Problems 10501 to 10600

Table 2.213: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

10501	$(a - b) y^{2} {y^{'}}^{2} - 2 b x y y^{'} - a b - b x^{2} + a y^{2} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	11.772

10502	$(a y^{2} + b x + c) {y^{'}}^{2} - b y y^{'} + d y^{2} = 0$	[‘y=_G(x,y’)‘]	✗	88.562

10503	${(a y - b x)}^{2} (a^{2} {y^{'}}^{2} + b^{2}) - c^{2} {(a y^{'} + b)}^{2} = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	16.930

10504	${(b 2 y + a 2 x + c 2)}^{2} {y^{'}}^{2} + (a 1 x + b 1 y + c 1) y^{'} + b 0 y + a 0 + c 0 = 0$	[_rational]	✗	474.263

10505	$x y^{2} {y^{'}}^{2} - (y^{3} + x^{3} - a) y^{'} + x^{2} y = 0$	[_rational]	✗	20.366

10506	$x y^{2} {y^{'}}^{2} - 2 y^{3} y^{'} + 2 x y^{2} - x^{3} = 0$	[_separable]	✓	1.157

10507	$x^{2} (x y^{2} - 1) {y^{'}}^{2} + 2 x^{2} y^{2} (y - x) y^{'} - y^{2} (x^{2} y - 1) = 0$	[‘y=_G(x,y’)‘]	✗	50.547

10508	$(y^{4} - a^{2} x^{2}) {y^{'}}^{2} + 2 a^{2} x y y^{'} + y^{2} (y^{2} - a^{2}) = 0$	[‘y=_G(x,y’)‘]	✗	40.982

10509	$(y^{4} + x^{2} y^{2} - x^{2}) {y^{'}}^{2} + 2 x y^{'} y - y^{2} = 0$	[‘y=_G(x,y’)‘]	✗	12.897

10510	$9 y^{4} (x^{2} - 1) {y^{'}}^{2} - 6 x y^{5} y^{'} - 4 x^{2} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	20.497

10511	$x^{2} (x^{2} y^{4} - 1) {y^{'}}^{2} + 2 x^{3} y^{3} (y^{2} - x^{2}) y^{'} - y^{2} (x^{4} y^{2} - 1) = 0$	[‘y=_G(x,y’)‘]	✗	158.652

10512	$(a^{2} \sqrt{x^{2} + y^{2}} - x^{2}) {y^{'}}^{2} + 2 x y^{'} y + a^{2} \sqrt{x^{2} + y^{2}} - y^{2} = 0$	[[_1st_order, _with_linear_symmetries]]	✗	157.535

10513	$(a {(x^{2} + y^{2})}^{3 / 2} - x^{2}) {y^{'}}^{2} + 2 x y^{'} y + a {(x^{2} + y^{2})}^{3 / 2} - y^{2} = 0$	[[_1st_order, _with_linear_symmetries]]	✗	52.798

10514	$\sin (y) {y^{'}}^{2} + 2 x y^{'} \cos {(y)}^{3} - \sin (y) \cos {(y)}^{4} = 0$	[‘y=_G(x,y’)‘]	✗	157.863

10515	${y^{'}}^{2} (a \cos (y) + b) - c \cos (y) + d = 0$	[_quadrature]	✓	10.715

10516	$f (x^{2} + y^{2}) (1 + {y^{'}}^{2}) - {(y^{'} x - y)}^{2} = 0$	[[_1st_order, _with_linear_symmetries]]	✗	11.676

10517	$(x^{2} + y^{2}) f (\frac{x}{\sqrt{x^{2} + y^{2}}}) (1 + {y^{'}}^{2}) - {(y^{'} x - y)}^{2} = 0$	[[_homogeneous, ‘class A‘]]	✓	9.041

10518	$(x^{2} + y^{2}) f (\frac{y}{\sqrt{x^{2} + y^{2}}}) (1 + {y^{'}}^{2}) - {(y^{'} x - y)}^{2} = 0$	[[_homogeneous, ‘class A‘]]	✓	8.937

10519	${y^{'}}^{3} - {(y - a)}^{2} {(y - b)}^{2} = 0$	[_quadrature]	✓	11.747

10520	${y^{'}}^{3} - f (x) {(a y^{2} + b y + c)}^{2} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	1.928

10521	${y^{'}}^{3} + y^{'} - y = 0$	[_quadrature]	✓	0.737

10522	${y^{'}}^{3} + y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.522

10523	${y^{'}}^{3} - (5 + x) y^{'} + y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.511

10524	${y^{'}}^{3} - a x y^{'} + x^{3} = 0$	[_quadrature]	✓	0.831

10525	${y^{'}}^{3} - 2 y y^{'} + y^{2} = 0$	[_quadrature]	✓	108.913

10526	${y^{'}}^{2} - a x y y^{'} + 2 a y^{2} = 0$	[_separable]	✓	0.722

10527	${y^{'}}^{3} - (x^{2} + x y + y^{2}) {y^{'}}^{2} + (x y^{3} + x^{2} y^{2} + x^{3} y) y^{'} - x^{3} y^{3} = 0$	[_quadrature]	✓	0.580

10528	${y^{'}}^{3} - x y^{4} y^{'} - y^{5} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	13.240

10529	${y^{'}}^{3} + a {y^{'}}^{2} + b y + a b x = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	1.014

10530	${y^{'}}^{3} + x {y^{'}}^{2} - y = 0$	[_dAlembert]	✓	2.886

10531	${y^{'}}^{3} - y {y^{'}}^{2} + y^{2} = 0$	[_quadrature]	✓	143.529

10532	${y^{'}}^{2} - (x^{2} + x y^{2} + y^{4}) {y^{'}}^{2} + (x y^{6} + x^{2} y^{4} + x^{3} y^{2}) y^{'} - x^{3} y^{6} = 0$	[‘y=_G(x,y’)‘]	✗	42.242

10533	$a {y^{'}}^{3} + b {y^{'}}^{2} + c y^{'} - y - d = 0$	[_quadrature]	✓	0.835

10534	$x {y^{'}}^{3} - y {y^{'}}^{2} + a = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.845

10535	$4 x {y^{'}}^{3} - 6 y {y^{'}}^{2} - x + 3 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.964

10536	$8 x {y^{'}}^{3} - 12 y {y^{'}}^{2} + 9 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.973

10537	$(- a^{2} + x^{2}) {y^{'}}^{3} + b x (- a^{2} + x^{2}) {y^{'}}^{2} + y^{'} + b x = 0$	[_quadrature]	✓	0.556

10538	$x^{3} {y^{'}}^{3} - 3 x^{2} y {y^{'}}^{2} + (3 x y^{2} + x^{6}) y^{'} - y^{3} - 2 x^{5} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	12.395

10539	$2 {(y^{'} x + y)}^{3} - y y^{'} = 0$	[[_homogeneous, ‘class G‘]]	✓	14.836

10540	${y^{'}}^{3} \sin (x) - (y \sin (x) - \cos {(x)}^{2}) {y^{'}}^{2} - (\cos {(x)}^{2} y + \sin (x)) y^{'} + y \sin (x) = 0$	[_quadrature]	✓	0.602

10541	$2 y {y^{'}}^{3} - y {y^{'}}^{2} + 2 y^{'} x - x = 0$	[_quadrature]	✓	1.307

10542	$y^{2} {y^{'}}^{3} + 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	111.208

10543	$16 y^{2} {y^{'}}^{3} + 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	111.191

10544	$x y^{2} {y^{'}}^{3} - y^{3} {y^{'}}^{2} + x (x^{2} + 1) y^{'} - x^{2} y = 0$	[‘y=_G(x,y’)‘]	✗	245.856

10545	$x^{7} y^{2} {y^{'}}^{3} - (3 x^{6} y^{3} - 1) {y^{'}}^{2} + 3 x^{5} y^{4} y^{'} - x^{4} y^{5} = 0$	[[_homogeneous, ‘class G‘]]	✓	125.545

10546	${y^{'}}^{4} - {(y - a)}^{3} {(y - b)}^{2} = 0$	[_quadrature]	✓	2.445

10547	${y^{'}}^{4} + 3 (x - 1) {y^{'}}^{2} - 3 (2 y - 1) y^{'} + 3 x = 0$	[_dAlembert]	✓	36.556

10548	${y^{'}}^{4} - 4 y {(y^{'} x - 2 y)}^{2} = 0$	[[_homogeneous, ‘class G‘]]	✓	0.794

10549	${y^{'}}^{6} - {(y - a)}^{4} {(y - b)}^{3} = 0$	[_quadrature]	✓	5.210

10550	$x^{2} {(1 + {y^{'}}^{2})}^{3} - a^{2} = 0$	[_quadrature]	✓	4.455

10551	${y^{'}}^{r} - a y^{s} - b x^{\frac{r s}{r - s}} = 0$	[[_homogeneous, ‘class G‘]]	✓	11.948

10552	${y^{'}}^{n} - f {(x)}^{n} {(y - a)}^{n + 1} {(y - b)}^{n - 1} = 0$	[_separable]	✓	51.067

10553	${y^{'}}^{n} - f (x) g (y) = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	3.045

10554	$a {y^{'}}^{m} + b {y^{'}}^{n} - y = 0$	[_quadrature]	✓	2.396

10555	$x^{n - 1} {y^{'}}^{n} - n x y^{'} + y = 0$	[‘y=_G(x,y’)‘]	✓	2.250

10556	$\sqrt{1 + {y^{'}}^{2}} + y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	✓	2.103

10557	$\sqrt{1 + {y^{'}}^{2}} + x {y^{'}}^{2} + y = 0$	[_dAlembert]	✓	78.454

10558	$x (\sqrt{1 + {y^{'}}^{2}} + y^{'}) - y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	40.293

10559	$a x \sqrt{1 + {y^{'}}^{2}} + y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	77.234

10560	$y \sqrt{1 + {y^{'}}^{2}} - a y y^{'} - a x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	17.049

10561	$a y \sqrt{1 + {y^{'}}^{2}} - 2 x y^{'} y + y^{2} - x^{2} = 0$	[_rational]	✓	40.054

10562	$f (x^{2} + y^{2}) \sqrt{1 + {y^{'}}^{2}} - y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries]]	✗	14.132

10563	$a {(1 + {y^{'}}^{3})}^{1 / 3} + b x y^{'} - y = 0$	[_dAlembert]	✓	90.707

10564	$\ln (y^{'}) + y^{'} x + a y + b = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	5.571

10565	$\ln (y^{'}) + a (y^{'} x - y) = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	2.756

10566	$y \ln (y^{'}) + y^{'} - y \ln (y) - x y = 0$	[_separable]	✓	5.833

10567	$\sin (y^{'}) + y^{'} - x = 0$	[_quadrature]	✓	0.764

10568	$a \cos (y^{'}) + b y^{'} + x = 0$	[_quadrature]	✓	0.619

10569	${y^{'}}^{2} \sin (y^{'}) - y = 0$	[_quadrature]	✓	1.724

10570	$(1 + {y^{'}}^{2}) \sin {(y^{'} x - y)}^{2} - 1 = 0$	[_Clairaut]	✓	8.652

10571	$(1 + {y^{'}}^{2}) (\arctan (y^{'}) + a x) + y^{'} = 0$	[_quadrature]	✓	1.220

10572	$a x^{n} f (y^{'}) + y^{'} x - y = 0$	[‘y=_G(x,y’)‘]	✓	1.418

10573	$f (x {y^{'}}^{2}) + 2 y^{'} x - y = 0$	[‘y=_G(x,y’)‘]	✓	0.587

10574	$f (x - \frac{3 {y^{'}}^{2}}{2}) + {y^{'}}^{3} - y = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	1.071

10575	$y^{'} = F (\frac{y}{x + a})$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	1.145

10576	$y^{'} = 2 x + F (y - x^{2})$	[[_1st_order, _with_linear_symmetries]]	✓	0.973

10577	$y^{'} = - \frac{a x}{2} + F (y + \frac{a x^{2}}{4} + \frac{b x}{2})$	[[_1st_order, _with_linear_symmetries]]	✓	1.166

10578	$y^{'} = F (y e^{- b x}) e^{b x}$	[[_1st_order, _with_linear_symmetries]]	✓	1.253

10579	$y^{'} = \frac{1 + 2 F (\frac{4 x^{2} y + 1}{4 x^{2}}) x}{2 x^{3}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	2.771

10580	$y^{'} = \frac{1 + F (\frac{y a x + 1}{a x}) a x^{2}}{a x^{2}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	2.826

10581	$y^{'} = - \frac{(a x^{2} - 2 F (y + \frac{a x^{4}}{8})) x}{2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	2.815

10582	$y^{'} = \frac{2 a}{y + 2 F (y^{2} - 4 a x) a}$	[[_1st_order, _with_linear_symmetries]]	✓	1.255

10583	$y^{'} = F (\ln (\ln (y)) - \ln (x)) y$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	3.898

10584	$y^{'} = \frac{F (\frac{y}{\sqrt{x^{2} + 1}}) x}{\sqrt{x^{2} + 1}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	3.948

10585	$y^{'} = \frac{(x^{3 / 2} + 2 F (y - \frac{x^{3}}{6})) \sqrt{x}}{2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	3.211

10586	$y^{'} = \frac{x + F (- (x - y) (x + y))}{y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	2.583

10587	$y^{'} = \frac{F (- \frac{- 1 + y \ln (x)}{y}) y^{2}}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	1.925

10588	$y^{'} = \frac{x}{- y + F (x^{2} + y^{2})}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	2.690

10589	$y^{'} = \frac{F (\frac{a y^{2} + b x^{2}}{a}) x}{\sqrt{a} y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	2.617

10590	$y^{'} = \frac{6 x^{3} + 5 \sqrt{x} + 5 F (y - \frac{2 x^{3}}{5} - 2 \sqrt{x})}{5 x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	3.758

10591	$y^{'} = \frac{F (y^{3 / 2} - \frac{3 e^{x}}{2}) e^{x}}{\sqrt{y}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	3.508

10592	$y^{'} = \frac{F (- \frac{- y^{2} + b}{x^{2}}) x}{y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	2.643

10593	$y^{'} = \frac{F (\frac{x y^{2} + 1}{x})}{y x^{2}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	2.696

10594	$y^{'} = \frac{- 2 x^{2} + x + F (y + x^{2} - x)}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	1.776

10595	$y^{'} = \frac{2 a}{x^{2} (- y + 2 F (\frac{x y^{2} - 4 a}{x}) a)}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	3.028

10596	$y^{'} = \frac{y + F (\frac{y}{x})}{x - 1}$	[[_homogeneous, ‘class D‘]]	✓	2.373

10597	$y^{'} = \frac{- x + F (x^{2} + y^{2})}{y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	2.783

10598	$y^{'} = \frac{F (- \frac{2 y \ln (x) - 1}{y}) y^{2}}{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	1.938

10599	$y^{'} = \frac{F (- (x - y) (x + y)) x}{y}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	2.471

10600	$y^{'} = \frac{y^{2} (2 + F (\frac{x^{2} - y}{y x^{2}}) x^{2})}{x^{3}}$	[NONE]	✗	3.112

2.2.106 Problems 10501 to 10600