Problems 13801 to 13900

Table 2.279: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

13801	$2 x + 2 y - 1 + (x + y - 2) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.873

13802	${y^{'}}^{3} - e^{2 x} y^{'} = 0$	[_quadrature]	✓	0.505

13803	$y = 5 y^{'} x - {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.592

13804	$y^{'} = x - y^{2}$ i.c.	[[_Riccati, _special]]	✓	19.311

13805	$y^{'} = {(x - 5 y)}^{1 / 3} + 2$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	1.825

13806	$y (x - y) - x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	1.741

13807	$x^{'} + 5 x = 10 t + 2$ i.c.	[[_linear, ‘class A‘]]	✓	2.845

13808	$x^{'} = \frac{x}{t} + \frac{x^{2}}{t^{3}}$ i.c.	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	2.842

13809	$y = y^{'} x + {y^{'}}^{2}$ i.c.	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.536

13810	$y = y^{'} x + {y^{'}}^{2}$ i.c.	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.562

13811	$y^{'} = \frac{3 x - 4 y - 2}{3 x - 4 y - 3}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.030

13812	$x^{'} - x \cot (t) = 4 \sin (t)$	[_linear]	✓	1.850

13813	$y = x^{2} + 2 y^{'} x + \frac{{y^{'}}^{2}}{2}$	[[_homogeneous, ‘class G‘]]	✓	1.710

13814	$y^{'} - \frac{3 y}{x} + x^{3} y^{2} = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	1.930

13815	$y (1 + {y^{'}}^{2}) = a$	[_quadrature]	✓	0.555

13816	$x^{2} - y + (x^{2} y^{2} + x) y^{'} = 0$	[_rational]	✓	1.279

13817	$3 y^{2} - x + 2 y (y^{2} - 3 x) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	4.699

13818	$y (x - y) - x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	1.691

13819	$y^{'} = \frac{x + y - 3}{y - x + 1}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.090

13820	$y^{'} x - y^{2} \ln (x) + y = 0$	[_Bernoulli]	✓	2.164

13821	$(x^{2} - 1) y^{'} + 2 x y - \cos (x) = 0$	[_linear]	✓	2.565

13822	$(3 + 2 x + 4 y) y^{'} - 2 y - x - 1 = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.958

13823	$(- x + y^{2}) y^{'} - y + x^{2} = 0$	[_exact, _rational]	✓	1.129

13824	$(y^{2} - x^{2}) y^{'} + 2 x y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	4.753

13825	$3 x y^{2} y^{'} + y^{3} - 2 x = 0$	[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]	✓	2.444

13826	${y^{'}}^{2} + (x + a) y^{'} - y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.580

13827	${y^{'}}^{2} - 2 y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.519

13828	${y^{'}}^{2} + 2 y y^{'} \cot (x) - y^{2} = 0$	[_separable]	✓	1.355

13829	$y^{''} - 6 y^{'} + 10 y = 100$ i.c.	[[_2nd_order, _missing_x]]	✓	0.747

13830	$x^{''} + x = \sin (t) - \cos (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.051

13831	$y^{'} + y^{'''} - 3 y^{''} = 0$	[[_3rd_order, _missing_x]]	✓	0.082

13832	$y^{''} + y = \frac{1}{\sin {(x)}^{3}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.825

13833	$x^{2} y^{''} - 4 y^{'} x + 6 y = 2$	[[_2nd_order, _with_linear_symmetries]]	✓	1.251

13834	$y^{''} + y = \cosh (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.764

13835	$y^{''} + \frac{2 {y^{'}}^{2}}{1 - y} = 0$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.407

13836	$x^{''} - 4 x^{'} + 4 x = e^{t} + e^{2 t} + 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.647

13837	$(x^{2} + 1) y^{''} + 1 + {y^{'}}^{2} = 0$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.879

13838	$x^{3} x^{''} + 1 = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	2.089

13839	$y^{''''} - 16 y = x^{2} - e^{x}$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.183

13840	${y^{'''}}^{2} + {y^{''}}^{2} = 1$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	✓	2.964

13841	$x^{(6)} - x^{''''} = 1$	[[_high_order, _missing_x]]	✓	0.141

13842	$x^{''''} - 2 x^{''} + x = t^{2} - 3$	[[_high_order, _with_linear_symmetries]]	✓	0.143

13843	$y^{''} + 4 x y = 0$	[[_Emden, _Fowler]]	✓	0.290

13844	$x^{2} y^{''} + y^{'} x + (9 x^{2} - \frac{1}{25}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.517

13845	$y^{''} + {y^{'}}^{2} = 1$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	✓	0.618

13846	$y^{''} = 3 \sqrt{y}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	4.458

13847	$y^{''} + y = 1 - \frac{1}{\sin (x)}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.769

13848	$u^{''} + \frac{2 u^{'}}{r} = 0$	[[_2nd_order, _missing_y]]	✓	0.520

13849	$y y^{''} + {y^{'}}^{2} = \frac{y y^{'}}{\sqrt{x^{2} + 1}}$	[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.584

13850	$y y^{'} y^{''} = {y^{'}}^{3} + {y^{''}}^{2}$	[[_2nd_order, _missing_x]]	✓	1.799

13851	$x^{''} + 9 x = t \sin (3 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.862

13852	$y^{''} + 2 y^{'} + y = \sinh (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.757

13853	$y^{'''} - y = e^{x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.145

13854	$y^{''} - 2 y^{'} + 2 y = x e^{x} \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.698

13855	$(x^{2} - 1) y^{''} - 6 y = 1$	[[_2nd_order, _with_linear_symmetries]]	✓	0.521

13856	$m x^{''} = f (x)$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.127

13857	$m x^{''} = f (x^{'})$	[[_2nd_order, _missing_x]]	✓	0.762

13858	$y^{(6)} - 3 y^{(5)} + 3 y^{''''} - y^{'''} = x$	[[_high_order, _missing_y]]	✓	0.157

13859	$x^{''''} + 2 x^{''} + x = \cos (t)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.853

13860	${(x + 1)}^{2} y^{''} + (x + 1) y^{'} + y = 2 \cos (\ln (x + 1))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.733

13861	$x^{3} y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.159

13862	$x^{''''} + x = t^{3}$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.151

13863	${y^{''}}^{3} + y^{''} + 1 = x$	[[_2nd_order, _quadrature]]	✓	1.408

13864	$x^{''} + 10 x^{'} + 25 x = 2^{t} + t e^{- 5 t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.851

13865	$x y y^{''} - x {y^{'}}^{2} - y y^{'} = 0$	[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.390

13866	$y^{(6)} - y = e^{2 x}$	[[_high_order, _with_linear_symmetries]]	✓	0.203

13867	$y^{(6)} + 2 y^{''''} + y^{''} = x + e^{x}$	[[_high_order, _missing_y]]	✓	0.188

13868	$6 y^{''} y^{''''} - 5 {y^{'''}}^{2} = 0$	[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]	✓	0.804

13869	$x y^{''} = y^{'} \ln (\frac{y^{'}}{x})$	[[_2nd_order, _missing_y]]	✓	0.721

13870	$y^{''} + y = \sin (3 x) \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.200

13871	$y^{''} = 2 y^{3}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✗	3.839

13872	$y y^{''} - {y^{'}}^{2} = y^{'}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.506

13873	$[\begin{matrix} x^{'} = y \\ y^{'} = - x \end{matrix}]$ i.c.	system_of_ODEs	✓	0.392

13874	$[\begin{matrix} x^{'} + 5 x + y = e^{t} \\ y^{'} - x - 3 y = e^{2 t} \end{matrix}]$	system_of_ODEs	✓	1.688

13875	$[\begin{matrix} x^{'} = y \\ y^{'} = z \\ z^{'} = x \end{matrix}]$	system_of_ODEs	✓	1.059

13876	$[\begin{matrix} x^{'} = y \\ y^{'} = \frac{y^{2}}{x} \end{matrix}]$	system_of_ODEs	✓	0.057

13877	$y^{'} = y e^{x + y} (x^{2} + 1)$	[_separable]	✓	1.641

13878	$x^{2} y^{'} = 1 + y^{2}$	[_separable]	✓	1.979

13879	$y^{'} = \sin (x y)$	[‘y=_G(x,y’)‘]	✗	1.463

13880	$x (e^{y} + 4) = e^{x + y} y^{'}$	[_separable]	✓	2.453

13881	$y^{'} = \cos (x + y)$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	1.979

13882	$y^{'} x + y = x y^{2}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	1.197

13883	$y^{'} = t \ln (y^{2 t}) + t^{2}$	[‘y=_G(x,y’)‘]	✗	1.900

13884	$y^{'} = x e^{- x + y^{2}}$	[_separable]	✓	1.409

13885	$y^{'} = \ln (x y)$	[‘y=_G(x,y’)‘]	✗	0.816

13886	$x {(1 + y)}^{2} = (x^{2} + 1) y e^{y} y^{'}$	[_separable]	✓	2.352

13887	$y^{''} + x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.440

13888	$y^{'''} + x y = \sin (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✗	0.102

13889	$y^{''} + y y^{'} = 1$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✗	5.984

13890	$y^{(5)} - y^{''''} + y^{'} = 2 x^{2} + 3$	[[_high_order, _missing_y]]	✓	0.177

13891	$y^{''} + y y^{''''} = 1$	[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]]	✗	0.070

13892	$y^{'''} + x y = \cosh (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✗	0.089

13893	$\cos (x) y^{'} + y e^{x^{2}} = \sinh (x)$	[_linear]	✓	39.522

13894	$y^{'''} + x y = \cosh (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✗	0.079

13895	$y y^{'} = 1$	[_quadrature]	✓	1.009

13896	$\sinh (x) {y^{'}}^{2} + 3 y = 0$	[‘y=_G(x,y’)‘]	✓	1.598

13897	$5 y^{'} - x y = 0$	[_separable]	✓	1.118

13898	${y^{'}}^{2} \sqrt{y} = \sin (x)$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	2.564

13899	$2 y^{''} + 3 y^{'} + 4 x^{2} y = 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.843

13900	$y^{'''} = 1$	[[_3rd_order, _quadrature]]	✓	0.112

2.2.139 Problems 13801 to 13900