Problems 12801 to 12900

Table 2.259: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

12801	$1 + e^{\frac{y}{x}} + e^{\frac{x}{y}} (1 - \frac{x}{y}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	4.723

12802	$y^{'} x - y^{2} \ln (x) + y = 0$	[_Bernoulli]	✓	2.303

12803	$y^{4} x^{3} + x^{2} y^{3} + x y^{2} + y + (x^{4} y^{3} - x^{3} y^{2} - x^{3} y + x) y^{'} = 0$	[_rational]	✗	3.391

12804	$(2 \sqrt{x y} - x) y^{'} + y = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	60.125

12805	${y^{'}}^{2} + (x + y) y^{'} + x y = 0$	[_quadrature]	✓	0.426

12806	$x {y^{'}}^{2} - 2 y y^{'} - x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.320

12807	${y^{'}}^{2} + y^{2} = 1$	[_quadrature]	✓	0.885

12808	${(2 y^{'} x - y)}^{2} = 8 x^{3}$	[_linear]	✓	0.689

12809	$(x^{2} + 1) {y^{'}}^{2} = 1$	[_quadrature]	✓	0.411

12810	${y^{'}}^{3} - (2 x + y^{2}) {y^{'}}^{2} + (x^{2} - y^{2} + 2 x y^{2}) y^{'} - (x^{2} - y^{2}) y^{2} = 0$	[_quadrature]	✓	0.625

12811	$2 y^{'} x - y + \ln (y^{'}) = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	3.633

12812	$4 x {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	35.447

12813	$x {y^{'}}^{2} - 2 y y^{'} - x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.143

12814	$y^{'} + 2 x y = x^{2} + y^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	1.910

12815	$y = - y^{'} x + x^{4} {y^{'}}^{2}$	[[_homogeneous, ‘class G‘], _rational]	✓	1.850

12816	${y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.562

12817	$x + y^{'} y (2 {y^{'}}^{2} + 3) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	6.648

12818	$a^{2} y {y^{'}}^{2} - 2 y^{'} x + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.442

12819	$x {y^{'}}^{2} - 2 y y^{'} - x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.292

12820	${y^{'}}^{3} - 4 x y^{'} y + 8 y^{2} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	9.790

12821	${(y^{'} x - y)}^{2} = 1 + {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	✓	0.644

12822	$4 e^{2 y} {y^{'}}^{2} + 2 y^{'} x - 1 = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	8.640

12823	$4 e^{2 y} {y^{'}}^{2} + 2 e^{2 x} y^{'} - e^{2 x} = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	1.359

12824	$e^{2 y} {y^{'}}^{3} + (e^{2 x} + e^{3 x}) y^{'} - e^{3 x} = 0$	[‘y=_G(x,y’)‘]	✗	303.730

12825	$x y^{2} {y^{'}}^{2} - y^{3} y^{'} + x = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	4.234

12826	$(x^{2} + y^{2}) {(y^{'} + 1)}^{2} - 2 (x + y) (y^{'} + 1) (y y^{'} + x) + {(y y^{'} + x)}^{2} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.790

12827	$y = 2 y^{'} x + y^{2} {y^{'}}^{3}$	[[_1st_order, _with_linear_symmetries]]	✓	109.359

12828	$a^{2} y {y^{'}}^{2} - 2 y^{'} x + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.453

12829	${(x - y^{'} - y)}^{2} = x^{2} (2 x y - x^{2} y^{'})$	[‘y=_G(x,y’)‘]	✗	80.614

12830	$(1 + {y^{'}}^{2}) y^{2} = a^{2}$	[_quadrature]	✓	0.598

12831	$y y^{'} = (x - b) {y^{'}}^{2} + a$	[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	✓	0.629

12832	$x^{3} {y^{'}}^{2} + x^{2} y y^{'} + 1 = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.737

12833	$3 x {y^{'}}^{2} - 6 y y^{'} + x + 2 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	2.042

12834	$y = (x + 1) {y^{'}}^{2}$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	0.982

12835	$(y^{'} x - y) (y y^{'} + x) = a^{2} y^{'}$	[_rational]	✓	25.194

12836	${y^{'}}^{2} + 2 y y^{'} \cot (x) = y^{2}$	[_separable]	✓	1.533

12837	$(x^{2} + 1) {y^{'}}^{2} - 2 x y^{'} y + y^{2} - 1 = 0$	[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	✓	0.759

12838	$x^{2} {y^{'}}^{2} - 2 (x y + 2 y^{'}) y^{'} + y^{2} = 0$	[_separable]	✓	0.520

12839	$y = y^{'} x + \frac{y {y^{'}}^{2}}{x^{2}}$	[[_1st_order, _with_linear_symmetries]]	✓	2.870

12840	$x^{2} {y^{'}}^{2} - 2 x y^{'} y + y^{2} = x^{2} y^{2} + x^{4}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	9.129

12841	$y = y^{'} x + \frac{1}{y^{'}}$	[[_homogeneous, ‘class G‘], _rational, _Clairaut]	✓	0.510

12842	$x {y^{'}}^{2} - 2 y y^{'} - x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.141

12843	$x^{2} {y^{'}}^{2} - 2 (x y - 2) y^{'} + y^{2} = 0$	[[_homogeneous, ‘class G‘], _Clairaut]	✓	0.657

12844	$x^{2} {y^{'}}^{2} - {(x - 1)}^{2} = 0$	[_quadrature]	✓	0.433

12845	$8 {(y^{'} + 1)}^{3} = 27 (x + y) {(1 - y^{'})}^{3}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	71.269

12846	$4 {y^{'}}^{2} = 9 x$	[_quadrature]	✓	0.433

12847	$y {(3 - 4 y)}^{2} {y^{'}}^{2} = 4 - 4 y$	[_quadrature]	✓	0.626

12848	$y^{''} - 3 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.318

12849	$y^{''} - 6 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓	0.521

12850	$y^{'''} - y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.071

12851	$y^{'''} - 2 y^{''} - y^{'} + 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.078

12852	$4 y^{'''} - 3 y^{'} + y = 0$	[[_3rd_order, _missing_x]]	✓	0.078

12853	$y^{'''} - y^{''} - y^{'} + y = 0$	[[_3rd_order, _missing_x]]	✓	0.074

12854	$y^{''''} + 2 y^{'''} - 2 y^{'} - y = 0$	[[_high_order, _missing_x]]	✓	0.080

12855	$y^{'''} - 6 y^{''} + 9 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.074

12856	$y^{''''} + 2 y^{''} + y = 0$	[[_high_order, _missing_x]]	✓	0.100

12857	$y^{'''} - y^{''} + y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.092

12858	$y^{'''} - y^{''} - 2 y^{'} = e^{- x}$	[[_3rd_order, _missing_y]]	✓	0.130

12859	$y^{''} + 3 y^{'} + 2 y = e^{e^{x}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.632

12860	$y^{'''} + 3 y^{''} + 3 y^{'} + y = 2 e^{- x} - x^{2} e^{- x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.197

12861	$y^{''} - 2 y^{'} + y = \frac{e^{x}}{{(1 - x)}^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.549

12862	$y^{''} - 3 y^{'} + 2 y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.430

12863	$y^{'''} - 3 y^{''} - y^{'} + 3 y = x^{2}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.135

12864	$y^{''} + y = \sec (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.709

12865	$y^{'''} - 4 y^{''} + 5 y^{'} - 2 y = x$	[[_3rd_order, _with_linear_symmetries]]	✓	0.128

12866	$y^{''} + y = \sec (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.742

12867	$y^{''} + y = \tan (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.776

12868	$y^{''} + 4 y = x^{2} + \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.839

12869	$y^{''} - 2 y^{'} + y = 2 x e^{2 x} - \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.413

12870	$y^{''} + y = 2 e^{x} + x^{3} - x$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.646

12871	$y^{''} + 2 y^{'} + y = 3 e^{2 x} - \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.858

12872	$y^{'''} - y = x^{2}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.141

12873	$y^{'''} - 2 y^{''} - 3 y^{'} = 3 x^{2} + \sin (x)$	[[_3rd_order, _missing_y]]	✓	0.224

12874	$y^{''''} - 2 y^{''} + y = e^{x} + 4$	[[_high_order, _with_linear_symmetries]]	✓	0.163

12875	$y^{''} - 2 y^{'} = e^{2 x} + 1$	[[_2nd_order, _missing_y]]	✓	1.253

12876	$y^{''''} + 2 y^{''} + y = \cos (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.869

12877	$x^{3} y^{'''} + y^{'} x - y = x \ln (x)$	[[_3rd_order, _with_linear_symmetries]]	✓	0.264

12878	$x^{3} y^{'''} + 2 x^{2} y^{''} + 2 y = 10 x + \frac{10}{x}$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓	0.875

12879	$x^{2} y^{''} + 3 y^{'} x + y = \frac{1}{{(1 - x)}^{2}}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.601

12880	${(x + 1)}^{2} y^{''} - (x + 1) y^{'} + 6 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	1.362

12881	$y^{''} - 5 y^{'} + 6 y = \cos (x) - e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.648

12882	$y^{''''} - y = e^{x} \cos (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.169

12883	$y^{''} + 2 y^{'} + y = 2 x^{3} - x e^{3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.653

12884	$y^{'''} - 4 y^{'} = x^{2} - 3 e^{2 x}$	[[_3rd_order, _missing_y]]	✓	0.183

12885	$y^{''''} - 2 y^{''} + y = \cos (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.178

12886	$x^{4} y^{''''} + 6 x^{3} y^{'''} + 9 x^{2} y^{''} + 3 y^{'} x + y = {(1 + \ln (x))}^{2}$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.834

12887	$y^{'''} + 2 y^{''} + y^{'} = x^{2} - x$	[[_3rd_order, _missing_y]]	✓	0.143

12888	$y^{''} + 4 y = \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.815

12889	$y^{''} + 4 y = \sec {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.999

12890	$y^{''''} - y^{'''} - 3 y^{''} + 5 y^{'} - 2 y = e^{3 x}$	[[_high_order, _with_linear_symmetries]]	✓	0.162

12891	$y^{''} + y = x \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.832

12892	$x^{3} y^{'''} + 2 x^{2} y^{''} - y^{'} x + y = \frac{1}{x}$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓	0.323

12893	$y^{'''} - y = x e^{x} + \cos {(x)}^{2}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	1.108

12894	$y^{''} - x^{2} y^{'} + x y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	1.303

12895	$x y^{''} - (2 x + 1) y^{'} + (x + 1) y = x^{2} - x - 1$	[[_2nd_order, _with_linear_symmetries]]	✓	0.512

12896	$(x^{2} + 1) y^{''} + 2 y^{'} x - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.895

12897	$(1 - x) y^{''} + y^{'} x - y = {(1 - x)}^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.870

12898	$\sin (x) y^{''} + 2 \cos (x) y^{'} + 3 y \sin (x) = e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.485

12899	$y^{''} - 2 y^{'} \tan (x) - (a^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.853

12900	$4 x^{2} y^{''} + 4 x^{3} y^{'} + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.878

2.2.129 Problems 12801 to 12900