Problems 11501 to 11600

Table 2.233: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

11501	$y^{''''} - 12 y^{''} + 12 y - 16 x^{4} e^{x^{2}} = 0$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.257

11502	$y^{''''} + 2 a^{2} y^{''} + a^{4} y - \cosh (a x) = 0$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.880

11503	$y^{''''} + (1 + λ) a^{2} y^{''} + λ a^{4} y = 0$	[[_high_order, _missing_x]]	✓	0.126

11504	$y^{''''} + a (b x - 1) y^{''} + a b y^{'} + λ y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.075

11505	$y^{''''} + (a x^{2} + b λ + c) y^{''} + (a x^{2} + β λ + γ) y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.089

11506	$y^{''''} + 2 y^{'''} - 3 y^{''} - 4 y^{'} + 4 y - 32 \sin (2 x) + 24 \cos (2 x) = 0$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.230

11507	$y^{''''} + 4 a x y^{'''} + 6 a^{2} x^{2} y^{''} + 4 a^{3} x^{3} y^{'} + a^{4} x^{4} y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.086

11508	$4 y^{''''} - 12 y^{'''} + 11 y^{''} - 3 y^{'} - 4 \cos (x) = 0$	[[_high_order, _missing_y]]	✓	0.178

11509	$x y^{''''} + 5 y^{'''} - 24 = 0$	[[_high_order, _missing_y]]	✓	1.204

11510	$x y^{''''} - (6 x^{2} + 1) y^{'''} + 12 x^{3} y^{''} - (9 x^{2} - 7) x^{2} y^{'} + 2 (x^{2} - 3) x^{3} y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.092

11511	$x^{2} y^{''''} - 2 (ν^{2} x^{2} + 6) y^{''} + ν^{2} (ν^{2} x^{2} + 4) y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.088

11512	$x^{2} y^{''''} + 2 x y^{'''} + a y - b x^{2} = 0$	[[_high_order, _linear, _nonhomogeneous]]	✗	0.081

11513	$x^{2} y^{''''} + 4 x y^{'''} + 2 y^{''} = 0$	[[_high_order, _missing_y]]	✓	0.131

11514	$x^{2} y^{''''} + 6 x y^{'''} + 6 y^{''} = 0$	[[_high_order, _missing_y]]	✓	0.262

11515	$x^{2} y^{''''} + 6 x y^{'''} + 6 y^{''} - λ^{2} y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.075

11516	$x^{2} y^{''''} + 8 x y^{'''} + 12 y^{''} = 0$	[[_high_order, _missing_y]]	✓	0.322

11517	$x^{2} y^{''''} + 8 x y^{'''} + 12 y^{''} - λ^{2} y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.070

11518	$x^{2} y^{''''} + (2 n - 2 ν + 4) x y^{'''} + (n - ν + 1) (n - ν + 2) y^{''} - \frac{b^{4} y}{16} = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.082

11519	$x^{3} y^{''''} + 2 x^{2} y^{'''} - x y^{''} + y^{'} - a^{4} x^{3} y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.075

11520	$x^{3} y^{''''} + 6 x^{2} y^{'''} + 6 x y^{''} = 0$	[[_high_order, _missing_y]]	✓	0.258

11521	$x^{4} y^{''''} - 2 n (n + 1) x^{2} y^{''} + 4 n (n + 1) x y^{'} + (a x^{4} + n (n + 1) (n + 3) (n - 2)) y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.090

11522	$x^{4} y^{''''} + 4 x^{3} y^{'''} - (4 n^{2} - 1) x^{2} y^{''} + (4 n^{2} - 1) x y^{'} - 4 y x^{4} = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.123

11523	$x^{4} y^{''''} + 4 x^{3} y^{'''} - (4 n^{2} - 1) x^{2} y^{''} - (4 n^{2} - 1) x y^{'} + (- 4 x^{4} + 4 n^{2} - 1) y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.090

11524	$x^{4} y^{''''} + 4 x^{3} y^{'''} - (4 n^{2} + 3) x^{2} y^{''} + (12 n^{2} - 3) x y^{'} - (4 x^{4} + 12 n^{2} - 3) y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.098

11525	$x^{4} y^{''''} + 6 x^{3} y^{'''} + (4 x^{4} + (- ρ^{2} - σ^{2} + 7) x^{2}) y^{''} + (16 x^{3} + (- ρ^{2} - σ^{2} + 1) x) y^{'} + (ρ^{2} σ^{2} + 8 x^{2}) y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.084

11526	$x^{4} y^{''''} + 6 x^{3} y^{'''} + (4 x^{4} + (- 2 μ^{2} - 2 ν^{2} + 7) x^{2}) y^{''} + (16 x^{3} + (- 2 μ^{2} - 2 ν^{2} + 1) x) y^{'} + (8 x^{2} + {(μ^{2} - ν^{2})}^{2}) y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.101

11527	$x^{4} y^{''''} + 8 x^{3} y^{'''} + 12 x^{2} y^{''} = 0$	[[_high_order, _missing_y]]	✓	0.142

11528	$x^{4} y^{''''} + 8 x^{3} y^{'''} + 12 x^{2} y^{''} + a y = 0$	[[_high_order, _with_linear_symmetries]]	✓	0.185

11529	$x^{4} y^{''''} + (6 - 4 a) x^{3} y^{'''} + (4 b^{2} c^{2} x^{2 c} + 6 {(a - 1)}^{2} - 2 c^{2} (μ^{2} + ν^{2}) + 1) x^{2} y^{''} + (4 (3 c - 2 a + 1) b^{2} c^{2} x^{2 c} + (2 a - 1) (2 c^{2} (μ^{2} + ν^{2}) - 2 a (a - 1) - 1)) x y^{'} + (4 (a - c) (a - 2 c) b^{2} c^{2} x^{2 c} + (c μ + c ν + a) (c μ + c ν - a) (c μ - c ν + a) (c μ - c ν - a)) y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.167

11530	$x^{4} y^{''''} + (6 - 4 a - 4 c) x^{3} y^{'''} + (- 2 ν^{2} c^{2} + 2 a^{2} + 4 {(a + c - 1)}^{2} + 4 (a - 1) (c - 1) - 1) x^{2} y^{''} + (2 ν^{2} c^{2} - 2 a^{2} - (2 a - 1) (2 c - 1)) (2 a + 2 c - 1) x y^{'} + ((- ν^{2} c^{2} + a^{2}) (- ν^{2} c^{2} + a^{2} + 4 a c + 4 c^{2}) - b^{4} c^{4} x^{4 c}) y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.155

11531	$ν^{4} x^{4} y^{''''} + (4 ν - 2) ν^{3} x^{3} y^{'''} + (ν - 1) (2 ν - 1) ν^{2} x^{2} y^{''} - \frac{b^{4} x^{\frac{2}{ν}} y}{16} = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.110

11532	${(x^{2} - 1)}^{2} y^{''''} + 10 x (x^{2} - 1) y^{'''} + (24 x^{2} - 8 - 2 (μ (μ + 1) + ν (ν + 1)) (x^{2} - 1)) y^{''} - 6 x (μ (μ + 1) + ν (ν + 1) - 2) y^{'} + ({(μ (μ + 1) - ν (ν + 1))}^{2} - 2 μ (μ + 1) - 2 ν (ν + 1)) y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.116

11533	$(e^{x} + 2 x) y^{''''} + 4 (e^{x} + 2) y^{'''} + 6 e^{x} y^{''} + 4 e^{x} y^{'} + y e^{x} - \frac{1}{x^{5}} = 0$	[[_high_order, _fully, _exact, _linear]]	✓	1.470

11534	$y^{''''} \sin {(x)}^{4} + 2 y^{'''} \sin {(x)}^{3} \cos (x) + y^{''} \sin {(x)}^{2} (\sin {(x)}^{2} - 3) + y^{'} \sin (x) \cos (x) (2 \sin {(x)}^{2} + 3) + (a^{4} \sin {(x)}^{4} - 3) y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.158

11535	$y^{''''} \sin {(x)}^{6} + 4 y^{'''} \sin {(x)}^{5} \cos (x) - 6 y^{''} \sin {(x)}^{6} - 4 y^{'} \sin {(x)}^{5} \cos (x) + y \sin {(x)}^{6} - f = 0$	[[_high_order, _linear, _nonhomogeneous]]	✗	0.131

11536	$f (y^{''''} - 2 a^{2} y^{''} + a^{4} y) + 2 df (y^{'''} - a^{2} y^{'}) = 0$	[[_high_order, _missing_x]]	✓	0.106

11537	$f y^{''''} = 0$	[[_high_order, _quadrature]]	✓	0.070

11538	$y^{''''} - 2 a^{2} y^{''} + a^{4} y - λ (a x - b) (y^{''} - a^{2} y) = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.101

11539	$y^{(5)} + 2 y^{'''} + y^{'} - a x - b \sin (x) - c \cos (x) = 0$	[[_high_order, _missing_y]]	✓	1.505

11540	$y^{(6)} + y - \sin (\frac{3 x}{2}) \sin (\frac{x}{2}) = 0$	[[_high_order, _linear, _nonhomogeneous]]	✓	3.016

11541	$y^{(5)} - y a x - b = 0$	[[_high_order, _linear, _nonhomogeneous]]	✗	0.073

11542	$y^{(5)} + a x^{ν} y^{'} + a ν x^{ν - 1} y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.106

11543	$y^{(5)} + a y^{''''} - f = 0$	[[_high_order, _missing_x]]	✓	0.130

11544	$x y^{(5)} - m n y^{''''} + y a x = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.076

11545	$x (a y^{'} + b y^{''} + c y^{'''} + e y^{''''}) y = 0$	[[_high_order, _missing_x]]	✓	0.306

11546	$x y^{(5)} - (a A_{1} - A_{0}) x - A_{1} - ((a A_{2} - A_{1}) x + A_{2}) y^{'} = 0$	[[_high_order, _missing_y]]	✗	0.129

11547	$x^{2} y^{''''} - a y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.079

11548	$x^{10} y^{(5)} - a y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.075

11549	$x^{5 / 2} y^{(5)} - a y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.116

11550	${(x - a)}^{5} {(x - b)}^{5} y^{(5)} - c y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.108

11551	$y^{''} - y^{2} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	3.849

11552	$y^{''} - 6 y^{2} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	3.776

11553	$y^{''} - 6 y^{2} - x = 0$	[[_Painleve, ‘1st‘]]	✗	0.279

11554	$y^{''} - 6 y^{2} + 4 y = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	3.818

11555	$y^{''} + a y^{2} + b x + c = 0$	[NONE]	✗	0.268

11556	$y^{''} - 2 y^{3} - x y + a = 0$	[[_Painleve, ‘2nd‘]]	✗	0.277

11557	$y^{''} - a y^{3} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	5.390

11558	$y^{''} - 2 a^{2} y^{3} + 2 a b x y - b = 0$	[NONE]	✗	0.285

11559	$y^{''} + d + b x y + c y + a y^{3} = 0$	[NONE]	✗	0.286

11560	$y^{''} + d + b y^{2} + c y + a y^{3} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	9.900

11561	$y^{''} + a x^{r} y^{2} = 0$	[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]	✗	0.273

11562	$y^{''} + 6 a^{10} y^{11} - y = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	5.404

11563	$y^{''} - \frac{1}{{(a y^{2} + b x y + c x^{2} + α y + β x + γ)}^{3 / 2}} = 0$	[NONE]	✗	0.469

11564	$y^{''} - e^{y} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.846

11565	$y^{''} + a e^{x} \sqrt{y} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.302

11566	$y^{''} + e^{x} \sin (y) = 0$	[NONE]	✗	0.483

11567	$y^{''} + a \sin (y) = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	170.463

11568	$y^{''} + a^{2} \sin (y) - β \sin (x) = 0$	[NONE]	✗	0.974

11569	$y^{''} + a^{2} \sin (y) - β f (x) = 0$	[NONE]	✗	0.776

11570	$y^{''} = \frac{f (\frac{y}{\sqrt{x}})}{x^{3 / 2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	0.629

11571	$y^{''} - 3 y^{'} - y^{2} - 2 y = 0$	[[_2nd_order, _missing_x]]	✗	2.114

11572	$y^{''} - 7 y^{'} - y^{3 / 2} + 12 y = 0$	[[_2nd_order, _missing_x]]	✗	7.250

11573	$y^{''} + 5 a y^{'} - 6 y^{2} + 6 a^{2} y = 0$	[[_2nd_order, _missing_x]]	✗	2.600

11574	$y^{''} + 3 a y^{'} - 2 y^{3} + 2 a^{2} y = 0$	[[_2nd_order, _missing_x]]	✗	2.926

11575	$y^{''} - \frac{(3 n + 4) y^{'}}{n} - \frac{2 (n + 1) (n + 2) y (y^{\frac{n}{n + 1}} - 1)}{n^{2}} = 0$	[[_2nd_order, _missing_x]]	✗	12.133

11576	$y^{''} + a y^{'} + b y^{n} + \frac{(a^{2} - 1) y}{4} = 0$	[[_2nd_order, _missing_x]]	✗	6.762

11577	$y^{''} + a y^{'} + b x^{v} y^{n} = 0$	[NONE]	✗	0.317

11578	$y^{''} + a y^{'} + b e^{y} - 2 a = 0$	[[_2nd_order, _missing_x]]	✗	6.238

11579	$y^{''} + a y^{'} + f (x) \sin (y) = 0$	[NONE]	✗	0.615

11580	$y^{''} + y y^{'} - y^{3} = 0$	[[_2nd_order, _missing_x]]	✓	1.498

11581	$y^{''} + y y^{'} - y^{3} + a y = 0$	[[_2nd_order, _missing_x]]	✗	6.041

11582	$y^{''} + (y + 3 a) y^{'} - y^{3} + a y^{2} + 2 a^{2} y = 0$	[[_2nd_order, _missing_x]]	✗	4.912

11583	$y^{''} + (y + 3 f (x)) y^{'} - y^{3} + y^{2} f (x) + y (f^{'} (x) + 2 f {(x)}^{2}) = 0$	[NONE]	✗	0.480

11584	$y^{''} + (3 y + f (x)) y^{'} + y^{3} + y^{2} f (x) = 0$	[[_2nd_order, _with_potential_symmetries]]	✗	0.363

11585	$y^{''} - 3 y y^{'} - 3 a y^{2} - 4 a^{2} y - b = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✗	4.056

11586	$y^{''} - (3 y + f (x)) y^{'} + y^{3} + y^{2} f (x) = 0$	[[_2nd_order, _with_potential_symmetries]]	✗	0.396

11587	$y^{''} - 2 a y y^{'} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	1.352

11588	$y^{''} + a y y^{'} + b y^{3} = 0$	[[_2nd_order, _missing_x]]	✓	14.081

11589	$y^{''} + a {y^{'}}^{2} + b y = 0$	[[_2nd_order, _missing_x]]	✓	2.206

11590	$y^{''} + a {y^{'}}^{2} + b y^{'} + c y = 0$	[[_2nd_order, _missing_x]]	✗	2.236

11591	$y^{''} + a {y^{'}}^{2} + b \sin (y) = 0$	[[_2nd_order, _missing_x]]	✓	14.244

11592	$y^{''} + a y^{'} \| y^{'} \| + b \sin (y) = 0$	[[_2nd_order, _missing_x]]	✗	4.012

11593	$y^{''} + a y {y^{'}}^{2} + b y = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	3.135

11594	$y^{''} + a y {(1 + {y^{'}}^{2})}^{2} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	7.687

11595	$y^{''} - a {(y^{'} x - y)}^{v} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.313

11596	$y^{''} - k x^{a} y^{b} {y^{'}}^{r} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.283

11597	$y^{''} = a \sqrt{1 + {y^{'}}^{2}}$	[[_2nd_order, _missing_x]]	✓	2.981

11598	$y^{''} = a \sqrt{1 + {y^{'}}^{2}} + b$	[[_2nd_order, _missing_x]]	✓	3.089

11599	$y^{''} = a \sqrt{{y^{'}}^{2} + b y^{2}}$	[[_2nd_order, _missing_x]]	✗	4.192

11600	$y^{''} = a {(1 + {y^{'}}^{2})}^{3 / 2}$	[[_2nd_order, _missing_x]]	✓	2.950

2.2.116 Problems 11501 to 11600