Problems 10801 to 10900

Table 2.219: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

10801	$y^{'} = \frac{_F1 (y^{2} - 2 \ln (x))}{\sqrt{y^{2}} x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	3.548

10802	$y^{'} = \frac{- \sin (2 y) x - \sin (2 y) + \cos (2 y) x^{4} + x^{4}}{2 x (x + 1)}$	[‘y=_G(x,y’)‘]	✗	19.254

10803	$y^{'} = \frac{x y + y + x^{4} \sqrt{x^{2} + y^{2}}}{x (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	7.327

10804	$y^{'} = \frac{- \sin (2 y) x - \sin (2 y) + x \cos (2 y) + x}{2 x (x + 1)}$	[‘y=_G(x,y’)‘]	✗	10.258

10805	$y^{'} = - \frac{1}{- x -_F1 (y - \ln (x)) y e^{y}}$	[NONE]	✗	3.543

10806	$y^{'} = \frac{(1 + 2 y) (1 + y)}{x (- 2 y - 2 + x + 2 x y)}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.367

10807	$y^{'} = \frac{- 125 + 300 x - 240 x^{2} + 64 x^{3} - 80 y^{2} + 64 x y^{2} + 64 y^{3}}{{(4 x - 5)}^{3}}$	[[_homogeneous, ‘class C‘], _rational, _Abel]	✓	150.006

10808	$y^{'} = \frac{x + y + y^{2} - 2 y \ln (x) x + x^{2} \ln {(x)}^{2}}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	2.243

10809	$y^{'} = \frac{x^{3} e^{y} + x^{4} + e^{y} y - e^{y} \ln (e^{y} + x) + x y - \ln (e^{y} + x) x + x}{x^{2}}$	[‘y=_G(x,y’)‘]	✗	41.790

10810	$y^{'} = \frac{x^{2}}{2} + \sqrt{x^{3} - 6 y} + x^{2} \sqrt{x^{3} - 6 y} + x^{3} \sqrt{x^{3} - 6 y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	46.575

10811	$y^{'} = \frac{(- \sqrt{a} x^{3} + 2 \sqrt{a x^{4} + 8 y} + 2 x^{2} \sqrt{a x^{4} + 8 y} + 2 x^{3} \sqrt{a x^{4} + 8 y}) \sqrt{a}}{2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	41.427

10812	$y^{'} = \frac{y (- 3 x^{3} y - 3 + y^{2} x^{7})}{x (x^{3} y + 1)}$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	2.775

10813	$y^{'} = \frac{{(3 + y)}^{3} e^{\frac{9 x^{2}}{2}} x e^{\frac{3 x^{2}}{2}} e^{- 3 x^{2}}}{243 e^{\frac{3 x^{2}}{2}} + 81 e^{\frac{3 x^{2}}{2}} y + 243 y}$	[[_Abel, ‘2nd type‘, ‘class C‘]]	✗	5.833

10814	$y^{'} = \frac{{(x - y)}^{3} {(x + y)}^{3} x}{(- y^{2} + x^{2} - 1) y}$	[_rational]	✗	2.765

10815	$y^{'} = \frac{- 2 \cos (y) + x^{3} \cos (2 y) \ln (x) + x^{3} \ln (x)}{2 \sin (y) \ln (x) x}$	[‘y=_G(x,y’)‘]	✗	63.088

10816	$y^{'} = \frac{y}{x (- 1 + x y + x y^{3} + x y^{4})}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	2.738

10817	$y^{'} = - \frac{2 x}{3} + \sqrt{x^{2} + 3 y} + x^{2} \sqrt{x^{2} + 3 y} + x^{3} \sqrt{x^{2} + 3 y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	37.112

10818	$y^{'} = \frac{- 2 \cos (y) + x^{2} \cos (2 y) \ln (x) + x^{2} \ln (x)}{2 \sin (y) \ln (x) x}$	[‘y=_G(x,y’)‘]	✗	63.029

10819	$y^{'} = \frac{y (x y + 1)}{x (- x y - 1 + y^{4} x^{3})}$	[_rational]	✓	2.063

10820	$y^{'} = \frac{(4 e^{- x^{2}} - 4 x^{2} e^{- x^{2}} + 4 y^{2} - 4 x^{2} e^{- x^{2}} y + x^{4} e^{- 2 x^{2}}) x}{4}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	3.686

10821	$y^{'} = \frac{y (x + y)}{x (x + y + y^{3} + y^{4})}$	[_rational]	✓	1.604

10822	$y^{'} = \frac{y (x^{3} + x^{2} y + y^{2})}{x^{2} (x - 1) (x + y)}$	[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	3.861

10823	$y^{'} = \frac{({(x^{2} + 1)}^{3 / 2} x^{2} + {(x^{2} + 1)}^{3 / 2} + y^{2} {(x^{2} + 1)}^{3 / 2} + x^{2} y^{3} + y^{3}) x}{{(x^{2} + 1)}^{3}}$	[_Abel]	✗	18.394

10824	$y^{'} = \frac{(3 x y^{2} + x + 3 y^{2}) y}{(6 y^{2} + x) x (x + 1)}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	2.801

10825	$y^{'} = - \frac{- y + x^{3} \sqrt{x^{2} + y^{2}} - x^{2} \sqrt{x^{2} + y^{2}} y}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	7.263

10826	$y^{'} = \frac{(1 + 2 y) (1 + y)}{x (- 2 y - 2 + x y^{3} + 2 x y^{4})}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	3.026

10827	$y^{'} = \frac{1 + 2 \sqrt{4 x^{2} y + 1} x^{3} + 2 x^{5} \sqrt{4 x^{2} y + 1} + 2 x^{6} \sqrt{4 x^{2} y + 1}}{2 x^{3}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	44.078

10828	$y^{'} = \frac{y (x - y)}{x (x - y - y^{3} - y^{4})}$	[_rational]	✓	1.635

10829	$y^{'} = \frac{2 a + \sqrt{- y^{2} + 4 a x} + x^{2} \sqrt{- y^{2} + 4 a x} + x^{3} \sqrt{- y^{2} + 4 a x}}{y}$	[‘y=_G(x,y’)‘]	✗	21.540

10830	$y^{'} = \frac{(x + y + 1) y}{(y^{4} + y^{3} + y^{2} + x) (x + 1)}$	[_rational]	✗	2.256

10831	$y^{'} = - \frac{- y + x^{4} \sqrt{x^{2} + y^{2}} - x^{3} \sqrt{x^{2} + y^{2}} y}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	7.265

10832	$y^{'} = \frac{(x^{4} + 3 x y^{2} + 3 y^{2}) y}{(6 y^{2} + x) x (x + 1)}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	3.142

10833	$y^{'} = - \frac{1}{- {(y^{3})}^{2 / 3} x -_F1 (y^{3} - 3 \ln (x)) {(y^{3})}^{1 / 3} x}$	[NONE]	✗	2.649

10834	$y^{'} = \frac{y (x - y) (1 + y)}{x (x y + x - y)}$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	1.789

10835	$y^{'} = \frac{30 x^{3} + 25 \sqrt{x} + 25 y^{2} - 20 x^{3} y - 100 y \sqrt{x} + 4 x^{6} + 40 x^{7 / 2} + 100 x}{25 x}$	[_rational, _Riccati]	✓	21.305

10836	$y^{'} = \frac{(e^{- \frac{y}{x}} y + e^{- \frac{y}{x}} x + x^{2}) e^{\frac{y}{x}}}{x}$	[[_1st_order, _with_linear_symmetries]]	✓	2.146

10837	$y^{'} = \frac{(e^{- \frac{y}{x}} y + e^{- \frac{y}{x}} x + x^{3}) e^{\frac{y}{x}}}{x}$	[[_1st_order, _with_linear_symmetries]]	✓	2.077

10838	$y^{'} = \frac{b x^{3} + c^{2} \sqrt{a} - 2 c b x^{2} \sqrt{a} + 2 c y^{2} a^{3 / 2} + b^{2} x^{4} \sqrt{a} - 2 y^{2} a^{3 / 2} b x^{2} + a^{5 / 2} y^{4}}{a x^{2} y}$	[_rational]	✗	5.024

10839	$y^{'} = \frac{y + x^{2} \ln {(x)}^{3} + 2 x^{2} \ln {(x)}^{2} y + x^{2} \ln (x) y^{2}}{x \ln (x)}$	[_Riccati]	✓	5.366

10840	$y^{'} = \frac{y + x^{3} \ln {(x)}^{3} + 2 x^{3} \ln {(x)}^{2} y + x^{3} \ln (x) y^{2}}{x \ln (x)}$	[_Riccati]	✓	3.199

10841	$y^{'} = \frac{y (x + y) (1 + y)}{x (x y + x + y)}$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	1.762

10842	$y^{'} = \frac{3 x^{3} + \sqrt{- 9 x^{4} + 4 y^{3}} + x^{2} \sqrt{- 9 x^{4} + 4 y^{3}} + x^{3} \sqrt{- 9 x^{4} + 4 y^{3}}}{y^{2}}$	[NONE]	✗	40.521

10843	$y^{'} = \frac{1}{- x + (\frac{1}{y} + 1) x +_F1 ((\frac{1}{y} + 1) x) x^{2} -_F1 ((\frac{1}{y} + 1) x) x^{2} (\frac{1}{y} + 1)}$	[‘y=_G(x,y’)‘]	✗	2.411

10844	$y^{'} = \frac{x}{2} + \frac{1}{2} + \sqrt{x^{2} + 2 x + 1 - 4 y} + x^{2} \sqrt{x^{2} + 2 x + 1 - 4 y} + x^{3} \sqrt{x^{2} + 2 x + 1 - 4 y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	37.993

10845	$y^{'} = \frac{\cosh (x)}{\sinh (x)} +_F1 (y - \ln (\sinh (x)))$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	5.128

10846	$y^{'} = - \frac{x}{2} + 1 + \sqrt{x^{2} - 4 x + 4 y} + x^{2} \sqrt{x^{2} - 4 x + 4 y} + x^{3} \sqrt{x^{2} - 4 x + 4 y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	38.015

10847	$y^{'} = \frac{1}{\sin (x)} +_F1 (y - \ln (\sin (x)) + \ln (\cos (x) + 1))$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	7.980

10848	$y^{'} = \frac{b^{3} + y^{2} b^{3} + 2 y b^{2} a x + x^{2} b a^{2} + y^{3} b^{3} + 3 y^{2} b^{2} a x + 3 y b a^{2} x^{2} + a^{3} x^{3}}{b^{3}}$	[[_homogeneous, ‘class C‘], _Abel]	✓	15.502

10849	$y^{'} = \frac{α^{3} + y^{2} α^{3} + 2 y α^{2} β x + α β^{2} x^{2} + y^{3} α^{3} + 3 y^{2} α^{2} β x + 3 y α β^{2} x^{2} + β^{3} x^{3}}{α^{3}}$	[[_homogeneous, ‘class C‘], _Abel]	✓	16.120

10850	$y^{'} = \frac{14 x y + 12 + 2 x + x^{3} y^{3} + 6 x^{2} y^{2}}{x^{2} (x y + 2 + x)}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	2.459

10851	$y^{'} = \frac{y (\ln (x) + \ln (y) - 1 + x^{2} \ln {(x)}^{2} + 2 x^{2} \ln (y) \ln (x) + x^{2} \ln {(y)}^{2})}{x}$	[NONE]	✗	4.259

10852	$y^{'} = \frac{y (\ln (y) - 1 + \ln (x) + x^{3} \ln {(x)}^{2} + 2 x^{3} \ln (y) \ln (x) + x^{3} \ln {(y)}^{2})}{x}$	[NONE]	✗	4.342

10853	$y^{'} = - \frac{(- \frac{1}{x} -_F1 (y^{2} - 2 x)) x}{\sqrt{y^{2}}}$	[NONE]	✗	2.764

10854	$y^{'} = - \frac{x}{4} + \frac{1}{4} + \sqrt{x^{2} - 2 x + 1 + 8 y} + x^{2} \sqrt{x^{2} - 2 x + 1 + 8 y} + x^{3} \sqrt{x^{2} - 2 x + 1 + 8 y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	38.138

10855	$y^{'} = \frac{a^{3} + y^{2} a^{3} + 2 a^{2} b x y + a b^{2} x^{2} + y^{3} a^{3} + 3 y^{2} a^{2} b x + 3 y a b^{2} x^{2} + b^{3} x^{3}}{a^{3}}$	[[_homogeneous, ‘class C‘], _Abel]	✓	15.397

10856	$y^{'} = - \frac{- x -_F1 (y^{2} - 2 x)}{\sqrt{y^{2}} x}$	[NONE]	✗	2.764

10857	$y^{'} = \frac{- \sin (2 y) + x \cos (2 y) + \cos (2 y) x^{3} + \cos (2 y) x^{4} + x + x^{3} + x^{4}}{2 x}$	[‘y=_G(x,y’)‘]	✓	4.998

10858	$y^{'} = - \frac{(- \frac{y e^{\frac{1}{x}}}{x} -_F1 (y e^{\frac{1}{x}})) e^{- \frac{1}{x}}}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	3.371

10859	$y^{'} = \frac{y + x \sqrt{x^{2} + y^{2}} + x^{3} \sqrt{x^{2} + y^{2}} + x^{4} \sqrt{x^{2} + y^{2}}}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	7.844

10860	$y^{'} = \frac{y (e^{- \frac{x^{2}}{2}} x y + e^{- \frac{x^{2}}{4}} x + 2 y^{2} e^{- \frac{3 x^{2}}{4}}) e^{\frac{x^{2}}{4}}}{2 y e^{- \frac{x^{2}}{4}} + 2}$	[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	4.117

10861	$y^{'} = (\frac{\ln (- 1 + y) y}{(1 - y) \ln (x) x} - \frac{\ln (- 1 + y)}{(1 - y) \ln (x) x} - f (x)) (1 - y)$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	3.971

10862	$y^{'} = - \frac{x}{2} - \frac{a}{2} + \sqrt{x^{2} + 2 a x + a^{2} + 4 y} + x^{2} \sqrt{x^{2} + 2 a x + a^{2} + 4 y} + x^{3} \sqrt{x^{2} + 2 a x + a^{2} + 4 y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	39.530

10863	$y^{'} = - \frac{2 x}{3} + 1 + y^{2} + \frac{2 x^{2} y}{3} + \frac{x^{4}}{9} + y^{3} + x^{2} y^{2} + \frac{y x^{4}}{3} + \frac{x^{6}}{27}$	[[_1st_order, _with_linear_symmetries], _Abel]	✓	1.764

10864	$y^{'} = 2 x + 1 + y^{2} - 2 x^{2} y + x^{4} + y^{3} - 3 x^{2} y^{2} + 3 y x^{4} - x^{6}$	[[_1st_order, _with_linear_symmetries], _Abel]	✓	1.743

10865	$y^{'} = \frac{- x + 1 - 2 y + 3 x^{2} - 2 x^{2} y + 2 x^{4} + x^{3} - 2 x^{3} y + 2 x^{5}}{x^{2} - y}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✗	2.611

10866	$y^{'} = \frac{(e^{- \frac{y}{x}} y + e^{- \frac{y}{x}} x + x + x^{3} + x^{4}) e^{\frac{y}{x}}}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	4.328

10867	$y^{'} = \frac{2 x y^{2} + 4 y \ln (2 x + 1) x + 2 \ln {(2 x + 1)}^{2} x + y^{2} - 2 + \ln {(2 x + 1)}^{2} + 2 y \ln (2 x + 1)}{2 x + 1}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	2.651

10868	$y^{'} = \frac{- 30 x^{3} y + 12 x^{6} + 70 x^{7 / 2} - 30 x^{3} - 25 y \sqrt{x} + 50 x - 25 \sqrt{x} - 25}{5 (- 5 y + 2 x^{3} + 10 \sqrt{x} - 5) x}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.607

10869	$y^{'} = \frac{1 + 2 y}{x (- 2 + x + x y^{2} + 3 x y^{3} + 2 x y + 2 x y^{4})}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	2.961

10870	$y^{'} = \frac{(- 256 a x^{2} + 512 + 512 y^{2} + 128 y a x^{4} + 8 a^{2} x^{8} + 512 y^{3} + 192 x^{4} a y^{2} + 24 y a^{2} x^{8} + a^{3} x^{12}) x}{512}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓	2.140

10871	$y^{'} = - \frac{- x y - y + x^{5} \sqrt{x^{2} + y^{2}} - x^{4} \sqrt{x^{2} + y^{2}} y}{x (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	31.346

10872	$y^{'} = - \frac{y^{2} (x^{2} y - 2 x - 2 x y + y)}{2 (- 2 + x y - 2 y) x}$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	3.062

10873	$y^{'} = \frac{- 2 x y + 2 x^{3} - 2 x - y^{3} + 3 x^{2} y^{2} - 3 y x^{4} + x^{6}}{- y + x^{2} - 1}$	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	1.951

10874	$y^{'} = \frac{1 + y^{4} - 8 a x y^{2} + 16 a^{2} x^{2} + y^{6} - 12 y^{4} a x + 48 y^{2} a^{2} x^{2} - 64 a^{3} x^{3}}{y}$	[_rational]	✗	3.232

10875	$y^{'} = - \frac{- x y - y + \sqrt{x^{2} + y^{2}} x^{2} - x \sqrt{x^{2} + y^{2}} y}{x (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	9.699

10876	$y^{'} = - \frac{2 a}{- y - 2 a - 2 a y^{4} + 16 a^{2} x y^{2} - 32 a^{3} x^{2} - 2 a y^{6} + 24 y^{4} a^{2} x - 96 y^{2} a^{3} x^{2} + 128 a^{4} x^{3}}$	[[_1st_order, _with_linear_symmetries]]	✓	1.896

10877	$y^{'} = \frac{- 18 x y - 6 x^{3} - 18 x + 27 y^{3} + 27 x^{2} y^{2} + 9 y x^{4} + x^{6}}{27 y + 9 x^{2} + 27}$	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	2.068

10878	$y^{'} = - \frac{(- 108 x^{3 / 2} - 216 - 216 y^{2} + 72 x^{3} y - 6 x^{6} - 216 y^{3} + 108 x^{3} y^{2} - 18 x^{6} y + x^{9}) \sqrt{x}}{216}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓	2.096

10879	$y^{'} = \frac{(a^{3} + y^{4} a^{3} + 2 y^{2} a^{2} b x^{2} + a x^{4} b^{2} + y^{6} a^{3} + 3 y^{4} a^{2} b x^{2} + 3 y^{2} a b^{2} x^{4} + b^{3} x^{6}) x}{a^{7 / 2} y}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	4.603

10880	$y^{'} = - \frac{(- 1 - y^{4} + 2 x^{2} y^{2} - x^{4} - y^{6} + 3 x^{2} y^{4} - 3 x^{4} y^{2} + x^{6}) x}{y}$	[_rational]	✗	2.559

10881	$y^{'} = - \frac{i (32 i x + 64 + 64 y^{4} + 32 x^{2} y^{2} + 4 x^{4} + 64 y^{6} + 48 x^{2} y^{4} + 12 x^{4} y^{2} + x^{6})}{128 y}$	[_rational]	✗	3.365

10882	$y^{'} = \frac{2 x^{2} - 4 x^{3} y + 1 + x^{4} y^{2} + x^{6} y^{3} - 3 x^{5} y^{2} + 3 y x^{4} - x^{3}}{x^{4}}$	[_rational, _Abel]	✓	2.450

10883	$y^{'} = \frac{a^{2} x y + a + a^{2} x + y^{3} a^{3} x^{3} + 3 y^{2} a^{2} x^{2} + 3 y a x + 1}{a^{2} x^{2} (y a x + 1 + a x)}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	2.591

10884	$y^{'} = \frac{6 x^{2} y - 2 x + 1 - 5 x^{3} y^{2} - 2 x y + x^{4} y^{3}}{x^{2} (x^{2} y - x + 1)}$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	2.979

10885	$y^{'} = - \frac{(- 8 - 8 y^{3} + 24 y^{3 / 2} e^{x} - 18 e^{2 x} - 8 y^{9 / 2} + 36 y^{3} e^{x} - 54 y^{3 / 2} e^{2 x} + 27 e^{3 x}) e^{x}}{8 \sqrt{y}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	43.803

10886	$y^{'} = \frac{x}{- y + 1 + y^{4} + 2 x^{2} y^{2} + x^{4} + y^{6} + 3 x^{2} y^{4} + 3 x^{4} y^{2} + x^{6}}$	[_rational]	✗	2.558

10887	$y^{'} = \frac{y^{2} (- 2 y + 2 x^{2} + 2 x^{2} y + y x^{4})}{x^{3} (x^{2} - y + x^{2} y)}$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✗	3.295

10888	$y^{'} = \frac{y^{2} + 2 x y + x^{2} + e^{- \frac{2}{- y^{2} + x^{2} - 1}}}{y^{2} + 2 x y + x^{2} - e^{- \frac{2}{- y^{2} + x^{2} - 1}}}$	[[_1st_order, _with_linear_symmetries]]	✓	3.281

10889	$y^{'} = \frac{6 x + x^{3} + x^{3} y^{2} + 4 x^{2} y + x^{3} y^{3} + 6 x^{2} y^{2} + 12 x y + 8}{x^{3}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓	2.043

10890	$y^{'} = - \frac{i (i x + 1 + x^{4} + 2 x^{2} y^{2} + y^{4} + x^{6} + 3 x^{4} y^{2} + 3 x^{2} y^{4} + y^{6})}{y}$	[_rational]	✗	3.299

10891	$y^{'} = \frac{(- 256 a x^{2} y - 32 a^{2} x^{6} - 256 a x^{2} + 512 y^{3} + 192 x^{4} a y^{2} + 24 y a^{2} x^{8} + a^{3} x^{12}) x}{512 y + 64 a x^{4} + 512}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✗	4.645

10892	$y^{'} = \frac{x + 1 + y^{4} - 2 x^{2} y^{2} + x^{4} + y^{6} - 3 x^{2} y^{4} + 3 x^{4} y^{2} - x^{6}}{y}$	[_rational]	✗	2.746

10893	$y^{'} = \frac{(- 108 x^{3 / 2} y + 18 x^{9 / 2} - 108 x^{3 / 2} - 216 y^{3} + 108 x^{3} y^{2} - 18 x^{6} y + x^{9}) \sqrt{x}}{- 216 y + 36 x^{3} - 216}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✗	6.225

10894	$y^{'} = \frac{32 x^{5} y + 8 x^{3} + 32 x^{5} + 64 x^{6} y^{3} + 48 x^{4} y^{2} + 12 x^{2} y + 1}{16 x^{6} (4 x^{2} y + 1 + 4 x^{2})}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✗	3.169

10895	$y^{'} = \frac{32 x^{5} + 64 x^{6} + 64 y^{2} x^{6} + 32 y x^{4} + 4 x^{2} + 64 x^{6} y^{3} + 48 x^{4} y^{2} + 12 x^{2} y + 1}{64 x^{8}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓	1.778

10896	$y^{'} = \frac{2 a (- y^{2} + 4 a x - 1)}{- y^{3} + 4 y a x - y - 2 a y^{6} + 24 y^{4} a^{2} x - 96 y^{2} a^{3} x^{2} + 128 a^{4} x^{3}}$	[[_1st_order, _with_linear_symmetries], _rational]	✓	1.996

10897	$y^{'} = \frac{(y - a \ln (y) x + x^{2}) y}{(- y \ln (y) - y \ln (x) - y + a x) x}$	[NONE]	✓	2.193

10898	$y^{'} = \frac{- x y^{2} + x^{3} - x - y^{6} + 3 x^{2} y^{4} - 3 x^{4} y^{2} + x^{6}}{(- y^{2} + x^{2} - 1) y}$	[_rational]	✗	3.052

10899	$y^{'} = \frac{\sin (\frac{y}{x}) (y + 2 x^{2} \sin (\frac{y}{2 x}) \cos (\frac{y}{2 x}))}{2 \sin (\frac{y}{2 x}) x \cos (\frac{y}{2 x})}$	[[_homogeneous, ‘class D‘]]	✓	8.804

10900	$y^{'} = \frac{\sin (\frac{y}{x}) (y + 2 x^{3} \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}))}{2 \sin (\frac{y}{2 x}) x \cos (\frac{y}{2 x})}$	[[_homogeneous, ‘class D‘]]	✓	11.846

2.2.109 Problems 10801 to 10900