Problems 10701 to 10800

Table 2.217: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

10701	$y^{'} = \frac{y (1 - x + y x^{2} \ln (x) + x^{3} y - x \ln (x) - x^{2})}{(x - 1) x}$	[_Bernoulli]	✓	3.608

10702	$y^{'} = \frac{y \ln (x) x - y + 2 x^{5} b + 2 a x^{3} y^{2}}{(x \ln (x) - 1) x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	9.654

10703	$y^{'} = \frac{(\ln (y) + x + x^{3} + x^{4}) y}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	2.496

10704	$y^{'} = - \frac{(- \ln (- 1 + y) + \ln (1 + y) + 2 \ln (x)) x {(1 + y)}^{2}}{8}$	[‘y=_G(x,y’)‘]	✗	9.521

10705	$y^{'} = \frac{{(- \ln (- 1 + y) + \ln (1 + y) + 2 \ln (x))}^{2} x {(1 + y)}^{2}}{16}$	[‘y=_G(x,y’)‘]	✗	12.931

10706	$y^{'} = \frac{{(- y^{2} + 4 a x)}^{3}}{(- y^{2} + 4 a x - 1) y}$	[_rational]	✗	3.321

10707	$y^{'} = \frac{2 a x + 2 a + x^{3} \sqrt{- y^{2} + 4 a x}}{(x + 1) y}$	[‘y=_G(x,y’)‘]	✗	50.295

10708	$y^{'} = \frac{- \ln (x) + e^{\frac{1}{x}} + 4 x^{2} y + 2 x + 2 x y^{2} + 2 x^{3}}{\ln (x) - e^{\frac{1}{x}}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	217.693

10709	$y^{'} = - \frac{(\ln (y) x + \ln (y) - 1) y}{x + 1}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	3.526

10710	$y^{'} = \frac{x^{2} + 2 x + 1 + 2 x^{3} \sqrt{x^{2} + 2 x + 1 - 4 y}}{2 x + 2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	6.970

10711	$y^{'} = \frac{- b y a + b^{2} + a b + b^{2} x - b a \sqrt{x} - a^{2}}{a (- a y + b + a + b x - a \sqrt{x})}$	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.901

10712	$y^{'} = - \frac{y (- \ln (\frac{1}{x}) + e^{x} + y x^{2} \ln (x) + x^{3} y - x \ln (x) - x^{2})}{(- \ln (\frac{1}{x}) + e^{x}) x}$	[_Bernoulli]	✓	4.310

10713	$y^{'} = \frac{- x^{2} + x + 2 + 2 x^{3} \sqrt{x^{2} - 4 x + 4 y}}{2 x + 2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	6.423

10714	$y^{'} = \frac{3 x^{4} + 3 x^{3} + \sqrt{9 x^{4} - 4 y^{3}}}{(x + 1) y^{2}}$	[_rational]	✗	42.248

10715	$y^{'} = - \frac{x^{2} + x + a x + a - 2 \sqrt{x^{2} + 2 a x + a^{2} + 4 y}}{2 (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	3.222

10716	$y^{'} = (1 + y^{2} e^{2 x^{2}} + y^{3} e^{3 x^{2}}) e^{- x^{2}} x$	[_Abel]	✓	2.542

10717	$y^{'} = \frac{y (- e^{x} + \ln (2 x) x^{2} y - \ln (2 x) x) e^{- x}}{x}$	[_Bernoulli]	✓	4.673

10718	$y^{'} = \frac{x^{3} (3 x + 3 + \sqrt{9 x^{4} - 4 y^{3}})}{(x + 1) y^{2}}$	[‘y=_G(x,y’)‘]	✗	40.160

10719	$y^{'} = \frac{(18 x^{3 / 2} + 36 y^{2} - 12 x^{3} y + x^{6}) \sqrt{x}}{36}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	4.748

10720	$y^{'} = - \frac{y^{3}}{(- 1 + 2 y \ln (x) - y) x}$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	2.774

10721	$y^{'} = \frac{2 a}{y + 2 a y^{4} - 16 a^{2} x y^{2} + 32 a^{3} x^{2}}$	[[_1st_order, _with_linear_symmetries]]	✓	2.056

10722	$y^{'} = - \frac{y^{3}}{(- 1 + y \ln (x) - y) x}$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	2.623

10723	$y^{'} = \frac{- \ln (x) + 2 \ln (2 x) x y + \ln (2 x) + \ln (2 x) y^{2} + \ln (2 x) x^{2}}{\ln (x)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	5.906

10724	$y^{'} = - \frac{b y a - b c + b^{2} x + b a \sqrt{x} - a^{2}}{a (a y - c + b x + a \sqrt{x})}$	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.591

10725	$y^{'} = \frac{(2 x + 2 + y) y}{(\ln (y) + 2 x - 1) (x + 1)}$	[‘x=_G(y,y’)‘]	✗	3.482

10726	$y^{'} = \frac{(x^{3} + 3 y^{2}) y}{(6 y^{2} + x) x}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	2.163

10727	$y^{'} = \frac{y (x - y)}{x (x - y^{3})}$	[_rational]	✓	1.660

10728	$y^{'} = \frac{{(2 y^{3 / 2} - 3 e^{x})}^{3} e^{x}}{4 (2 y^{3 / 2} - 3 e^{x} + 2) \sqrt{y}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	8.891

10729	$y^{'} = \frac{1 + 2 y}{x (- 2 + x y^{2} + 2 x y^{3})}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	3.081

10730	$y^{'} = \frac{- x^{2} - x - a x - a + 2 x^{3} \sqrt{x^{2} + 2 a x + a^{2} + 4 y}}{2 x + 2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	7.971

10731	$y^{'} = \frac{2 x \sin (x) - \ln (2 x) + \ln (2 x) x^{4} - 2 \ln (2 x) x^{2} y + \ln (2 x) y^{2}}{\sin (x)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✗	158.892

10732	$y^{'} = \frac{(- \ln (y) x - \ln (y) + x^{3}) y}{x + 1}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	3.361

10733	$y^{'} = \frac{{(2 y \ln (x) - 1)}^{3}}{(- 1 + 2 y \ln (x) - y) x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	2.884

10734	$y^{'} = \frac{2 x^{2} + 2 x + x^{4} - 2 x^{2} y - 1 + y^{2}}{x + 1}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	3.437

10735	$y^{'} = \frac{x (- 1 + x - 2 x y + 2 x^{3})}{x^{2} - y}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✗	2.424

10736	$y^{'} = \frac{2 a}{- x^{2} y + 2 a y^{4} x^{2} - 16 a^{2} x y^{2} + 32 a^{3}}$	[‘y=_G(x,y’)‘]	✓	3.304

10737	$y^{'} = \frac{1 + 2 y}{x (- 2 + x y + 2 x y^{2})}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	2.704

10738	$y^{'} = \frac{x + y^{4} - 2 x^{2} y^{2} + x^{4}}{y}$	[_rational]	✗	3.183

10739	$y^{'} = \frac{{(a y^{2} + b x^{2})}^{3} x}{a^{5 / 2} (a y^{2} + b x^{2} + a) y}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	4.465

10740	$y^{'} = - \frac{\cos (y) (x - \cos (y) + 1)}{(x \sin (y) - 1) (x + 1)}$	[‘y=_G(x,y’)‘]	✗	55.287

10741	$y^{'} = - \frac{i (8 i x + 16 y^{4} + 8 x^{2} y^{2} + x^{4})}{32 y}$	[_rational]	✗	1.567

10742	$y^{'} = \frac{x}{- y + x^{4} + 2 x^{2} y^{2} + y^{4}}$	[_rational]	✗	3.408

10743	$y^{'} = \frac{{(- 1 + y \ln (x))}^{3}}{(- 1 + y \ln (x) - y) x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	3.009

10744	$y^{'} = - \frac{i (i x + x^{4} + 2 x^{2} y^{2} + y^{4})}{y}$	[_rational]	✗	1.511

10745	$y^{'} = - \frac{y (\tan (x) + \ln (2 x) x - \ln (2 x) x^{2} y)}{x \tan (x)}$	[_Bernoulli]	✓	40.076

10746	$y^{'} = \frac{y (x + y)}{x (y^{3} + x)}$	[_rational]	✓	1.584

10747	$y^{'} = \frac{{(x - y)}^{2} {(x + y)}^{2} x}{y}$	[_rational]	✗	2.703

10748	$y^{'} = \frac{(x^{2} + 3 y^{2}) y}{(6 y^{2} + x) x}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	1.977

10749	$y^{'} = \frac{(\ln (y) x + \ln (y) + x^{4}) y}{x (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	2.992

10750	$y^{'} = \frac{\cos (y) (\cos (y) x^{3} - x - 1)}{(x \sin (y) - 1) (x + 1)}$	[‘y=_G(x,y’)‘]	✗	87.011

10751	$y^{'} = \frac{(x + 1 + x^{4} \ln (y)) y \ln (y)}{x (x + 1)}$	[‘x=_G(y,y’)‘]	✗	3.858

10752	$y^{'} = \frac{x y + x^{3} + x y^{2} + y^{3}}{x^{2}}$	[[_homogeneous, ‘class D‘], _rational, _Abel]	✓	2.244

10753	$y^{'} = \frac{y^{3 / 2}}{y^{3 / 2} + x^{2} - 2 x y + y^{2}}$	[[_1st_order, _with_linear_symmetries], _rational]	✓	2.549

10754	$y^{'} = \frac{2 x^{3} y + x^{6} + x^{2} y^{2} + y^{3}}{x^{4}}$	[_rational, _Abel]	✗	3.847

10755	$y^{'} = \frac{- 4 x y + x^{3} + 2 x^{2} - 4 x - 8}{- 8 y + 2 x^{2} + 4 x - 8}$	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.457

10756	$y^{'} = \frac{(2 x + 2 + x^{3} y) y}{(\ln (y) + 2 x - 1) (x + 1)}$	[‘x=_G(y,y’)‘]	✗	3.513

10757	$y^{'} = - \frac{i (54 i x^{2} + 81 y^{4} + 18 x^{4} y^{2} + x^{8}) x}{243 y}$	[_rational]	✗	1.548

10758	$y^{'} = \frac{{(x y^{2} + 1)}^{3}}{x^{4} (x y^{2} + 1 + x) y}$	[_rational]	✗	3.546

10759	$y^{'} = \frac{- 4 x y - x^{3} + 4 x^{2} - 4 x + 8}{8 y + 2 x^{2} - 8 x + 8}$	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.432

10760	$y^{'} = - \frac{(\ln (y) x + \ln (y) - x) y}{x (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	3.729

10761	$y^{'} = \frac{(\ln (y) x + \ln (y) + x) y}{x (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	2.590

10762	$y^{'} = \frac{(- \ln (y) x - \ln (y) + x^{4}) y}{x (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	3.507

10763	$y^{'} = \frac{y (- 1 - \ln (\frac{(x - 1) (x + 1)}{x}) + \ln (\frac{(x - 1) (x + 1)}{x}) x y)}{x}$	[_Bernoulli]	✓	14.547

10764	$y^{'} = \frac{y (- \ln (x) - x \ln (\frac{(x - 1) (x + 1)}{x}) + \ln (\frac{(x - 1) (x + 1)}{x}) x^{2} y)}{x \ln (x)}$	[_Bernoulli]	✓	5.926

10765	$y^{'} = \frac{- 8 x y - x^{3} + 2 x^{2} - 8 x + 32}{32 y + 4 x^{2} - 8 x + 32}$	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.475

10766	$y^{'} = \frac{y (1 + y)}{x (- y - 1 + x y)}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.130

10767	$y^{'} = - \frac{i (16 i x^{2} + 16 y^{4} + 8 x^{4} y^{2} + x^{8}) x}{32 y}$	[_rational]	✗	1.520

10768	$y^{'} = \frac{2 y^{6}}{y^{3} + 2 + 16 x y^{2} + 32 x^{2} y^{4}}$	[_rational]	✓	3.646

10769	$y^{'} = \frac{- 4 y a x - a^{2} x^{3} - 2 a b x^{2} - 4 a x + 8}{8 y + 2 a x^{2} + 4 b x + 8}$	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.267

10770	$y^{'} = \frac{(x + 1 + \ln (y) x) \ln (y) y}{x (x + 1)}$	[‘x=_G(y,y’)‘]	✗	3.909

10771	$y^{'} = \frac{x y + x + y^{2}}{(x - 1) (x + y)}$	[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	3.084

10772	$y^{'} = \frac{- 4 x y - x^{3} - 2 a x^{2} - 4 x + 8}{8 y + 2 x^{2} + 4 a x + 8}$	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.764

10773	$y^{'} = \frac{x - y + \sqrt{y}}{x - y + \sqrt{y} + 1}$	[[_1st_order, _with_linear_symmetries], _rational]	✓	1.674

10774	$y^{'} = \frac{y (- \ln (\frac{1}{x}) - \ln (\frac{x^{2} + 1}{x}) x + \ln (\frac{x^{2} + 1}{x}) x^{2} y)}{x \ln (\frac{1}{x})}$	[_Bernoulli]	✓	9.052

10775	$y^{'} = \frac{y (1 + y)}{x (- y - 1 + x y^{4})}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	2.913

10776	$y^{'} = \frac{- 3 x^{2} y + 1 + y^{2} x^{6} + y^{3} x^{9}}{x^{3}}$	[_rational, _Abel]	✗	3.384

10777	$y^{'} = \frac{x^{3} y + x^{3} + x y^{2} + y^{3}}{(x - 1) x^{3}}$	[[_homogeneous, ‘class D‘], _rational, _Abel]	✓	3.325

10778	$y^{'} = \frac{x y + y + x \sqrt{x^{2} + y^{2}}}{x (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	11.961

10779	$y^{'} = \frac{(x^{4} + x^{3} + x + 3 y^{2}) y}{(6 y^{2} + x) x}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	2.344

10780	$y^{'} = \frac{y (- \tanh (\frac{1}{x}) - \ln (\frac{x^{2} + 1}{x}) x + \ln (\frac{x^{2} + 1}{x}) x^{2} y)}{x \tanh (\frac{1}{x})}$	[_Bernoulli]	✓	45.736

10781	$y^{'} = - \frac{y (\tanh (x) + \ln (2 x) x - \ln (2 x) x^{2} y)}{x \tanh (x)}$	[_Bernoulli]	✓	47.904

10782	$y^{'} = \frac{- \sinh (x) + x^{2} \ln (x) + 2 y \ln (x) x + \ln (x) + y^{2} \ln (x)}{\sinh (x)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	22.263

10783	$y^{'} = - \frac{\ln (x) - \sinh (x) x^{2} - 2 \sinh (x) x y - \sinh (x) - \sinh (x) y^{2}}{\ln (x)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	53.865

10784	$y^{'} = \frac{y \ln (x) + \cosh (x) x a y^{2} + \cosh (x) x^{3} b}{x \ln (x)}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	66.694

10785	$y^{'} = \frac{x (- x - 1 + x^{2} - 2 x^{2} y + 2 x^{4})}{(x^{2} - y) (x + 1)}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	✗	2.491

10786	$y^{'} = - \frac{y (\ln (x - 1) + \coth (x + 1) x - \coth (x + 1) x^{2} y)}{x \ln (x - 1)}$	[_Bernoulli]	✓	44.418

10787	$y^{'} = - \frac{\ln (x - 1) - \coth (x + 1) x^{2} - 2 \coth (x + 1) x y - \coth (x + 1) - \coth (x + 1) y^{2}}{\ln (x - 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	194.484

10788	$y^{'} = \frac{2 x \ln (\frac{1}{x - 1}) - \coth (\frac{x + 1}{x - 1}) + \coth (\frac{x + 1}{x - 1}) y^{2} - 2 \coth (\frac{x + 1}{x - 1}) x^{2} y + \coth (\frac{x + 1}{x - 1}) x^{4}}{\ln (\frac{1}{x - 1})}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✗	342.402

10789	$y^{'} = \frac{2 x^{2} \cosh (\frac{1}{x - 1}) - 2 x \cosh (\frac{1}{x - 1}) - 1 + y^{2} - 2 x^{2} y + x^{4} - x + x y^{2} - 2 x^{3} y + x^{5}}{(x - 1) \cosh (\frac{1}{x - 1})}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✗	173.689

10790	$y^{'} = \frac{y (- \cosh (\frac{1}{x + 1}) x + \cosh (\frac{1}{x + 1}) - x + x^{2} y - x^{2} + x^{3} y)}{x (x - 1) \cosh (\frac{1}{x + 1})}$	[_Bernoulli]	✓	8.972

10791	$y^{'} = - \frac{y (x y + 1)}{x (x y + 1 - y)}$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.299

10792	$y^{'} = \frac{y}{x (- 1 + y + x^{2} y^{3} + y^{4} x^{3})}$	[_rational]	✗	3.407

10793	$y^{'} = \frac{x^{3} + 3 a x^{2} + 3 a^{2} x + a^{3} + x y^{2} + a y^{2} + y^{3}}{{(x + a)}^{3}}$	[[_homogeneous, ‘class C‘], _rational, _Abel]	✓	150.615

10794	$y^{'} = \frac{y^{3} x e^{3 x^{2}} e^{- \frac{9 x^{2}}{2}}}{9 e^{\frac{3 x^{2}}{2}} + 3 e^{\frac{3 x^{2}}{2}} y + 9 y}$	[[_Abel, ‘2nd type‘, ‘class C‘]]	✗	4.836

10795	$y^{'} = \frac{y (- 1 - \cosh (\frac{x + 1}{x - 1}) x + \cosh (\frac{x + 1}{x - 1}) x^{2} y - \cosh (\frac{x + 1}{x - 1}) x^{2} + \cosh (\frac{x + 1}{x - 1}) x^{3} y)}{x}$	[_Bernoulli]	✓	42.171

10796	$y^{'} = \frac{(x + y + 1) y}{(2 y^{3} + y + x) (x + 1)}$	[_rational]	✗	2.744

10797	$y^{'} = \frac{y (- 1 - x e^{\frac{x + 1}{x - 1}} + x^{2} e^{\frac{x + 1}{x - 1}} y - x^{2} e^{\frac{x + 1}{x - 1}} + x^{3} e^{\frac{x + 1}{x - 1}} y)}{x}$	[_Bernoulli]	✓	5.182

10798	$y^{'} = \frac{- b^{3} + 6 b^{2} x - 12 b x^{2} + 8 x^{3} - 4 b y^{2} + 8 x y^{2} + 8 y^{3}}{{(2 x - b)}^{3}}$	[[_homogeneous, ‘class C‘], _rational, _Abel]	✓	152.022

10799	$y^{'} = \frac{(y e^{- \frac{x^{2}}{4}} x + 2 + 2 y^{2} e^{- \frac{x^{2}}{2}} + 2 y^{3} e^{- \frac{3 x^{2}}{4}}) e^{\frac{x^{2}}{4}}}{2}$	[_Abel]	✓	4.369

10800	$y^{'} = - \frac{- \frac{1}{x} -_F1 (y + \frac{1}{x})}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	2.597

2.2.108 Problems 10701 to 10800