9 \\ - 16 & - 13 \end{array}]$	Eigenvectors	✓	0.092

11905	$[\begin{array}{ccc} 1 & 3 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{array}]$	Eigenvectors	✓	0.223

11906	$[\begin{array}{ccc} 2 & - 2 & 1 \\ 2 & - 2 & 1 \\ 2 & - 2 & 1 \end{array}]$	Eigenvectors	✓	0.228

11907	$[\begin{array}{ccc} 3 & - 3 & 1 \\ 2 & - 2 & 1 \\ 0 & 0 & 1 \end{array}]$	Eigenvectors	✓	0.233

11908	$[\begin{array}{ccc} 3 & - 2 & 0 \\ 0 & 1 & 0 \\ - 4 & 4 & 1 \end{array}]$	Eigenvectors	✓	0.223

11909	$[\begin{array}{ccc} 7 & - 8 & 3 \\ 6 & - 7 & 3 \\ 2 & - 2 & 2 \end{array}]$	Eigenvectors	✓	0.285

11910	$[\begin{array}{ccc} 6 & - 5 & 2 \\ 4 & - 3 & 2 \\ 2 & - 2 & 3 \end{array}]$	Eigenvectors	✓	0.283

11911	$[\begin{array}{ccc} 1 & 1 & - 1 \\ - 2 & 4 & - 1 \\ - 4 & 4 & 1 \end{array}]$	Eigenvectors	✓	0.281

11912	$[\begin{array}{ccc} 2 & 0 & 0 \\ - 6 & 11 & 2 \\ 6 & - 15 & 0 \end{array}]$	Eigenvectors	✓	0.292

11913	$[\begin{array}{ccc} 0 & 1 & 0 \\ - 1 & 2 & 0 \\ - 1 & 1 & 1 \end{array}]$	Eigenvectors	✓	0.107

11914	$[\begin{array}{ccc} 2 & - 2 & 1 \\ - 1 & 2 & 0 \\ - 5 & 7 & - 1 \end{array}]$	Eigenvectors	✓	0.109

11915	$[\begin{array}{ccc} - 2 & 4 & - 1 \\ - 3 & 5 & - 1 \\ - 1 & 1 & 1 \end{array}]$	Eigenvectors	✓	0.219

11916	$[\begin{array}{ccc} 3 & - 2 & 1 \\ 1 & 0 & 1 \\ - 1 & 1 & 2 \end{array}]$	Eigenvectors	✓	0.219

11917	$[\begin{array}{cccc} 1 & 0 & - 2 & 0 \\ 0 & 1 & - 2 & 0 \\ 0 & 0 & - 1 & 0 \\ 0 & 0 & 0 & - 1 \end{array}]$	Eigenvectors	✓	0.245

11918	$[\begin{array}{cccc} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 2 \end{array}]$	Eigenvectors	✓	0.245

11919	$[\begin{array}{cccc} 1 & 1 & 0 & 0 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 2 \end{array}]$	Eigenvectors	✓	0.227

11920	$[\begin{array}{cccc} 1 & 1 & 0 & 1 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 2 & 1 \\ 0 & 0 & 0 & 2 \end{array}]$	Eigenvectors	✓	0.225

11921	$[\begin{array}{ccccc} 2 & 1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 & 0 \\ 0 & 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 2 & 1 \\ 0 & 0 & 0 & 0 & 2 \end{array}]$	Eigenvectors	✓	0.188

11922	$y^{'} = f (x)$	[_quadrature]	✓	0.175

11923	$y^{'} = f (y)$	[_quadrature]	✓	0.936

11924	$y^{'} = f (x) g (y)$	[_separable]	✓	1.073

11925	$g (x) y^{'} = f_{1} (x) y + f_{0} (x)$	[_linear]	✓	1.460

11926	$g (x) y^{'} = f_{1} (x) y + f_{n} (x) y^{n}$	[_Bernoulli]	✓	2.284

11927	$y^{'} = f (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	1.418

11928	$y^{'} = a y^{2} + b x + c$	[_Riccati]	✓	1.289

11929	$y^{'} = y^{2} - a^{2} x^{2} + 3 a$	[_Riccati]	✓	1.942

11930	$y^{'} = y^{2} + a^{2} x^{2} + b x + c$	[_Riccati]	✓	9.487

11931	$y^{'} = a y^{2} + b x^{n}$	[[_Riccati, _special]]	✓	1.720

11932	$y^{'} = y^{2} + a n x^{n - 1} - a^{2} x^{2 n}$	[_Riccati]	✗	768.667

11933	$y^{'} = a y^{2} + b x^{2 n} + c x^{n - 1}$	[_Riccati]	✓	3.789

11934	$y^{'} = a x^{n} y^{2} + b x^{- n - 2}$	[[_homogeneous, ‘class G‘], _Riccati]	✓	2.300

11935	$y^{'} = a x^{n} y^{2} + b x^{m}$	[_Riccati]	✓	2.281

11936	$y^{'} = y^{2} + k {(a x + b)}^{n} {(c x + d)}^{- n - 4}$	[_Riccati]	✗	10.591

11937	$y^{'} = a x^{n} y^{2} + b m x^{m - 1} - a b^{2} x^{n + 2 m}$	[_Riccati]	✗	413.367

11938	$y^{'} = (a x^{2 n} + b x^{n - 1}) y^{2} + c$	[_Riccati]	✓	55.196

11939	$(a_{2} x + b_{2}) (y^{'} + λ y^{2}) + a_{0} x + b_{0} = 0$	[_rational, _Riccati]	✓	3.780

11940	$x^{2} y^{'} = a x^{2} y^{2} + b$	[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]	✓	1.893

11941	$x^{2} y^{'} = y^{2} x^{2} - a^{2} x^{4} + a (1 - 2 b) x^{2} - b (b + 1)$	[_rational, _Riccati]	✓	3.007

11942	$x^{2} y^{'} = a x^{2} y^{2} + b x^{n} + c$	[_rational, _Riccati]	✓	2.590

11943	$x^{2} y^{'} = y^{2} x^{2} + a x^{2 m} {(b x^{m} + c)}^{n} - \frac{n^{2}}{4} + \frac{1}{4}$	[_Riccati]	✗	5.095

11944	$(c_{2} x^{2} + b_{2} x + a_{2}) (y^{'} + λ y^{2}) + a_{0} = 0$	[_rational, _Riccati]	✓	13.347

11945	$x^{4} y^{'} = - x^{4} y^{2} - a^{2}$	[_rational, [_Riccati, _special]]	✓	3.404

11946	$a x^{2} {(- 1 + x)}^{2} (y^{'} + λ y^{2}) + b x^{2} + c x + s = 0$	[_rational, _Riccati]	✓	4.817

11947	${(a x^{2} + b x + c)}^{2} (y^{'} + y^{2}) + A = 0$	[_rational, _Riccati]	✓	3.604

11948	$x^{n + 1} y^{'} = a x^{2 n} y^{2} + c x^{m} + d$	[_Riccati]	✓	3.558

11949	$(a x^{n} + b) y^{'} = b y^{2} + a x^{n - 2}$	[_rational, _Riccati]	✓	4.545

11950	$(a x^{n} + b x^{m} + c) (y^{'} - y^{2}) + a n (n - 1) x^{n - 2} + b m (m - 1) x^{m - 2} = 0$	[_rational, _Riccati]	✓	5.698

11951	$y^{'} = a y^{2} + b y + c x + k$	[_Riccati]	✓	1.596

11952	$y^{'} = y^{2} + a x^{n} y + a x^{n - 1}$	[_Riccati]	✓	2.839

11953	$y^{'} = y^{2} + a x^{n} y + b x^{n - 1}$	[_Riccati]	✓	4.050

11954	$y^{'} = y^{2} + (α x + β) y + a x^{2} + b x + c$	[_Riccati]	✓	39.063

11955	$y^{'} = y^{2} + a x^{n} y - a b x^{n} - b^{2}$	[_Riccati]	✗	4.004

11956	$y^{'} = - (n + 1) x^{n} y^{2} + a x^{n + m + 1} - a x^{m}$	[_Riccati]	✗	5.790

11957	$y^{'} = a x^{n} y^{2} + b x^{m} y + b c x^{m} - a c^{2} x^{n}$	[_Riccati]	✗	5.211

11958	$y^{'} = a x^{n} y^{2} - a x^{n} (b x^{m} + c) y + b m x^{m - 1}$	[_Riccati]	✓	7.361

11959	$y^{'} = - a n x^{n - 1} y^{2} + c x^{m} (a x^{n} + b) y - c x^{m}$	[_Riccati]	✓	13.411

11960	$y^{'} = a x^{n} y^{2} + b x^{m} y + c k x^{k - 1} - b c x^{m + k} - a c^{2} x^{n + 2 k}$	[_Riccati]	✗	9.790

11961	$x y^{'} = a y^{2} + b y + c x^{2 b}$	[_rational, _Riccati]	✓	2.872

11962	$x y^{'} = a y^{2} + b y + c x^{n}$	[_rational, _Riccati]	✓	2.454

11963	$x y^{'} = a y^{2} + (n + b x^{n}) y + c x^{2 n}$	[_rational, _Riccati]	✓	3.519

11964	$x y^{'} = x y^{2} + a y + b x^{n}$	[_rational, _Riccati]	✓	2.503

11965	$x y^{'} + a_{3} x y^{2} + a_{2} y + a_{1} x + a_{0} = 0$	[_rational, _Riccati]	✓	6.638

11966	$x y^{'} = a x^{n} y^{2} + b y + c x^{- n}$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	2.650

11967	$x y^{'} = a x^{n} y^{2} + m y - a b^{2} x^{n + 2 m}$	[_rational, _Riccati]	✓	2.470

11968	$x y^{'} = x^{2 n} y^{2} + (m - n) y + x^{2 m}$	[_rational, _Riccati]	✓	2.528

11969	$x y^{'} = a x^{n} y^{2} + b y + c x^{m}$	[_rational, _Riccati]	✓	3.370

11970	$x y^{'} = a x^{2 n} y^{2} + (b x^{n} - n) y + c$	[_rational, _Riccati]	✓	4.328

11971	$x y^{'} = a x^{2 n + m} y^{2} + (b x^{m + n} - n) y + c x^{m}$	[_rational, _Riccati]	✓	41.580

11972	$(a_{2} x + b_{2}) (y^{'} + λ y^{2}) + (a_{1} x + b_{1}) y + a_{0} x + b_{0} = 0$	[_rational, _Riccati]	✓	21.223

11973	$(a x + c) y^{'} = α {(b x + a y)}^{2} + β (b x + a y) - b x + γ$	[[_1st_order, _with_linear_symmetries], _rational, _Riccati]	✓	3.499

11974	$2 x^{2} y^{'} = 2 y^{2} + x y - 2 a^{2} x$	[_rational, _Riccati]	✓	1.446

11975	$2 x^{2} y^{'} = 2 y^{2} + 3 x y - 2 a^{2} x$	[_rational, _Riccati]	✓	1.972

11976	$x^{2} y^{'} = a x^{2} y^{2} + b x y + c$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	2.351

11977	$x^{2} y^{'} = c x^{2} y^{2} + (a x^{2} + b x) y + α x^{2} + β x + γ$	[_rational, _Riccati]	✓	7.492

11978	$x^{2} y^{'} = a x^{2} y^{2} + b x y + c x^{n} + s$	[_rational, _Riccati]	✓	3.045

11979	$x^{2} y^{'} = a x^{2} y^{2} + b x y + c x^{2 n} + s x^{n}$	[_rational, _Riccati]	✓	4.397

11980	$x^{2} y^{'} = c x^{2} y^{2} + (a x^{n} + b) x y + α x^{2 n} + β x^{n} + γ$	[_rational, _Riccati]	✓	35.227

11981	$x^{2} y^{'} = (α x^{2 n} + β x^{n} + γ) y^{2} + (a x^{n} + b) x y + c x^{2}$	[_rational, _Riccati]	✗	597.533

11982	$(x^{2} - 1) y^{'} + λ (y^{2} - 2 x y + 1) = 0$	[_rational, _Riccati]	✗	7.472

11983	$(a x^{2} + b) y^{'} + α y^{2} + β x y + \frac{b (a + β)}{α} = 0$	[_rational, _Riccati]	✓	472.467

11984	$(a x^{2} + b) y^{'} + α y^{2} + β x y + γ = 0$	[_rational, _Riccati]	✓	505.818

11985	$(a x^{2} + b) y^{'} + y^{2} - 2 x y + (1 - a) x^{2} - b = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	2.865

11986	$(a x^{2} + b x + c) y^{'} = y^{2} + (2 λ x + b) y + λ (λ - a) x^{2} + μ$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	4.966

11987	$(a x^{2} + b x + c) y^{'} = y^{2} + (a x + μ) y - λ^{2} x^{2} + λ (b - μ) x + λ c$	[_rational, _Riccati]	✗	480.184

11988	$(a_{2} x^{2} + b_{2} x + c_{2}) y^{'} = y^{2} + (a_{1} x + b_{1}) y - λ (λ + a_{1} - a_{2}) x^{2} + λ (b_{2} - b_{1}) x + λ c_{2}$	[_rational, _Riccati]	✓	51.929

11989	$(a_{2} x^{2} + b_{2} x + c_{2}) y^{'} = y^{2} + (a_{1} x + b_{1}) y + a_{0} x^{2} + b_{0} x + c_{0}$	[_rational, _Riccati]	✓	46.097

11990	$(x - a) (x - b) y^{'} + y^{2} + k (y + x - a) (y + x - b) = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	3.325

11991	$(c_{2} x^{2} + b_{2} x + a_{2}) (y^{'} + λ y^{2}) + (b_{1} x + a_{1}) y + a_{0} = 0$	[_rational, _Riccati]	✓	23.987

11992	$x^{3} y^{'} = a x^{3} y^{2} + (b x^{2} + c) y + s x$	[_rational, _Riccati]	✓	11.829

11993	$x^{3} y^{'} = a x^{3} y^{2} + x (b x + c) y + α x + β$	[_rational, _Riccati]	✓	5.363

11994	$x (x^{2} + a) (y^{'} + λ y^{2}) + (b x^{2} + c) y + s x = 0$	[_rational, _Riccati]	✓	5.281

11995	$x^{2} (x + a) (y^{'} + λ y^{2}) + x (b x + c) y + α x + β = 0$	[_rational, _Riccati]	✓	6.910

11996	$(a x^{2} + b x + e) (- y + x y^{'}) - y^{2} + x^{2} = 0$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	2.213

11997	$x^{2} (x^{2} + a) (y^{'} + λ y^{2}) + x (b x^{2} + c) y + s = 0$	[_rational, _Riccati]	✓	7.786

11998	$a (x^{2} - 1) (y^{'} + λ y^{2}) + b x (x^{2} - 1) y + c x^{2} + d x + s = 0$	[_rational, _Riccati]	✗	6.226

11999	$x^{n + 1} y^{'} = a x^{2 n} y^{2} + b x^{n} y + c x^{m} + d$	[_Riccati]	✓	4.492

12000	$x (a x^{k} + b) y^{'} = α x^{n} y^{2} + (β - a n x^{k}) y + γ x^{- n}$	[_rational, _Riccati]	✓	43.495

2.2.120 Problems 11901 to 12000