Problems 11401 to 11500

Table 2.231: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

11401	$y^{''} = \frac{2 y}{\sin {(x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.141

11402	$y^{''} = - \frac{a y}{\sin {(x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.103

11403	$\sin {(x)}^{2} y^{''} - (a \sin {(x)}^{2} + n (n - 1)) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.894

11404	$y^{''} = - \frac{(- a^{2} \cos {(x)}^{2} - (3 - 2 a) \cos (x) - 3 + 3 a) y}{\sin {(x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	5.517

11405	$\sin {(x)}^{2} y^{''} - (a^{2} \cos {(x)}^{2} + b \cos (x) + \frac{b^{2}}{{(2 a - 3)}^{2}} + 3 a + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	14.514

11406	$y^{''} = - \frac{(- (a^{2} b^{2} - {(a + 1)}^{2}) \sin {(x)}^{2} - a (a + 1) b \sin (2 x) - a (a - 1)) y}{\sin {(x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	6.709

11407	$y^{''} = - \frac{(a \cos {(x)}^{2} + b \sin {(x)}^{2} + c) y}{\sin {(x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	2.853

11408	$y^{''} = - \frac{\cos (x) y^{'}}{\sin (x)} + \frac{y}{\sin {(x)}^{2}}$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	2.251

11409	$y^{''} = - \frac{\cos (x) y^{'}}{\sin (x)} - \frac{(v (v + 1) \sin {(x)}^{2} - n^{2}) y}{\sin {(x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	4.103

11410	$y^{''} = \frac{\cos (2 x) y^{'}}{\sin (2 x)} - 2 y$	[[_2nd_order, _with_linear_symmetries]]	✗	2.698

11411	$y^{''} = - \frac{\cos (x) y^{'}}{\sin (x)} - \frac{(- 17 \sin {(x)}^{2} - 1) y}{4 \sin {(x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	2.911

11412	$y^{''} = - \frac{\sin (x) y^{'}}{\cos (x)} - \frac{(2 x^{2} + x^{2} \sin {(x)}^{2} - 24 \cos {(x)}^{2}) y}{4 x^{2} \cos {(x)}^{2}} + \sqrt{\cos (x)}$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	7.200

11413	$y^{''} = - \frac{b \cos (x) y^{'}}{\sin (x) a} - \frac{(c \cos {(x)}^{2} + d \cos (x) + e) y}{a \sin {(x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	5.589

11414	$y^{''} = - \frac{4 \sin (3 x) y}{\sin {(x)}^{3}}$	[[_2nd_order, _with_linear_symmetries]]	✗	2.855

11415	$y^{''} = - \frac{(4 v (v + 1) \sin {(x)}^{2} - \cos {(x)}^{2} + 2 - 4 n^{2}) y}{4 \sin {(x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	4.270

11416	$y^{''} = \frac{(3 \sin {(x)}^{2} + 1) y^{'}}{\cos (x) \sin (x)} + \frac{\sin {(x)}^{2} y}{\cos {(x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.980

11417	$y^{''} = - \frac{(- a \cos {(x)}^{2} \sin {(x)}^{2} - m (m - 1) \sin {(x)}^{2} - n (n - 1) \cos {(x)}^{2}) y}{\cos {(x)}^{2} \sin {(x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	6.350

11418	$y^{''} = - \frac{x y^{'}}{f (x)} + \frac{y}{f (x)}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.035

11419	$y^{''} = - \frac{f^{'} (x) y^{'}}{2 f (x)} - \frac{g (x) y}{f (x)}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.073

11420	$y^{''} = - \frac{(2 f (x) {g^{'} (x)}^{2} g (x) - (g {(x)}^{2} - 1) (f (x) g^{''} (x) + 2 f^{'} (x) g^{'} (x))) y^{'}}{f (x) g^{'} (x) (g {(x)}^{2} - 1)} - \frac{((g {(x)}^{2} - 1) (f^{'} (x) (f (x) g^{''} (x) + 2 f^{'} (x) g^{'} (x)) - f (x) f^{''} (x) g^{'} (x)) - (2 f^{'} (x) g (x) + v (v + 1) f (x) g^{'} (x)) f (x) {g^{'} (x)}^{2}) y}{f {(x)}^{2} g^{'} (x) (g {(x)}^{2} - 1)}$	[[_2nd_order, _with_linear_symmetries]]	✗	3.630

11421	$y^{''} = - \frac{y^{'}}{x} - \frac{(x - 1) y}{x^{4}}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.577

11422	$y^{''} = - \frac{y^{'}}{x} - \frac{(- x - 1) y}{x^{4}}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.562

11423	$y^{''} = - \frac{b^{2} y}{{(- a^{2} + x^{2})}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.923

11424	$y^{'''} - λ y = 0$	[[_3rd_order, _missing_x]]	✓	0.097

11425	$y^{'''} + y a x^{3} - b x = 0$	[[_3rd_order, _linear, _nonhomogeneous]]	✗	0.070

11426	$y^{'''} - a x^{b} y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.085

11427	$y^{'''} + 3 y^{'} - 4 y = 0$	[[_3rd_order, _missing_x]]	✓	0.083

11428	$y^{'''} - a^{2} y^{'} - e^{2 a x} \sin {(x)}^{2} = 0$	[[_3rd_order, _missing_y]]	✓	0.280

11429	$y^{'''} + 2 a x y^{'} + a y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.082

11430	$y^{'''} - x^{2} y^{''} + (a + b - 1) x y^{'} - b y a = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.080

11431	$y^{'''} + x^{2 c - 2} y^{'} + (c - 1) x^{2 c - 3} y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.104

11432	$y^{'''} - (6 k^{2} \sin {(x)}^{2} + a) y^{'} + b y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.119

11433	$y^{'''} + 2 f (x) y^{'} + f^{'} (x) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.079

11434	$y^{'''} - 2 y^{''} - 3 y^{'} + 10 y = 0$	[[_3rd_order, _missing_x]]	✓	0.082

11435	$y^{'''} - 2 y^{''} - a^{2} y^{'} + 2 a^{2} y - \sinh (x) = 0$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.712

11436	$y^{'''} - 3 a y^{''} + 3 a^{2} y^{'} - a^{3} y - e^{a x} = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.176

11437	$y^{'''} + a 2 y^{''} + a 1 y^{'} + a 0 y = 0$	[[_3rd_order, _missing_x]]	✓	0.183

11438	$y^{'''} - 6 x y^{''} + 2 (4 x^{2} + 2 a - 1) y^{'} - 8 y a x = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.105

11439	$y^{'''} + 3 a x y^{''} + 3 a^{2} x^{2} y^{'} + a^{3} x^{3} y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.106

11440	$y^{'''} - \sin (x) y^{''} - 2 \cos (x) y^{'} + y \sin (x) - \ln (x) = 0$	[[_3rd_order, _fully, _exact, _linear]]	✓	1.042

11441	$y^{'''} + f (x) y^{''} + y^{'} + f (x) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.074

11442	$y^{'''} + f (x) (x^{2} y^{''} - 2 y^{'} x + 2 y) = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.089

11443	$4 y^{'''} - 8 y^{''} - 11 y^{'} - 3 y + 18 e^{x} = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.148

11444	$x y^{'''} + 3 y^{''} + x y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.081

11445	$x y^{'''} + 3 y^{''} - a x^{2} y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.081

11446	$x y^{'''} + (a + b) y^{''} - y^{'} x - a y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.077

11447	$x y^{'''} - (x + 2 v) y^{''} - (x - 2 v - 1) y^{'} + (x - 1) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.086

11448	$x y^{'''} + (x^{2} - 3) y^{''} + 4 y^{'} x + 2 y - f (x) = 0$	[[_3rd_order, _fully, _exact, _linear]]	✓	1.635

11449	$2 x y^{'''} + 3 y^{''} + y a x - b = 0$	[[_3rd_order, _linear, _nonhomogeneous]]	✗	0.079

11450	$2 x y^{'''} - 4 (x + ν - 1) y^{''} + (2 x + 6 ν - 5) y^{'} + (1 - 2 ν) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.079

11451	$2 x y^{'''} + 3 (2 a x + k) y^{''} + 6 (a k + b x) y^{'} + (3 b k + 2 c x) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.081

11452	$(x - 2) x y^{'''} - x (x - 2) y^{''} - 2 y^{'} + 2 y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	1.138

11453	$(2 x - 1) y^{'''} - 8 y^{'} x + 8 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.074

11454	$(2 x - 1) y^{'''} + (x + 4) y^{''} + 2 y^{'} = 0$	[[_3rd_order, _missing_y]]	✓	1.744

11455	$x^{2} y^{'''} - 6 y^{'} + a x^{2} y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.081

11456	$x^{2} y^{'''} + (x + 1) y^{''} - y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.076

11457	$x^{2} y^{'''} - x y^{''} + (x^{2} + 1) y^{'} = 0$	[[_3rd_order, _missing_y]]	✓	0.485

11458	$x^{2} y^{'''} + 3 x y^{''} + (4 a^{2} x^{2 a} + 1 - 4 ν^{2} a^{2}) y^{'} = 4 a^{3} x^{2 a - 1} y$	[[_3rd_order, _with_linear_symmetries]]	✓	0.932

11459	$x^{2} y^{'''} - 3 (x - m) x y^{''} + (2 x^{2} + 4 (n - m) x + m (2 m - 1)) y^{'} - 2 n (2 x - 2 m + 1) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.088

11460	$x^{2} y^{'''} + 4 x y^{''} + (x^{2} + 2) y^{'} + 3 x y - f (x) = 0$	[[_3rd_order, _linear, _nonhomogeneous]]	✗	0.079

11461	$x^{2} y^{'''} + 5 x y^{''} + 4 y^{'} - \ln (x) = 0$	[[_3rd_order, _missing_y]]	✓	0.290

11462	$x^{2} y^{'''} + 6 x y^{''} + 6 y^{'} = 0$	[[_3rd_order, _missing_y]]	✓	0.214

11463	$x^{2} y^{'''} + 6 x y^{''} + 6 y^{'} + a x^{2} y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.083

11464	$x^{2} y^{'''} - 3 (p + q) x y^{''} + 3 p (3 q + 1) y^{'} - x^{2} y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.082

11465	$x^{2} y^{'''} - 2 (n + 1) x y^{''} + (a x^{2} + 6 n) y^{'} - 2 y a x = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.078

11466	$x^{2} y^{'''} - (x^{2} - 2 x) y^{''} - (x^{2} + ν^{2} - \frac{1}{4}) y^{'} + (x^{2} - 2 x + ν^{2} - \frac{1}{4}) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.090

11467	$x^{2} y^{'''} - (x + ν) x y^{''} + ν (2 x + 1) y^{'} - ν (x + 1) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.089

11468	$x^{2} y^{'''} - 2 (x^{2} - x) y^{''} + (x^{2} - 2 x + \frac{1}{4} - ν^{2}) y^{'} + (ν^{2} - \frac{1}{4}) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.097

11469	$x^{2} y^{'''} - (x^{4} - 6 x) y^{''} - (2 x^{3} - 6) y^{'} + 2 x^{2} y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.089

11470	$(x^{2} + 1) y^{'''} + 8 x y^{''} + 10 y^{'} - 3 + \frac{1}{x^{2}} - 2 \ln (x) = 0$	[[_3rd_order, _missing_y]]	✓	1.199

11471	$(x^{2} + 2) y^{'''} - 2 x y^{''} + (x^{2} + 2) y^{'} - 2 x y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.083

11472	$2 x (x - 1) y^{'''} + 3 (2 x - 1) y^{''} + (2 a x + b) y^{'} + a y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.089

11473	$x^{3} y^{'''} + (- ν^{2} + 1) x y^{'} + (a x^{3} + ν^{2} - 1) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.098

11474	$x^{3} y^{'''} + (4 x^{3} + (- 4 ν^{2} + 1) x) y^{'} + (4 ν^{2} - 1) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.071

11475	$x^{3} y^{'''} + (a x^{2 ν} + 1 - ν^{2}) x y^{'} + (b x^{3 ν} + a (ν - 1) x^{2 ν} + ν^{2} - 1) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.135

11476	$x^{3} y^{'''} + 3 x^{2} y^{''} - 2 y^{'} x + 2 y - 6 x^{3} (x - 1) \ln (x) + x^{3} (8 + x) = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.318

11477	$x^{3} y^{'''} + 3 x^{2} y^{''} + (- a^{2} + 1) x y^{'} = 0$	[[_3rd_order, _missing_y]]	✓	0.285

11478	$x^{3} y^{'''} - 4 x^{2} y^{''} + (x^{2} + 8) x y^{'} - 2 (x^{2} + 4) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.091

11479	$x^{3} y^{'''} + 6 x^{2} y^{''} + (a x^{3} - 12) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.260

11480	$x^{3} y^{'''} + 3 (1 - a) x^{2} y^{''} + (4 b^{2} c^{2} x^{2 c + 1} + 1 - 4 ν^{2} c^{2} + 3 a (a - 1) x) y^{'} + (4 b^{2} c^{2} (c - a) x^{2 c} + a (4 ν^{2} c^{2} - a^{2})) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.127

11481	$x^{3} y^{'''} + (3 + x) x^{2} y^{''} + 5 (x - 6) x y^{'} + (4 x + 30) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.073

11482	$x^{3} y^{'''} + x^{2} y^{''} + \ln (x) + 2 y^{'} x - y - 2 x^{3} = 0$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	14.023

11483	$(x^{2} + 1) x y^{'''} + 3 (2 x^{2} + 1) y^{''} - 12 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.088

11484	$(3 + x) x^{2} y^{'''} - 3 x (x + 2) y^{''} + 6 (x + 1) y^{'} - 6 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.079

11485	$2 (x - a 1) (x - a 2) (x - a 3) y^{'''} + (9 x^{2} - 6 (a 1 + a 2 + a 3) x + 3 a 1 a 2 + 3 a 1 a 3 + 3 a 2 a 3) y^{''} - 2 ((n^{2} + n - 3) x + b) y^{'} - n (n + 1) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.098

11486	$x^{3} (x + 1) y^{'''} - (2 + 4 x) x^{2} y^{''} + (4 + 10 x) x y^{'} - 4 (3 x + 1) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.091

11487	$4 x^{4} y^{'''} - 4 x^{3} y^{''} + 4 x^{2} y^{'} - 1 = 0$	[[_3rd_order, _missing_y]]	✓	0.406

11488	$x^{3} (x^{2} + 1) y^{'''} - (4 x^{2} + 2) x^{2} y^{''} + (10 x^{2} + 4) x y^{'} - 4 (3 x^{2} + 1) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.098

11489	$x^{6} y^{'''} + x^{2} y^{''} - 2 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.075

11490	$x^{6} y^{'''} + 6 x^{5} y^{''} + a y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.075

11491	$x^{2} (x^{4} + 2 x^{2} + 2 x + 1) y^{'''} - (2 x^{6} + 3 x^{4} - 6 x^{2} - 6 x - 1) y^{''} + (x^{6} - 6 x^{3} - 15 x^{2} - 12 x - 2) y^{'} + (x^{4} + 4 x^{3} + 8 x^{2} + 6 x + 1) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.095

11492	${(x - a)}^{3} {(x - b)}^{3} y^{'''} - c y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.094

11493	$y^{'''} \sin (x) + (2 \cos (x) + 1) y^{''} - y^{'} \sin (x) - \cos (x) = 0$	[[_3rd_order, _missing_y]]	✓	2.749

11494	$(\sin (x) + x) y^{'''} + 3 (\cos (x) + 1) y^{''} - 3 y^{'} \sin (x) - \cos (x) y + \sin (x) = 0$	[[_3rd_order, _fully, _exact, _linear]]	✓	2.282

11495	$y^{'''} \sin {(x)}^{2} + 3 y^{''} \sin (x) \cos (x) + (\cos (2 x) + 4 ν (ν + 1) \sin {(x)}^{2}) y^{'} + 2 ν (ν + 1) y \sin (2 x) = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.135

11496	$y^{'''} + y^{'} x + n y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.078

11497	$y^{'''} - y^{'} x - n y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.074

11498	$y^{''''} = 0$	[[_high_order, _quadrature]]	✓	0.075

11499	$y^{''''} + 4 y - f = 0$	[[_high_order, _missing_x]]	✓	0.144

11500	$y^{''''} + λ y = 0$	[[_high_order, _missing_x]]	✓	0.093

2.2.115 Problems 11401 to 11500