Problems 11301 to 11400

Table 2.229: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

11301	$x^{2} (x + 1) y^{''} + 2 x (3 x + 2) y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	1.065

11302	$y^{''} = - \frac{2 (- 2 + x) y^{'}}{x (- 1 + x)} + \frac{2 (x + 1) y}{x^{2} (- 1 + x)}$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.031

11303	$y^{''} = \frac{(5 x - 4) y^{'}}{x (- 1 + x)} - \frac{(9 x - 6) y}{x^{2} (- 1 + x)}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.313

11304	$y^{''} = - \frac{((a + 1 + b) x + α + β - 1) y^{'}}{x (- 1 + x)} - \frac{(a b x - α β) y}{x^{2} (- 1 + x)}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.856

11305	$y^{''} = - \frac{y^{'}}{x + 1} - \frac{y}{x {(x + 1)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.961

11306	$y^{''} = \frac{2 y^{'}}{x (- 2 + x)} - \frac{y}{x^{2} (- 2 + x)}$	[[_2nd_order, _with_linear_symmetries]]	✗	147.952

11307	$y^{''} = \frac{2 y}{x {(- 1 + x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.783

11308	$y^{''} = - \frac{((α + β + 1) x^{2} - (α + β + 1 + a (γ + δ) - δ) x + a γ) y^{'}}{x (- 1 + x) (x - a)} - \frac{(α β x - q) y}{x (- 1 + x) (x - a)}$	[[_2nd_order, _with_linear_symmetries]]	✗	2.707

11309	$y^{''} = - \frac{(A x^{2} + B x + C) y^{'}}{(x - a) (x - b) (x - c)} - \frac{(DD x + E) y}{(x - a) (x - b) (x - c)}$	[[_2nd_order, _with_linear_symmetries]]	✗	3.353

11310	$y^{''} = \frac{(x - 4) y^{'}}{2 x (- 2 + x)} - \frac{(x - 3) y}{2 x^{2} (- 2 + x)}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.051

11311	$y^{''} = \frac{y^{'}}{x + 1} - \frac{(3 x + 1) y}{4 x^{2} (x + 1)}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.006

11312	$y^{''} = - \frac{(3 x - 1) y^{'}}{2 x (- 1 + x)} + \frac{v (v + 1) y}{4 x^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.113

11313	$y^{''} = - \frac{((a + 1) x - 1) y^{'}}{x (- 1 + x)} - \frac{((a^{2} - b^{2}) x + c^{2}) y}{4 x^{2} (- 1 + x)}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.361

11314	$y^{''} = - \frac{(3 x - 1) y^{'}}{2 x (- 1 + x)} - \frac{(a x + b) y}{4 x {(- 1 + x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	0.952

11315	$y^{''} = - \frac{(- 3 x + 1) y}{(- 1 + x) {(2 x - 1)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.030

11316	$y^{''} = - \frac{(3 x + a + 2 b) y^{'}}{2 (x + a) (x + b)} - \frac{(a - b) y}{4 {(x + a)}^{2} (x + b)}$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	3.227

11317	$y^{''} = \frac{(6 x - 1) y^{'}}{3 x (- 2 + x)} + \frac{y}{3 x^{2} (- 2 + x)}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.247

11318	$y^{''} = - \frac{(a (b + 2) x^{2} + (c - d + 1) x) y^{'}}{(a x + 1) x^{2}} - \frac{(a b x - c d) y}{(a x + 1) x^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.761

11319	$y^{''} = \frac{2 (a x + 2 b) y^{'}}{x (a x + b)} - \frac{(2 a x + 6 b) y}{(a x + b) x^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.898

11320	$y^{''} = - \frac{(2 a x + b) y^{'}}{x (a x + b)} - \frac{(a v x - b) y}{(a x + b) x^{2}} + A x$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	143.371

11321	$y^{''} = - \frac{a y}{x^{4}}$	[[_Emden, _Fowler]]	✓	3.602

11322	$y^{''} = - \frac{(x^{2} a (1 - a) - b (x + b)) y}{x^{4}}$	[[_2nd_order, _with_linear_symmetries]]	✗	0.645

11323	$y^{''} = - \frac{(e^{\frac{2}{x}} - v^{2}) y}{x^{4}}$	[[_2nd_order, _with_linear_symmetries]]	✗	0.355

11324	$y^{''} = - \frac{y^{'}}{x^{3}} + \frac{2 y}{x^{4}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.230

11325	$y^{''} = \frac{(a + b) y^{'}}{x^{2}} - \frac{((a + b) x + a b) y}{x^{4}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.499

11326	$y^{''} = - \frac{y^{'}}{x} - \frac{y}{x^{4}}$	[[_Emden, _Fowler]]	✓	0.665

11327	$y^{''} = - \frac{y^{'}}{x} - \frac{(b x^{2} + a (x^{4} + 1)) y}{x^{4}}$	[[_2nd_order, _with_linear_symmetries]]	✗	0.975

11328	$y^{''} = - \frac{(x^{2} + 1) y^{'}}{x^{3}} - \frac{y}{x^{4}}$	[[_2nd_order, _with_linear_symmetries]]	✗	0.745

11329	$y^{''} = - \frac{2 y^{'}}{x} - \frac{a^{2} y}{x^{4}}$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.188

11330	$y^{''} = - \frac{(2 x^{2} + 1) y^{'}}{x^{3}} + \frac{y}{x^{4}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.250

11331	$y^{''} = - \frac{2 (x + a) y^{'}}{x^{2}} - \frac{b y}{x^{4}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.780

11332	$y^{''} = \frac{(2 x^{2} - 1) y^{'}}{x^{3}} - \frac{y}{x^{4}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.911

11333	$y^{''} = \frac{(2 x^{2} - 1) y^{'}}{x^{3}} - \frac{2 y}{x^{4}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.510

11334	$y^{''} = - \frac{(x^{3} - 1) y^{'}}{x (x^{3} + 1)} + \frac{x y}{x^{3} + 1}$	[[_2nd_order, _with_linear_symmetries]]	✓	2.397

11335	$y^{''} = - \frac{(2 x^{2} + 1) y^{'}}{x (x^{2} + 1)} - \frac{(- v (v + 1) x^{2} - n^{2}) y}{x^{2} (x^{2} + 1)}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.296

11336	$y^{''} = - \frac{(a x^{2} + a - 1) y^{'}}{x (x^{2} + 1)} - \frac{(b x^{2} + c) y}{x^{2} (x^{2} + 1)}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.388

11337	$y^{''} = \frac{(x^{2} - 2) y^{'}}{x (x^{2} - 1)} - \frac{(x^{2} - 2) y}{x^{2} (x^{2} - 1)}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.237

11338	$y^{''} = - \frac{2 x y^{'}}{x^{2} - 1} - \frac{v (v + 1) y}{x^{2} (x^{2} - 1)}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.150

11339	$y^{''} = - \frac{2 x y^{'}}{x^{2} - 1} + \frac{v (v + 1) y}{x^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.152

11340	$y^{''} = \frac{2 x y^{'}}{x^{2} - 1} - \frac{(a (a + 1) - a x^{2} (a + 3)) y}{x^{2} (x^{2} - 1)}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.654

11341	$x^{2} (x^{2} - 1) y^{''} - 2 x^{3} y^{'} - ((a - n) (a + n + 1) x^{2} (x^{2} - 1) + 2 a x^{2} + n (n + 1) (x^{2} - 1)) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	2.363

11342	$y^{''} = - \frac{(a x^{2} + a - 2) y^{'}}{x (x^{2} - 1)} - \frac{b y}{x^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.797

11343	$y^{''} = \frac{(2 b c x^{c} (x^{2} - 1) + 2 (a - 1) x^{2} - 2 a) y^{'}}{x (x^{2} - 1)} - \frac{(b^{2} c^{2} x^{2 c} (x^{2} - 1) + b c x^{c + 2} (2 a - c - 1) - b c x^{c} (2 a - c + 1) + x^{2} (a (a - 1) - v (v + 1)) - a (a + 1)) y}{x^{2} (x^{2} - 1)}$	[[_2nd_order, _with_linear_symmetries]]	✗	5.164

11344	$y^{''} = - \frac{a y}{{(x^{2} + 1)}^{2}}$	[_Halm]	✓	1.474

11345	$y^{''} = - \frac{2 x y^{'}}{x^{2} + 1} - \frac{y}{{(x^{2} + 1)}^{2}}$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.918

11346	$y^{''} = - \frac{2 x y^{'}}{x^{2} + 1} - \frac{(a^{2} {(x^{2} + 1)}^{2} - n (n + 1) (x^{2} + 1) + m^{2}) y}{{(x^{2} + 1)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.271

11347	$y^{''} = - \frac{a x y^{'}}{x^{2} + 1} - \frac{b y}{{(x^{2} + 1)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.233

11348	$y^{''} = - \frac{a y}{{(x^{2} - 1)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.311

11349	$y^{''} = - \frac{2 x y^{'}}{x^{2} - 1} + \frac{a^{2} y}{{(x^{2} - 1)}^{2}}$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.358

11350	$y^{''} = - \frac{2 x y^{'}}{x^{2} - 1} - \frac{(- a^{2} - λ (x^{2} - 1)) y}{{(x^{2} - 1)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.115

11351	$y^{''} = - \frac{2 x y^{'}}{x^{2} - 1} - \frac{((x^{2} - 1) (a x^{2} + b x + c) - k^{2}) y}{{(x^{2} - 1)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.292

11352	$y^{''} = - \frac{2 x y^{'}}{x^{2} - 1} - \frac{(- a^{2} {(x^{2} - 1)}^{2} - n (n + 1) (x^{2} - 1) - m^{2}) y}{{(x^{2} - 1)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.288

11353	$y^{''} = \frac{2 x (2 a - 1) y^{'}}{x^{2} - 1} - \frac{(x^{2} (2 a (2 a - 1) - v (v + 1)) + 2 a + v (v + 1)) y}{{(x^{2} - 1)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.449

11354	$y^{''} = - \frac{2 x (n + 1 - 2 a) y^{'}}{x^{2} - 1} - \frac{(4 a x^{2} (a - n) - (x^{2} - 1) (2 a + (v - n) (v + n + 1))) y}{{(x^{2} - 1)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.434

11355	$y^{''} = - \frac{(2 x^{2} + a) y^{'}}{x (x^{2} + a)} - \frac{b y}{x^{2} (x^{2} + a)}$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	4.000

11356	$y^{''} = - \frac{b^{2} y}{{(a^{2} + x^{2})}^{2}}$	[[_Emden, _Fowler]]	✓	1.679

11357	$y^{''} = - \frac{2 (x^{2} - 1) y^{'}}{x {(- 1 + x)}^{2}} - \frac{(- 2 x^{2} + 2 x + 2) y}{x^{2} {(- 1 + x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.180

11358	$y^{''} = \frac{12 y}{{(x + 1)}^{2} (x^{2} + 2 x + 3)}$	[[_2nd_order, _with_linear_symmetries]]	✓	4.307

11359	$y^{''} = - \frac{b y}{x^{2} {(x - a)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.523

11360	$y^{''} = - \frac{b y}{x^{2} {(x - a)}^{2}} + c$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.137

11361	$y^{''} = \frac{c y}{{(x - a)}^{2} {(x - b)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	2.517

11362	$y^{''} = - \frac{((α + β + 1) {(x - a)}^{2} (x - b) + (1 - α - β) {(x - b)}^{2} (x - a)) y^{'}}{{(x - a)}^{2} {(x - b)}^{2}} - \frac{α β {(a - b)}^{2} y}{{(x - a)}^{2} {(x - b)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	5.805

11363	$y^{''} = - \frac{(- x^{2} (a^{2} - 1) + 2 (a + 3) b x - b^{2}) y}{4 x^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.093

11364	$y^{''} = - \frac{(a x^{2} + a - 3) y}{4 {(x^{2} + 1)}^{2}}$	[_Halm]	✓	1.860

11365	$y^{''} = \frac{18 y}{{(2 x + 1)}^{2} (x^{2} + x + 1)}$	[[_2nd_order, _with_linear_symmetries]]	✓	4.175

11366	$y^{''} = \frac{3 y}{4 {(x^{2} + x + 1)}^{2}}$	[[_Emden, _Fowler]]	✓	1.927

11367	$y^{''} = - \frac{(3 x - 1) y^{'}}{2 x (- 1 + x)} - \frac{(v (v + 1) (- 1 + x) - a^{2} x) y}{4 x^{2} {(- 1 + x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.201

11368	$y^{''} = - \frac{(3 x - 1) y^{'}}{2 x (- 1 + x)} - \frac{(- v (v + 1) {(- 1 + x)}^{2} - 4 n^{2} x) y}{4 x^{2} {(- 1 + x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.192

11369	$y^{''} = - \frac{3 y}{16 x^{2} {(- 1 + x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.792

11370	$y^{''} = \frac{(7 a x^{2} + 5) y^{'}}{x (a x^{2} + 1)} - \frac{(15 a x^{2} + 5) y}{x^{2} (a x^{2} + 1)}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.030

11371	$y^{''} = - \frac{b x y^{'}}{(x^{2} - 1) a} - \frac{(c x^{2} + d x + e) y}{a {(x^{2} - 1)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.443

11372	$y^{''} = - \frac{(b x^{2} + c x + d) y}{a x^{2} {(- 1 + x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	0.910

11373	$y^{''} = - \frac{2 y^{'}}{x} - \frac{c y}{x^{2} {(a x + b)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.632

11374	$y^{''} = - \frac{y}{{(a x + b)}^{4}}$	[[_Emden, _Fowler]]	✓	1.583

11375	$y^{''} = - \frac{A y}{{(a x^{2} + b x + c)}^{2}}$	[[_Emden, _Fowler]]	✓	2.540

11376	$y^{''} = - \frac{y^{'}}{x^{4}} + \frac{y}{x^{5}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.441

11377	$y^{''} = - \frac{(3 x^{2} - 1) y^{'}}{(x^{2} - 1) x} - \frac{(x^{2} - 1 - {(2 v + 1)}^{2}) y}{{(x^{2} - 1)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.197

11378	$y^{''} = \frac{(3 x + 1) y^{'}}{(- 1 + x) (x + 1)} - \frac{36 {(x + 1)}^{2} y}{{(- 1 + x)}^{2} {(3 x + 5)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.480

11379	$y^{''} = \frac{y^{'}}{x} - \frac{a y}{x^{6}}$	[[_Emden, _Fowler]]	✓	2.391

11380	$y^{''} = - \frac{(3 x^{2} + a) y^{'}}{x^{3}} - \frac{b y}{x^{6}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.109

11381	$y^{''} = - \frac{((1 - 4 a) x^{2} - 1) y^{'}}{x (x^{2} - 1)} - \frac{((- v^{2} + x^{2}) {(x^{2} - 1)}^{2} + 4 a (a + 1) x^{4} - 2 a x^{2} (x^{2} - 1)) y}{x^{2} {(x^{2} - 1)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	3.041

11382	$y^{''} = - (\frac{1 - a 1 - b 1}{x - c 1} + \frac{1 - a 2 - b 2}{x - c 2} + \frac{1 - a 3 - b 3}{x - c 3}) y^{'} - \frac{(\frac{a 1 b 1 (c 1 - c 3) (c 1 - c 2)}{x - c 1} + \frac{a 2 b 2 (c 2 - c 1) (c 2 - c 3)}{x - c 2} + \frac{a 3 b 3 (c 3 - c 2) (c 3 - c 1)}{x - c 3}) y}{(x - c 1) (x - c 2) (x - c 3)}$	[[_2nd_order, _with_linear_symmetries]]	✗	8.112

11383	$y^{''} = - \frac{(2 x^{2} + 1) y^{'}}{x^{3}} - \frac{(- 2 x^{2} + 1) y}{4 x^{6}}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.754

11384	$y^{''} = \frac{(2 x^{2} + 1) y^{'}}{x^{3}} - \frac{(a x^{4} + 10 x^{2} + 1) y}{4 x^{6}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.226

11385	$y^{''} = - \frac{27 x y}{16 {(x^{3} - 1)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	4.744

11386	$y^{''} = - (\frac{(1 - al 1 - bl 1) b 1}{b 1 x - a 1} + \frac{(1 - al 2 - bl 2) b 2}{b 2 x - a 2} + \frac{(1 - al 3 - bl 3) b 3}{b 3 x - a 3}) y^{'} - \frac{(\frac{al 1 bl 1 (a 1 b 2 - a 2 b 1) (- a 1 b 3 + a 3 b 1)}{b 1 x - a 1} + \frac{al 2 bl 2 (a 2 b 3 - a 3 b 2) (a 1 b 2 - a 2 b 1)}{b 2 x - a 2} + \frac{al 3 bl 3 (- a 1 b 3 + a 3 b 1) (a 2 b 3 - a 3 b 2)}{b 3 x - a 3}) y}{(b 1 x - a 1) (b 2 x - a 2) (b 3 x - a 3)}$	[[_2nd_order, _with_linear_symmetries]]	✗	10.058

11387	$y^{''} = - \frac{(x^{2} ((x^{2} - a 1) (x^{2} - a 2) + (x^{2} - a 2) (x^{2} - a 3) + (x^{2} - a 3) (x^{2} - a 1)) - (x^{2} - a 1) (x^{2} - a 2) (x^{2} - a 3)) y^{'}}{x (x^{2} - a 1) (x^{2} - a 2) (x^{2} - a 3)} - \frac{(A x^{2} + B) y}{x (x^{2} - a 1) (x^{2} - a 2) (x^{2} - a 3)}$	[[_2nd_order, _with_linear_symmetries]]	✗	8.419

11388	$y^{''} = - a x^{2 a - 1} x^{- 2 a} y^{'} - b^{2} x^{- 2 a} y$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.792

11389	$y^{''} = - \frac{(a p x^{b} + q) y^{'}}{x (a x^{b} - 1)} - \frac{(a r x^{b} + s) y}{x^{2} (a x^{b} - 1)}$	[[_2nd_order, _with_linear_symmetries]]	✗	2.124

11390	$y^{''} = \frac{y}{e^{x} + 1}$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✗	0.310

11391	$y^{''} = \frac{y^{'}}{x \ln (x)} + \ln {(x)}^{2} y$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.676

11392	$y^{''} = \frac{y^{'}}{x (\ln (x) - 1)} - \frac{y}{x^{2} (\ln (x) - 1)}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.693

11393	$y^{''} = - \frac{(- a^{2} \sinh {(x)}^{2} - n (n - 1)) y}{\sinh {(x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✗	1.429

11394	$y^{''} = - \frac{2 n \cosh (x) y^{'}}{\sinh (x)} - (- a^{2} + n^{2}) y$	[[_2nd_order, _with_linear_symmetries]]	✗	2.086

11395	$y^{''} = - \frac{(2 n + 1) \cos (x) y^{'}}{\sin (x)} - (v + n + 1) (v - n) y$	[[_2nd_order, _with_linear_symmetries]]	✗	2.901

11396	$y^{''} = - \frac{(\sin {(x)}^{2} - \cos (x)) y^{'}}{\sin (x)} - y \sin {(x)}^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	4.792

11397	$y^{''} = - \frac{x \sin (x) y^{'}}{\cos (x) x - \sin (x)} + \frac{\sin (x) y}{\cos (x) x - \sin (x)}$	[[_2nd_order, _with_linear_symmetries]]	✓	10.481

11398	$y^{''} = - \frac{(x^{2} \sin (x) - 2 \cos (x) x) y^{'}}{x^{2} \cos (x)} - \frac{(2 \cos (x) - x \sin (x)) y}{x^{2} \cos (x)}$	[[_2nd_order, _with_linear_symmetries]]	✓	2.273

11399	$\cos {(x)}^{2} y^{''} - (a \cos {(x)}^{2} + n (n - 1)) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.506

11400	$y^{''} = - \frac{a (n - 1) \sin (2 a x) y^{'}}{\cos {(a x)}^{2}} - \frac{n a^{2} ((n - 1) \sin {(a x)}^{2} + \cos {(a x)}^{2}) y}{\cos {(a x)}^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	5.523

2.2.114 Problems 11301 to 11400