Problems 10901 to 11000

Table 2.221: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

10901	$y^{'} = \frac{a^{2} x + a^{3} x^{3} + a^{3} x^{3} y^{2} + 2 a^{2} x^{2} y + a x + y^{3} a^{3} x^{3} + 3 y^{2} a^{2} x^{2} + 3 y a x + 1}{a^{3} x^{3}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓	2.083

10902	$y^{'} = \frac{x (x^{2} + y^{2} + 1)}{- y^{3} - x^{2} y - y + y^{6} + 3 x^{2} y^{4} + 3 x^{4} y^{2} + x^{6}}$	[_rational]	✗	2.933

10903	$y^{'} = \frac{- 2 x \cos (x) + 2 x^{2} \sin (x) + 2 x + 2 y^{2} + 4 y \cos (x) x - 4 x y + x^{2} \cos (2 x) + 3 x^{2} - 4 x^{2} \cos (x)}{2 x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	6.461

10904	$y^{'} = \frac{4 x (a - 1) (a + 1)}{4 y + a^{2} y^{4} - 2 a^{4} y^{2} x^{2} + 4 y^{2} a^{2} x^{2} + a^{6} x^{4} - 3 a^{4} x^{4} + 3 a^{2} x^{4} - y^{4} - 2 x^{2} y^{2} - x^{4}}$	[_rational]	✗	3.688

10905	$y^{'} = \frac{x^{3} + y^{4} x^{3} + 2 x^{2} y^{2} + x + x^{3} y^{6} + 3 x^{2} y^{4} + 3 x y^{2} + 1}{x^{5} y}$	[_rational]	✗	3.219

10906	$y^{'} = \frac{- 2 x - y + 1 + x^{2} y^{2} + 2 x^{3} y + x^{4} + x^{3} y^{3} + 3 x^{4} y^{2} + 3 x^{5} y + x^{6}}{x}$	[_rational, _Abel]	✗	3.345

10907	$y^{'} = - (- \frac{\ln (y)}{x} + \frac{\cos (x) \ln (y)}{\sin (x)} -_F1 (x)) y$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	28.525

10908	$y^{'} = \frac{2 a x}{- x^{3} y + 2 a x^{3} + 2 a y^{4} x^{3} - 16 y^{2} a^{2} x^{2} + 32 a^{3} x + 2 a y^{6} x^{3} - 24 y^{4} a^{2} x^{2} + 96 y^{2} x a^{3} - 128 a^{4}}$	[_rational]	✓	4.210

10909	$y^{'} = - \frac{- y^{3} - y + 2 y^{2} \ln (x) - \ln {(x)}^{2} y^{3} - 1 + 3 y \ln (x) - 3 \ln {(x)}^{2} y^{2} + \ln {(x)}^{3} y^{3}}{y x}$	[[_Abel, ‘2nd type‘, ‘class C‘]]	✓	3.101

10910	$y^{'} = \frac{2 a (x y^{2} - 4 a + x)}{- x^{3} y^{3} + 4 a x^{2} y - x^{3} y + 2 a y^{6} x^{3} - 24 y^{4} a^{2} x^{2} + 96 y^{2} x a^{3} - 128 a^{4}}$	[_rational]	✓	3.549

10911	$y^{'} = - \frac{- y^{3} - y + 4 y^{2} \ln (x) - 4 \ln {(x)}^{2} y^{3} - 1 + 6 y \ln (x) - 12 \ln {(x)}^{2} y^{2} + 8 \ln {(x)}^{3} y^{3}}{y x}$	[[_Abel, ‘2nd type‘, ‘class C‘]]	✓	3.236

10912	$y^{'} = \frac{y (\ln (y) x + \ln (y) - x - 1 + x \ln (x) + \ln (x) + x^{4} \ln {(x)}^{2} + 2 x^{4} \ln (y) \ln (x) + x^{4} \ln {(y)}^{2})}{x (x + 1)}$	[NONE]	✗	6.290

10913	$y^{'} = \frac{y (x \ln (x) + \ln (x) + \ln (y) x + \ln (y) - x - 1 + x \ln {(x)}^{2} + 2 x \ln (y) \ln (x) + x \ln {(y)}^{2})}{x (x + 1)}$	[NONE]	✗	5.423

10914	$y^{'} = \frac{2 y^{8}}{y^{5} + 2 y^{6} + 2 y^{2} + 16 x y^{4} + 32 y^{6} x^{2} + 2 + 24 x y^{2} + 96 x^{2} y^{4} + 128 x^{3} y^{6}}$	[_rational]	✓	2.316

10915	$y^{'} = \frac{y^{3 / 2} (x - y + \sqrt{y})}{x y^{3 / 2} - y^{5 / 2} + y^{2} + x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3}}$	[[_1st_order, _with_linear_symmetries], _rational]	✓	15.001

10916	$y^{'} = \frac{2 y^{6} (1 + 4 x y^{2} + y^{2})}{y^{3} + 4 y^{5} x + y^{5} + 2 + 24 x y^{2} + 96 x^{2} y^{4} + 128 x^{3} y^{6}}$	[_rational]	✗	3.302

10917	$y^{'} = - (- \frac{\ln (y)}{x} + \frac{\ln (y)}{x \ln (x)} -_F1 (x)) y$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	3.952

10918	$y^{'} = \frac{y^{2}}{y^{2} + y^{3 / 2} + x^{2} \sqrt{y} - 2 x y^{3 / 2} + y^{5 / 2} + x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3}}$	[[_1st_order, _with_linear_symmetries], _rational]	✓	2.329

10919	$y^{'} = \frac{y^{2} + 2 x y + x^{2} + e^{- 2 (x - y) (x + y)}}{y^{2} + 2 x y + x^{2} - e^{- 2 (x - y) (x + y)}}$	[[_1st_order, _with_linear_symmetries]]	✓	2.601

10920	$y^{'} = - \frac{(- \frac{\ln {(y)}^{2}}{2 x} -_F1 (x)) y}{\ln (y)}$	[NONE]	✓	3.040

10921	$y^{'} = \frac{y^{2} + 2 x y + x^{2} + e^{2 {(x - y)}^{2} {(x + y)}^{2}}}{y^{2} + 2 x y + x^{2} - e^{2 {(x - y)}^{2} {(x + y)}^{2}}}$	[[_1st_order, _with_linear_symmetries]]	✓	2.592

10922	$y^{'} = \frac{- 8 x^{2} y^{3} + 16 x y^{2} + 16 x y^{3} - 8 + 12 x y - 6 x^{2} y^{2} + x^{3} y^{3}}{16 (- 2 + x y - 2 y) x}$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	3.264

10923	$y^{'} = - \frac{(- 8 e^{- x^{2}} + 8 x^{2} e^{- x^{2}} - 8 - 8 y^{2} + 8 x^{2} e^{- x^{2}} y - 2 x^{4} e^{- 2 x^{2}} - 8 y^{3} + 12 x^{2} e^{- x^{2}} y^{2} - 6 y x^{4} e^{- 2 x^{2}} + x^{6} e^{- 3 x^{2}}) x}{8}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓	6.557

10924	$y^{'} = \frac{(e^{- \frac{y}{x}} y x + e^{- \frac{y}{x}} y + e^{- \frac{y}{x}} x^{2} + e^{- \frac{y}{x}} x + x) e^{\frac{y}{x}}}{x (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	6.765

10925	$y^{'} = - \frac{16 x y^{3} - 8 y^{3} - 8 y + 8 x y^{2} - 2 x^{2} y^{3} - 8 + 12 x y - 6 x^{2} y^{2} + x^{3} y^{3}}{32 y x}$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	2.680

10926	$y^{'} = \frac{(e^{- \frac{y}{x}} y x + e^{- \frac{y}{x}} y + e^{- \frac{y}{x}} x^{2} + e^{- \frac{y}{x}} x + x^{4}) e^{\frac{y}{x}}}{x (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	4.025

10927	$y^{'} = \frac{- 3 x^{2} y - 2 x^{3} - 2 x - x y^{2} - y + x^{3} y^{3} + 3 x^{4} y^{2} + 3 x^{5} y + x^{6}}{x (x^{2} + x y + 1)}$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	4.205

10928	$y^{'} = \frac{(27 y^{3} + 27 e^{3 x^{2}} y + 18 e^{3 x^{2}} y^{2} + 3 y^{3} e^{3 x^{2}} + 27 e^{\frac{9 x^{2}}{2}} + 27 e^{\frac{9 x^{2}}{2}} y + 9 e^{\frac{9 x^{2}}{2}} y^{2} + e^{\frac{9 x^{2}}{2}} y^{3}) e^{3 x^{2}} x e^{- \frac{9 x^{2}}{2}}}{243 y}$	[[_Abel, ‘2nd type‘, ‘class C‘]]	✗	84.360

10929	$y^{'} = - \frac{- x^{2} - x y - x^{3} - x y^{2} + 2 y x^{2} \ln (x) - x^{3} \ln {(x)}^{2} - y^{3} + 3 x y^{2} \ln (x) - 3 x^{2} \ln {(x)}^{2} y + x^{3} \ln {(x)}^{3}}{x^{2}}$	[_Abel]	✗	4.155

10930	$y^{'} = \frac{x}{2} + 1 + y^{2} + \frac{x^{2} y}{4} - x y - \frac{x^{4}}{8} + \frac{x^{3}}{8} + \frac{x^{2}}{4} + y^{3} - \frac{3 x^{2} y^{2}}{4} - \frac{3 x y^{2}}{2} + \frac{3 y x^{4}}{16} + \frac{3 x^{3} y}{4} - \frac{x^{6}}{64} - \frac{3 x^{5}}{32}$	[[_1st_order, _with_linear_symmetries], _Abel]	✓	2.256

10931	$y^{'} = - \frac{x}{2} + 1 + y^{2} + \frac{7 x^{2} y}{2} - 2 x y + \frac{13 x^{4}}{16} - \frac{3 x^{3}}{2} + x^{2} + y^{3} + \frac{3 x^{2} y^{2}}{4} - 3 x y^{2} + \frac{3 y x^{4}}{16} - \frac{3 x^{3} y}{2} + \frac{x^{6}}{64} - \frac{3 x^{5}}{16}$	[[_1st_order, _with_linear_symmetries], _Abel]	✓	2.461

10932	$y^{'} = - \frac{x}{4} + 1 + y^{2} + \frac{7 x^{2} y}{16} - \frac{x y}{2} + \frac{5 x^{4}}{128} - \frac{5 x^{3}}{64} + \frac{x^{2}}{16} + y^{3} + \frac{3 x^{2} y^{2}}{8} - \frac{3 x y^{2}}{4} + \frac{3 y x^{4}}{64} - \frac{3 x^{3} y}{16} + \frac{x^{6}}{512} - \frac{3 x^{5}}{256}$	[[_1st_order, _with_linear_symmetries], _Abel]	✓	2.329

10933	$y^{'} = \frac{- 2 y - 2 \ln (2 x + 1) - 2 + 2 x y^{3} + y^{3} + 6 y^{2} \ln (2 x + 1) x + 3 y^{2} \ln (2 x + 1) + 6 y \ln {(2 x + 1)}^{2} x + 3 y \ln {(2 x + 1)}^{2} + 2 \ln {(2 x + 1)}^{3} x + \ln {(2 x + 1)}^{3}}{(2 x + 1) (y + \ln (2 x + 1) + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✗	41.747

10934	$y^{'} = \frac{- x^{2} + x + 1 + y^{2} + 5 x^{2} y - 2 x y + 4 x^{4} - 3 x^{3} + y^{3} + 3 x^{2} y^{2} - 3 x y^{2} + 3 y x^{4} - 6 x^{3} y + x^{6} - 3 x^{5}}{x}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓	2.405

10935	$y^{'} = \frac{- 32 x y + 16 x^{3} + 16 x^{2} - 32 x - 64 y^{3} + 48 x^{2} y^{2} + 96 x y^{2} - 12 y x^{4} - 48 x^{3} y - 48 x^{2} y + x^{6} + 6 x^{5} + 12 x^{4}}{- 64 y + 16 x^{2} + 32 x - 64}$	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	2.434

10936	$y^{'} = \frac{y \ln (x) x + x^{2} \ln (x) - 2 x y - x^{2} - y^{2} - y^{3} + 3 x y^{2} \ln (x) - 3 x^{2} \ln {(x)}^{2} y + x^{3} \ln {(x)}^{3}}{x (- y + x \ln (x) - x)}$	[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	5.244

10937	$y^{'} = \frac{- 32 x y - 72 x^{3} + 32 x^{2} - 32 x + 64 y^{3} + 48 x^{2} y^{2} - 192 x y^{2} + 12 y x^{4} - 96 x^{3} y + 192 x^{2} y + x^{6} - 12 x^{5} + 48 x^{4}}{64 y + 16 x^{2} - 64 x + 64}$	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	2.226

10938	$y^{'} = - \frac{y^{2} + 2 x y + x^{2} + e^{\frac{2 {(x - y)}^{3} {(x + y)}^{3}}{- y^{2} + x^{2} - 1}}}{- y^{2} - 2 x y - x^{2} + e^{\frac{2 {(x - y)}^{3} {(x + y)}^{3}}{- y^{2} + x^{2} - 1}}}$	[[_1st_order, _with_linear_symmetries]]	✓	13.549

10939	$y^{'} = \frac{- 128 x y - 24 x^{3} + 32 x^{2} - 128 x + 512 y^{3} + 192 x^{2} y^{2} - 384 x y^{2} + 24 y x^{4} - 96 x^{3} y + 96 x^{2} y + x^{6} - 6 x^{5} + 12 x^{4}}{512 y + 64 x^{2} - 128 x + 512}$	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	2.076

10940	$y^{'} = \frac{- 32 y a x - 8 a^{2} x^{3} - 16 a b x^{2} - 32 a x + 64 y^{3} + 48 a x^{2} y^{2} + 96 b x y^{2} + 12 y a^{2} x^{4} + 48 y a x^{3} b + 48 b^{2} x^{2} y + a^{3} x^{6} + 6 a^{2} x^{5} b + 12 a x^{4} b^{2} + 8 b^{3} x^{3}}{64 y + 16 a x^{2} + 32 b x + 64}$	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	2.107

10941	$y^{'} = \frac{- 32 x y - 8 x^{3} - 16 a x^{2} - 32 x + 64 y^{3} + 48 x^{2} y^{2} + 96 a x y^{2} + 12 y x^{4} + 48 y a x^{3} + 48 a^{2} x^{2} y + x^{6} + 6 x^{5} a + 12 a^{2} x^{4} + 8 a^{3} x^{3}}{64 y + 16 x^{2} + 32 a x + 64}$	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	1.815

10942	$y^{'} = \frac{(- 8 e^{- x^{2}} y + 4 x^{2} e^{- 2 x^{2}} - 8 e^{- x^{2}} + 8 x^{2} e^{- x^{2}} y - 4 x^{4} e^{- 2 x^{2}} + 8 x^{2} e^{- x^{2}} - 8 y^{3} + 12 x^{2} e^{- x^{2}} y^{2} - 6 y x^{4} e^{- 2 x^{2}} + x^{6} e^{- 3 x^{2}}) x}{- 8 y + 4 x^{2} e^{- x^{2}} - 8}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✗	57.245

10943	$y^{'} = \frac{2 x^{2} \cos (x) + 2 \sin (x) x^{3} - 2 x \sin (x) + 2 x + 2 x^{2} y^{2} - 4 x \sin (x) y + 4 x^{2} \cos (x) y + 4 x y + 3 - \cos (2 x) - 2 x \sin (2 x) - 4 \sin (x) + x^{2} \cos (2 x) + x^{2} + 4 x \cos (x)}{2 x^{3}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	22.666

10944	$y^{'} = - \frac{216 y}{- 216 y^{4} - 252 y^{3} - 396 y^{2} - 216 y + 36 x^{2} - 72 x y + 60 y^{5} - 36 x y^{3} - 72 x y^{2} - 24 x y^{4} + 4 y^{8} + 12 y^{7} + 33 y^{6}}$	[_rational]	✓	3.745

10945	$y^{'} = \frac{x^{2} y + x^{4} + 2 x^{3} - 3 x^{2} + x y + x + y^{3} + 3 x^{2} y^{2} - 3 x y^{2} + 3 y x^{4} - 6 x^{3} y + x^{6} - 3 x^{5}}{x (y + x^{2} - x + 1)}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	2.859

10946	$y^{'} = - \frac{a x}{2} + 1 + y^{2} + \frac{a x^{2} y}{2} + b x y + \frac{a^{2} x^{4}}{16} + \frac{a x^{3} b}{4} + \frac{b^{2} x^{2}}{4} + y^{3} + \frac{3 a x^{2} y^{2}}{4} + \frac{3 b x y^{2}}{2} + \frac{3 y a^{2} x^{4}}{16} + \frac{3 y a x^{3} b}{4} + \frac{3 b^{2} x^{2} y}{4} + \frac{a^{3} x^{6}}{64} + \frac{3 a^{2} x^{5} b}{32} + \frac{3 a x^{4} b^{2}}{16} + \frac{b^{3} x^{3}}{8}$	[[_1st_order, _with_linear_symmetries], _Abel]	✓	2.014

10947	$y^{'} = - \frac{x}{2} + 1 + y^{2} + \frac{x^{2} y}{2} + y a x + \frac{x^{4}}{16} + \frac{a x^{3}}{4} + \frac{a^{2} x^{2}}{4} + y^{3} + \frac{3 x^{2} y^{2}}{4} + \frac{3 a x y^{2}}{2} + \frac{3 y x^{4}}{16} + \frac{3 y a x^{3}}{4} + \frac{3 a^{2} x^{2} y}{4} + \frac{x^{6}}{64} + \frac{3 x^{5} a}{32} + \frac{3 a^{2} x^{4}}{16} + \frac{a^{3} x^{3}}{8}$	[[_1st_order, _with_linear_symmetries], _Abel]	✓	1.943

10948	$y^{'} = - \frac{- y + \sqrt{x^{2} + y^{2}} x^{2} - x \sqrt{x^{2} + y^{2}} y + x^{4} \sqrt{x^{2} + y^{2}} - x^{3} \sqrt{x^{2} + y^{2}} y + x^{5} \sqrt{x^{2} + y^{2}} - x^{4} \sqrt{x^{2} + y^{2}} y}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	46.803

10949	$y^{'} = \frac{y (\ln (x) + \ln (y) - 1 + x \ln {(x)}^{2} + 2 x \ln (y) \ln (x) + x \ln {(y)}^{2} + x^{3} \ln {(x)}^{2} + 2 x^{3} \ln (y) \ln (x) + x^{3} \ln {(y)}^{2} + x^{4} \ln {(x)}^{2} + 2 x^{4} \ln (y) \ln (x) + x^{4} \ln {(y)}^{2})}{x}$	[NONE]	✗	15.378

10950	$y^{'} = \frac{150 x^{3} + 125 \sqrt{x} + 125 + 125 y^{2} - 100 x^{3} y - 500 y \sqrt{x} + 20 x^{6} + 200 x^{7 / 2} + 500 x + 125 y^{3} - 150 x^{3} y^{2} - 750 y^{2} \sqrt{x} + 60 x^{6} y + 600 y x^{7 / 2} + 1500 x y - 8 x^{9} - 120 x^{13 / 2} - 600 x^{4} - 1000 x^{3 / 2}}{125 x}$	[_rational, _Abel]	✓	5.356

10951	$y^{'} = \frac{- 150 x^{3} y + 60 x^{6} + 350 x^{7 / 2} - 150 x^{3} - 125 y \sqrt{x} + 250 x - 125 \sqrt{x} - 125 y^{3} + 150 x^{3} y^{2} + 750 y^{2} \sqrt{x} - 60 x^{6} y - 600 y x^{7 / 2} - 1500 x y + 8 x^{9} + 120 x^{13 / 2} + 600 x^{4} + 1000 x^{3 / 2}}{25 (- 5 y + 2 x^{3} + 10 \sqrt{x} - 5) x}$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✗	34.075

10952	$y^{'} = \frac{y (- 1 - x^{\frac{2}{1 + \ln (x)}} e^{\frac{2 \ln {(x)}^{2}}{1 + \ln (x)}} x^{2} - x^{\frac{2}{1 + \ln (x)}} e^{\frac{2 \ln {(x)}^{2}}{1 + \ln (x)}} x^{2} \ln (x) + x^{\frac{2}{1 + \ln (x)}} e^{\frac{2 \ln {(x)}^{2}}{1 + \ln (x)}} x^{2} y + 2 x^{\frac{2}{1 + \ln (x)}} e^{\frac{2 \ln {(x)}^{2}}{1 + \ln (x)}} x^{2} y \ln (x) + x^{\frac{2}{1 + \ln (x)}} e^{\frac{2 \ln {(x)}^{2}}{1 + \ln (x)}} x^{2} y \ln {(x)}^{2})}{(1 + \ln (x)) x}$	[_Bernoulli]	✗	46.470

10953	$y^{'} = \frac{y (- 1 - x^{3} x^{\frac{2}{1 + \ln (x)}} e^{\frac{2 \ln {(x)}^{2}}{1 + \ln (x)}} - x^{3} x^{\frac{2}{1 + \ln (x)}} e^{\frac{2 \ln {(x)}^{2}}{1 + \ln (x)}} \ln (x) + x^{3} x^{\frac{2}{1 + \ln (x)}} e^{\frac{2 \ln {(x)}^{2}}{1 + \ln (x)}} y + 2 x^{3} x^{\frac{2}{1 + \ln (x)}} e^{\frac{2 \ln {(x)}^{2}}{1 + \ln (x)}} y \ln (x) + x^{3} x^{\frac{2}{1 + \ln (x)}} e^{\frac{2 \ln {(x)}^{2}}{1 + \ln (x)}} y \ln {(x)}^{2})}{(1 + \ln (x)) x}$	[_Bernoulli]	✗	47.045

10954	$y^{'} = \frac{2 x + 4 y \ln (2 x + 1) x + 6 y^{2} \ln (2 x + 1) x + 6 y \ln {(2 x + 1)}^{2} x + 2 \ln {(2 x + 1)}^{3} x + 2 x y^{3} + 2 \ln {(2 x + 1)}^{2} x + 2 x y^{2} - 1 + 3 y^{2} \ln (2 x + 1) + 3 y \ln {(2 x + 1)}^{2} + y^{2} + y^{3} + 2 y \ln (2 x + 1) + \ln {(2 x + 1)}^{2} + \ln {(2 x + 1)}^{3}}{2 x + 1}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓	2.857

10955	$y^{'} = \frac{- y \sin (\frac{y}{x}) + y \sin (\frac{3 y}{2 x}) \cos (\frac{y}{2 x}) + y \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) + 2 \sin (\frac{y}{x}) x^{3} \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x})}{2 \cos (\frac{y}{x}) \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) x}$	[[_homogeneous, ‘class D‘]]	✓	14.447

10956	$y^{'} = \frac{- y \sin (\frac{y}{x}) + y \sin (\frac{3 y}{2 x}) \cos (\frac{y}{2 x}) + y \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) + 2 \sin (\frac{y}{x}) x^{2} \sin (\frac{y}{2 x}) \cos (\frac{y}{2 x})}{2 \cos (\frac{y}{x}) \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) x}$	[[_homogeneous, ‘class D‘]]	✓	11.722

10957	$y^{'} = \frac{y^{2} + 2 x y + x^{2} + e^{2 + 2 y^{4} - 4 x^{2} y^{2} + 2 x^{4} + 2 y^{6} - 6 x^{2} y^{4} + 6 x^{4} y^{2} - 2 x^{6}}}{y^{2} + 2 x y + x^{2} - e^{2 + 2 y^{4} - 4 x^{2} y^{2} + 2 x^{4} + 2 y^{6} - 6 x^{2} y^{4} + 6 x^{4} y^{2} - 2 x^{6}}}$	[[_1st_order, _with_linear_symmetries]]	✓	3.449

10958	$y^{'} = \frac{4 x (a - 1) (a + 1) (- y^{2} + a^{2} x^{2} - x^{2} - 2)}{- 4 y^{3} + 4 a^{2} x^{2} y - 4 x^{2} y - 8 y - a^{2} y^{6} + 3 a^{4} y^{4} x^{2} - 6 y^{4} a^{2} x^{2} - 3 a^{6} y^{2} x^{4} + 9 y^{2} a^{4} x^{4} - 9 y^{2} a^{2} x^{4} + a^{8} x^{6} - 4 a^{6} x^{6} + 6 a^{4} x^{6} - 4 a^{2} x^{6} + y^{6} + 3 x^{2} y^{4} + 3 x^{4} y^{2} + x^{6}}$	[_rational]	✗	6.155

10959	$y^{'} = \frac{- 4 x \cos (x) + 4 x^{2} \sin (x) + 4 x + 4 + 4 y^{2} + 8 y \cos (x) x - 8 x y + 2 x^{2} \cos (2 x) + 6 x^{2} - 8 x^{2} \cos (x) + 4 y^{3} + 12 y^{2} \cos (x) x - 12 x y^{2} + 6 y x^{2} \cos (2 x) + 18 x^{2} y - 24 x^{2} \cos (x) y + x^{3} \cos (3 x) + 15 x^{3} \cos (x) - 6 x^{3} \cos (2 x) - 10 x^{3}}{4 x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓	19.880

10960	$y^{'} = - \frac{8 x (a - 1) (a + 1)}{8 + 3 x^{2} y^{4} - a^{2} y^{6} + a^{8} x^{6} - 4 a^{6} x^{6} + 6 a^{4} x^{6} + 3 a^{4} y^{4} x^{2} - 6 y^{4} a^{2} x^{2} - 3 a^{6} y^{2} x^{4} + 9 y^{2} a^{4} x^{4} - 9 y^{2} a^{2} x^{4} + 3 x^{4} y^{2} - 4 a^{2} x^{6} - 2 a^{2} y^{4} - 2 a^{6} x^{4} + 6 a^{4} x^{4} - 6 a^{2} x^{4} - 8 y^{2} a^{2} x^{2} + 4 a^{4} y^{2} x^{2} + 2 y^{4} - 8 a^{2} + 4 x^{2} y^{2} + y^{6} + 2 x^{4} - 8 y + x^{6}}$	[_rational]	✗	6.541

10961	$y^{'} = \frac{- y \sin (\frac{y}{x}) + y \sin (\frac{3 y}{2 x}) \cos (\frac{y}{2 x}) + y \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) + 2 \sin (\frac{y}{x}) \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) x + 2 \sin (\frac{y}{x}) x^{3} \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) + 2 \sin (\frac{y}{x}) x^{4} \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x})}{2 \cos (\frac{y}{x}) \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) x}$	[[_homogeneous, ‘class D‘]]	✓	21.883

10962	$y^{'} = - \frac{1296 y}{216 - 216 x^{2} y^{4} + 216 x y^{2} - 648 x^{2} y - 1728 y^{3} - 324 x^{2} y^{3} - 432 x y - 570 y^{8} - 846 y^{7} - 126 y^{10} - 315 y^{9} - 8 y^{12} - 36 y^{11} - 2376 y^{2} + 72 y^{8} x - 1944 y^{4} - 612 y^{5} + 1080 x y^{3} - 648 x^{2} y^{2} + 216 y^{7} x + 1080 y^{5} x + 594 x y^{6} + 1152 x y^{4} - 882 y^{6} + 216 x^{2} + 216 x^{3} - 1296 y}$	[_rational]	✓	3.064

10963	$y^{'} = - \frac{x (- 513 - 288 y x^{8} + 288 y x^{7} + 720 x^{3} y + 864 x^{5} y^{2} - 594 x^{2} y + 432 x^{3} y^{2} - 972 x^{4} y^{2} - 216 y^{3} - 648 x^{2} y^{3} - 648 x^{4} y^{3} - 540 y^{2} - 216 y x^{4} - 288 x^{6} y - 1296 x^{2} y^{2} - 576 x^{5} - 216 y^{2} x^{6} + 432 y^{2} x^{7} + 1008 x^{5} y - 216 x^{6} y^{3} + 64 x^{9} - 1134 x^{2} - 144 x^{7} - 756 x^{3} - 432 x - 96 x^{8} - 864 x^{4} - 378 y - 456 x^{6})}{216 {(x^{2} + 1)}^{4}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓	3.291

10964	$y^{'} = \frac{- \sin (\frac{y}{x}) y x - y \sin (\frac{y}{x}) + y \sin (\frac{3 y}{2 x}) \cos (\frac{y}{2 x}) x + y \sin (\frac{3 y}{2 x}) \cos (\frac{y}{2 x}) + y \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) x + y \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) + 2 \sin (\frac{y}{x}) x^{4} \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x})}{2 \cos (\frac{y}{x}) \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) x (x + 1)}$	[[_homogeneous, ‘class D‘]]	✓	46.087

10965	$y^{'} = \frac{y \sin (\frac{3 y}{2 x}) \cos (\frac{y}{2 x}) x + y \sin (\frac{3 y}{2 x}) \cos (\frac{y}{2 x}) + y \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) x + y \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) - \sin (\frac{y}{x}) y x - y \sin (\frac{y}{x}) + 2 \sin (\frac{y}{x}) \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) x}{2 \cos (\frac{y}{x}) \sin (\frac{y}{2 x}) x \cos (\frac{y}{2 x}) (x + 1)}$	[[_homogeneous, ‘class D‘]]	✓	45.778

10966	$y^{'} = - \frac{216 y (- 2 y^{4} - 3 y^{3} - 6 y^{2} - 6 y + 6 x + 6)}{- 216 x^{2} y^{4} - 1944 x y^{2} - 648 x^{2} y + 1728 y^{3} - 324 x^{2} y^{3} - 1296 x y - 18 y^{8} + 594 y^{7} - 126 y^{10} - 315 y^{9} - 8 y^{12} - 36 y^{11} - 1296 y^{2} + 72 y^{8} x + 2808 y^{4} + 4428 y^{5} - 648 x y^{3} - 648 x^{2} y^{2} + 216 y^{7} x + 1080 y^{5} x + 594 x y^{6} - 432 x y^{4} + 2484 y^{6} + 216 x^{3} - 1296 y}$	[_rational]	✗	4.925

10967	$y^{'} = \frac{{(x y + 1)}^{3}}{x^{5}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓	3.262

10968	$y^{'} = \frac{x (- x^{2} + 2 x^{2} y - 2 x^{4} + 1)}{y - x^{2}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✗	2.460

10969	$y^{'} = y (y^{2} + y e^{b x} + e^{2 b x}) e^{- 2 b x}$	[[_1st_order, _with_linear_symmetries], _Abel]	✓	2.345

10970	$y^{'} = y^{3} - 3 x^{2} y^{2} + 3 y x^{4} - x^{6} + 2 x$	[[_1st_order, _with_linear_symmetries], _Abel]	✓	1.601

10971	$y^{'} = y^{3} + x^{2} y^{2} + \frac{y x^{4}}{3} + \frac{x^{6}}{27} - \frac{2 x}{3}$	[[_1st_order, _with_linear_symmetries], _Abel]	✓	1.701

10972	$y^{'} = \frac{y (y^{2} x^{7} + y x^{4} + x - 3)}{x}$	[_rational, _Abel]	✗	3.197

10973	$y^{'} = y (y^{2} + e^{- x^{2}} y + e^{- 2 x^{2}}) e^{2 x^{2}} x$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Abel]	✓	6.472

10974	$y^{'} = \frac{y (y^{2} + x y + x^{2} + x)}{x^{2}}$	[[_homogeneous, ‘class D‘], _rational, _Abel]	✓	2.286

10975	$y^{'} = \frac{y^{3} - 3 x y^{2} + 3 x^{2} y - x^{3} + x}{x}$	[[_1st_order, _with_linear_symmetries], _rational, _Abel]	✓	1.696

10976	$y^{'} = \frac{x^{3} y^{3} + 6 x^{2} y^{2} + 12 x y + 8 + 2 x}{x^{3}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓	2.393

10977	$y^{'} = \frac{y^{3} a^{3} x^{3} + 3 y^{2} a^{2} x^{2} + 3 y a x + 1 + a^{2} x}{x^{3} a^{3}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓	2.316

10978	$y^{'} = \frac{y e^{- \frac{x^{2}}{2}} (2 y^{2} + 2 y e^{\frac{x^{2}}{4}} + 2 e^{\frac{x^{2}}{2}} + x e^{\frac{x^{2}}{2}})}{2}$	[_Abel]	✓	43.415

10979	$y^{'} = \frac{y^{3} - 3 x y^{2} + 3 x^{2} y - x^{3} + x^{2}}{(x - 1) (x + 1)}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓	3.083

10980	$y^{'} = \frac{y (x^{2} y^{2} + y x e^{x} + e^{2 x}) e^{- 2 x} (x - 1)}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Abel]	✗	5.914

10981	$y^{'} = \frac{(x y + 1) (x^{2} y^{2} + x^{2} y + 2 x y + 1 + x + x^{2})}{x^{5}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓	2.220

10982	$y^{'} = \frac{y^{3} - 3 x y^{2} \ln (x) + 3 x^{2} \ln {(x)}^{2} y - x^{3} \ln {(x)}^{3} + x^{2} + x y}{x^{2}}$	[_Abel]	✓	2.270

10983	$y^{'} = - F (x) (- a x^{2} + y^{2}) + \frac{y}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	3.390

10984	$y^{'} = - F (x) (- x^{2} - 2 x y + y^{2}) + \frac{y}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	2.890

10985	$y^{'} = - F (x) (- a y^{2} - b x^{2}) + \frac{y}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	3.867

10986	$y^{'} = - F (x) (- y^{2} + 2 x^{2} y + 1 - x^{4}) + 2 x$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	3.025

10987	$y^{'} = - F (x) (x^{2} + 2 x y - y^{2}) + \frac{y}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	2.878

10988	$y^{'} = - F (x) (- 7 x y^{2} - x^{3}) + \frac{y}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	2.728

10989	$y^{'} = - F (x) (- y^{2} - 2 y \ln (x) - \ln {(x)}^{2}) + \frac{y}{x \ln (x)}$	[_Riccati]	✓	3.224

10990	$y^{'} = - x^{3} (- y^{2} - 2 y \ln (x) - \ln {(x)}^{2}) + \frac{y}{x \ln (x)}$	[_Riccati]	✓	3.404

10991	$y^{'} = {(y - e^{x})}^{2} + e^{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	1.886

10992	$y^{'} = \frac{{(y - Si (x))}^{2} + \sin (x)}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	5.951

10993	$y^{'} = {(y + \cos (x))}^{2} + \sin (x)$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	2.561

10994	$y^{'} = \frac{{(y - \ln (x) - Ci (x))}^{2} + \cos (x)}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	37.596

10995	$y^{'} = \frac{{(y - x + \ln (x + 1))}^{2} + x}{x + 1}$	[[_1st_order, _with_linear_symmetries], _Riccati]	✓	2.262

10996	$y^{'} = \frac{2 x^{2} y + x^{3} + y \ln (x) x - y^{2} - x y}{x^{2} (x + \ln (x))}$	[_Riccati]	✓	2.626

10997	$y^{''} = 0$	[[_2nd_order, _quadrature]]	✓	0.727

10998	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	1.479

10999	$y^{''} + y - \sin (n x) = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.682

11000	$y^{''} + y - a \cos (b x) = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.787

2.2.110 Problems 10901 to 11000