Problems 10601 to 10700

Table 2.215: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

10601	$y^{'} = \frac{2 F (y + \ln (2 x + 1)) x + F (y + \ln (2 x + 1)) - 2}{2 x + 1}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	3.022

10602	$y^{'} = \frac{2 y^{3}}{1 + 2 F (\frac{1 + 4 x y^{2}}{y^{2}}) y}$	[‘x=_G(y,y’)‘]	✗	2.557

10603	$y^{'} = - \frac{y^{2} (2 x - F (- \frac{x y - 2}{2 y}))}{4 x}$	[NONE]	✓	2.322

10604	$y^{'} = - (- e^{- x^{2}} + x^{2} e^{- x^{2}} - F (y - \frac{x^{2} e^{- x^{2}}}{2})) x$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	3.421

10605	$y^{'} = \frac{2 y + F (\frac{y}{x^{2}}) x^{3}}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	2.326

10606	$y^{'} = \frac{\sqrt{y}}{\sqrt{y} + F (\frac{x - y}{\sqrt{y}})}$	[[_1st_order, _with_linear_symmetries]]	✓	1.461

10607	$y^{'} = \frac{- 3 x^{2} y + F (x^{3} y)}{x^{3}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	2.493

10608	$y^{'} = \frac{y + F (\frac{y}{x}) x^{2}}{x}$	[[_homogeneous, ‘class D‘]]	✓	1.135

10609	$y^{'} = \frac{- 2 x - y + F ((x + y) x)}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	2.791

10610	$y^{'} = \frac{(y e^{- \frac{x^{2}}{4}} x + 2 F (y e^{- \frac{x^{2}}{4}})) e^{\frac{x^{2}}{4}}}{2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	2.000

10611	$y^{'} = \frac{x + y + F (- \frac{- y + \ln (x) x}{x}) x^{2}}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	3.083

10612	$y^{'} = \frac{x (a - 1) (a + 1)}{y + F (\frac{y^{2}}{2} - \frac{a^{2} x^{2}}{2} + \frac{x^{2}}{2}) a^{2} - F (\frac{y^{2}}{2} - \frac{a^{2} x^{2}}{2} + \frac{x^{2}}{2})}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	2.728

10613	$y^{'} = \frac{y}{x (- 1 + F (x y) y)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	6.499

10614	$y^{'} = - \frac{- x^{2} + 2 x^{3} y - F ((x y - 1) x)}{x^{4}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	1.632

10615	$y^{'} = \frac{F (\frac{(3 + y) e^{\frac{3 x^{2}}{2}}}{3 y}) x y^{2} e^{3 x^{2}} e^{- \frac{9 x^{2}}{2}}}{9}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	3.497

10616	$y^{'} = \frac{(y + 1) ((y - \ln (y + 1) - \ln (x)) x + 1)}{y x}$	[‘y=_G(x,y’)‘]	✗	4.616

10617	$y^{'} = \frac{6 y}{8 y^{4} + 9 y^{3} + 12 y^{2} + 6 y - F (- \frac{y^{4}}{3} - \frac{y^{3}}{2} - y^{2} - y + x)}$	[‘x=_G(y,y’)‘]	✗	3.169

10618	$y^{'} = \frac{y^{2} + 2 x y + x^{2} + e^{2 F (- (x - y) (x + y))}}{y^{2} + 2 x y + x^{2} - e^{2 F (- (x - y) (x + y))}}$	[[_1st_order, _with_linear_symmetries]]	✓	2.878

10619	$y^{'} = \frac{1}{y + \sqrt{x}}$	[[_homogeneous, ‘class G‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	1.524

10620	$y^{'} = \frac{1}{y + 2 + \sqrt{3 x + 1}}$	[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	6.560

10621	$y^{'} = \frac{x^{2}}{y + x^{3 / 2}}$	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	6.266

10622	$y^{'} = \frac{x^{5 / 3}}{y + x^{4 / 3}}$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	2.150

10623	$y^{'} = \frac{i x^{2} (i - 2 \sqrt{- x^{3} + 6 y})}{2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	34.940

10624	$y^{'} = \frac{x}{y + \sqrt{x^{2} + 1}}$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✗	4.677

10625	$y^{'} = \frac{{(- 1 + y \ln (x))}^{2}}{x}$	[_Riccati]	✓	2.508

10626	$y^{'} = \frac{x (- 2 + 3 \sqrt{x^{2} + 3 y})}{3}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	3.334

10627	$y^{'} = \frac{{(- 1 + 2 y \ln (x))}^{2}}{x}$	[_Riccati]	✓	2.805

10628	$y^{'} = \frac{e^{b x}}{y e^{- b x} + 1}$	[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	3.944

10629	$y^{'} = \frac{x^{2} (1 + 2 \sqrt{x^{3} - 6 y})}{2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	4.107

10630	$y^{'} = \frac{e^{x}}{y e^{- x} + 1}$	[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	4.375

10631	$y^{'} = \frac{e^{\frac{2 x}{3}}}{y e^{- \frac{2 x}{3}} + 1}$	[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	3.895

10632	$y^{'} = \frac{1 + 2 x^{5} \sqrt{4 x^{2} y + 1}}{2 x^{3}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	36.608

10633	$y^{'} = \frac{x (x + 2 \sqrt{x^{3} - 6 y})}{2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	3.956

10634	$y^{'} = (- \ln (y) + x^{2}) y$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	1.601

10635	$y^{'} = \frac{e^{- x^{2}} x}{y e^{x^{2}} + 1}$	[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	2.887

10636	$y^{'} = - (- \ln (\ln (y)) + \ln (x)) y$	[‘x=_G(y,y’)‘]	✗	3.416

10637	$y^{'} = {(- \ln (\ln (y)) + \ln (x))}^{2} y$	[‘y=_G(x,y’)‘]	✗	3.900

10638	$y^{'} = \frac{y}{\ln (\ln (y)) - \ln (x) + 1}$	[‘y=_G(x,y’)‘]	✗	4.207

10639	$y^{'} = \frac{1 + 2 \sqrt{4 x^{2} y + 1} x^{4}}{2 x^{3}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	36.757

10640	$y^{'} = \frac{{(- y^{2} + 4 a x)}^{2}}{y}$	[_rational]	✗	2.733

10641	$y^{'} = \frac{x (- 2 + 3 x \sqrt{x^{2} + 3 y})}{3}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	3.354

10642	$y^{'} = - \frac{x^{2} (a x - 2 \sqrt{a (a x^{4} + 8 y)})}{2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	6.514

10643	$y^{'} = (- \ln (y) + x) y$	[[_1st_order, _with_linear_symmetries]]	✓	1.160

10644	$y^{'} = \frac{x^{3} + x^{2} + 2 \sqrt{x^{3} - 6 y}}{2 x + 2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	3.347

10645	$y^{'} = \frac{{(a y^{2} + b x^{2})}^{2} x}{a^{5 / 2} y}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	3.299

10646	$y^{'} = - \frac{x^{3} (\sqrt{a} x + \sqrt{a} - 2 \sqrt{a x^{4} + 8 y}) \sqrt{a}}{2 (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	6.954

10647	$y^{'} = - \frac{x}{4} + \frac{1}{4} + x \sqrt{x^{2} - 2 x + 1 + 8 y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	3.683

10648	$y^{'} = - \frac{x}{2} - \frac{a}{2} + x \sqrt{x^{2} + 2 a x + a^{2} + 4 y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	3.679

10649	$y^{'} = \frac{(\ln (y) + x^{2}) y}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	1.626

10650	$y^{'} = \frac{2 a + x \sqrt{- y^{2} + 4 a x}}{y}$	[‘y=_G(x,y’)‘]	✗	38.286

10651	$y^{'} = - \frac{x}{2} + 1 + x \sqrt{x^{2} - 4 x + 4 y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	3.762

10652	$y^{'} = - \frac{2 x^{2} + 2 x - 3 \sqrt{x^{2} + 3 y}}{3 (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	2.786

10653	$y^{'} = \frac{y^{3} e^{- \frac{4 x}{3}}}{y e^{- \frac{2 x}{3}} + 1}$	[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	3.392

10654	$y^{'} = \frac{(\ln (y) + x^{3}) y}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	1.714

10655	$y^{'} = - \frac{x}{4} + \frac{1}{4} + x^{2} \sqrt{x^{2} - 2 x + 1 + 8 y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	3.829

10656	$y^{'} = - \frac{x^{2} - 1 - 4 \sqrt{x^{2} - 2 x + 1 + 8 y}}{4 (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	2.604

10657	$y^{'} = - \frac{a x}{2} - \frac{b}{2} + x \sqrt{a^{2} x^{2} + 2 a b x + b^{2} + 4 a y - 4 c}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	3.885

10658	$y^{'} = - \frac{x}{2} - \frac{a}{2} + x^{2} \sqrt{x^{2} + 2 a x + a^{2} + 4 y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	3.635

10659	$y^{'} = - \frac{a x}{2} - \frac{b}{2} + x^{2} \sqrt{a^{2} x^{2} + 2 a b x + b^{2} + 4 a y - 4 c}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	3.943

10660	$y^{'} = \frac{x}{2} + \frac{1}{2} + x^{2} \sqrt{x^{2} + 2 x + 1 - 4 y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	3.538

10661	$y^{'} = \frac{2 a + x^{2} \sqrt{- y^{2} + 4 a x}}{y}$	[‘y=_G(x,y’)‘]	✗	36.801

10662	$y^{'} = - \frac{x}{2} + 1 + x^{2} \sqrt{x^{2} - 4 x + 4 y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	3.812

10663	$y^{'} = - \frac{(\sqrt{a} x^{4} + \sqrt{a} x^{3} - 2 \sqrt{a x^{4} + 8 y}) \sqrt{a}}{2 (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	37.631

10664	$y^{'} = (- \ln (y) + 1 + x^{2} + x^{3}) y$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	2.737

10665	$y^{'} = \frac{y^{3} e^{- 2 b x}}{y e^{- b x} + 1}$	[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	1.891

10666	$y^{'} = \frac{y^{3} e^{- 2 x}}{y e^{- x} + 1}$	[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	3.140

10667	$y^{'} = \frac{{(- 2 y^{3 / 2} + 3 e^{x})}^{2} e^{x}}{4 \sqrt{y}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	4.548

10668	$y^{'} = \frac{i x (i - 2 \sqrt{- x^{2} + 4 \ln (a) + 4 \ln (y)}) y}{2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	5.838

10669	$y^{'} = \frac{{(1 + x y^{2})}^{2}}{y x^{4}}$	[_rational]	✗	2.832

10670	$y^{'} = \frac{x^{2} (3 x + \sqrt{- 9 x^{4} + 4 y^{3}})}{y^{2}}$	[‘y=_G(x,y’)‘]	✗	45.883

10671	$y^{'} = \frac{- \sin (2 y) + \cos (2 y) x^{2} + x^{2}}{2 x}$	[‘y=_G(x,y’)‘]	✓	2.621

10672	$y^{'} = - \frac{x^{2} - x - 2 - 2 \sqrt{x^{2} - 4 x + 4 y}}{2 (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	2.612

10673	$y^{'} = \frac{y + x^{3} a e^{x} + a x^{4} + a x^{3} - x y^{2} e^{x} - y^{2} x^{2} - x y^{2}}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	11.606

10674	$y^{'} = \frac{x + 1 + 2 x^{6} \sqrt{4 x^{2} y + 1}}{2 x^{3} (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	7.796

10675	$y^{'} = \frac{y + x^{3} a \ln (x + 1) + a x^{4} + a x^{3} - x y^{2} \ln (x + 1) - y^{2} x^{2} - x y^{2}}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	26.950

10676	$y^{'} = \frac{x^{2} (x + 1 + 2 x \sqrt{x^{3} - 6 y})}{2 x + 2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	5.835

10677	$y^{'} = \frac{y + x^{3} \ln (x) + x^{4} + x^{3} + 7 x y^{2} \ln (x) + 7 y^{2} x^{2} + 7 x y^{2}}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	7.273

10678	$y^{'} = \frac{x^{2} + 2 x + 1 + 2 \sqrt{x^{2} + 2 x + 1 - 4 y}}{2 x + 2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	2.611

10679	$y^{'} = \frac{y + x^{3} b \ln (\frac{1}{x}) + x^{4} b + b x^{3} + x a y^{2} \ln (\frac{1}{x}) + a x^{2} y^{2} + a x y^{2}}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	18.122

10680	$y^{'} = \frac{2 a}{x (- x y + 2 a x y^{2} - 8 a^{2})}$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	2.428

10681	$y^{'} = \frac{y (- 1 + \ln (x (x + 1)) y x^{4} - \ln (x (x + 1)) x^{3})}{x}$	[_Bernoulli]	✓	5.516

10682	$y^{'} = \frac{y + \sqrt{x^{2} + y^{2}} x^{2}}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	10.576

10683	$y^{'} = \frac{y + \ln ((- 1 + x) (x + 1)) x^{3} + 7 \ln ((- 1 + x) (x + 1)) x y^{2}}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	2.725

10684	$y^{'} = \frac{y^{3} x e^{2 x^{2}}}{y e^{x^{2}} + 1}$	[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	3.309

10685	$y^{'} = \frac{y - \ln (\frac{x + 1}{- 1 + x}) x^{3} + \ln (\frac{x + 1}{- 1 + x}) x y^{2}}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	2.731

10686	$y^{'} = \frac{y + e^{\frac{x + 1}{- 1 + x}} x^{3} + e^{\frac{x + 1}{- 1 + x}} x y^{2}}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	3.257

10687	$y^{'} = \frac{x y - y - e^{x + 1} x^{3} + e^{x + 1} x y^{2}}{(- 1 + x) x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	2.417

10688	$y^{'} = \frac{- x^{2} + 1 + 4 x^{3} \sqrt{x^{2} - 2 x + 1 + 8 y}}{4 x + 4}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	7.033

10689	$y^{'} = \frac{- \sin (2 y) + \cos (2 y) x^{3} + x^{3}}{2 x}$	[‘y=_G(x,y’)‘]	✓	2.671

10690	$y^{'} = \frac{y + x^{3} \sqrt{x^{2} + y^{2}}}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	3.503

10691	$y^{'} = (1 + y^{2} e^{- 2 b x} + y^{3} e^{- 3 b x}) e^{b x}$	[[_1st_order, _with_linear_symmetries], _Abel]	✓	1.476

10692	$y^{'} = \frac{x + 1 + 2 \sqrt{4 x^{2} y + 1} x^{3}}{2 x^{3} (x + 1)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	6.347

10693	$y^{'} = \frac{y \ln (- 1 + x) + x^{4} + x^{3} + y^{2} x^{2} + x y^{2}}{\ln (- 1 + x) x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	2.844

10694	$y^{'} = \frac{y \ln (- 1 + x) + e^{x + 1} x^{3} + 7 e^{x + 1} x y^{2}}{\ln (- 1 + x) x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	3.477

10695	$y^{'} = (1 + y^{2} e^{- \frac{4 x}{3}} + y^{3} e^{- 2 x}) e^{\frac{2 x}{3}}$	[[_1st_order, _with_linear_symmetries], _Abel]	✓	2.087

10696	$y^{'} = (1 + y^{2} e^{- 2 x} + y^{3} e^{- 3 x}) e^{x}$	[[_1st_order, _with_linear_symmetries], _Abel]	✓	1.707

10697	$y^{'} = \frac{x (- 2 x - 2 + 3 x^{2} \sqrt{x^{2} + 3 y})}{3 x + 3}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	6.119

10698	$y^{'} = \frac{1}{x (x y^{2} + 1 + x) y}$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.889

10699	$y^{'} = \frac{2 x e^{x} - 2 x - \ln (x) - 1 + x^{4} \ln (x) + x^{4} - 2 y x^{2} \ln (x) - 2 x^{2} y + y^{2} \ln (x) + y^{2}}{- 1 + e^{x}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✗	21.853

10700	$y^{'} = \frac{- y e^{x} + x y - x^{3} \ln (x) - x^{3} - x y^{2} \ln (x) - x y^{2}}{(- e^{x} + x) x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓	3.248

2.2.107 Problems 10601 to 10700