Problems 14201 to 14300

Table 2.287: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

14201	$x \cos (\frac{y}{x}) y^{'} = y \cos (\frac{y}{x}) - x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	5.373

14202	$y^{''} - 4 y = e^{2 x} \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.879

14203	$x y^{'} - y^{2} \ln (x) + y = 0$	[_Bernoulli]	✓	2.470

14204	$2 x + 2 y - 1 + (x + y - 2) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.869

14205	$3 e^{x} \tan (y) + (1 - e^{x}) \sec {(y)}^{2} y^{'} = 0$	[_separable]	✓	3.513

14206	$[\begin{matrix} x^{'} = 2 x - 3 y \\ y^{'} = 5 x + 6 y \end{matrix}]$	system_of_ODEs	✓	0.804

14207	$[\begin{matrix} x^{'} = - 4 x - 10 y \\ y^{'} = x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.571

14208	$[\begin{matrix} x^{'} = 12 x + 18 y \\ y^{'} = - 8 x - 12 y \end{matrix}]$	system_of_ODEs	✓	0.420

14209	$y^{'} = x + y^{2}$ i.c.	[[_Riccati, _special]]	✓	2.055

14210	$y^{'} + \frac{y}{x} = e^{x}$ i.c.	[_linear]	✓	1.484

14211	$[\begin{matrix} x^{'} = y - x \\ y^{'} = - x - 3 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.564

14212	$[\begin{matrix} x^{'} = x - 5 y \\ y^{'} = x - y \end{matrix}]$	system_of_ODEs	✓	0.526

14213	$[\begin{matrix} x^{'} = x + y \\ y^{'} = x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.588

14214	$[\begin{matrix} x^{'} = - 4 x + 2 y \\ y^{'} = 3 x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.684

14215	$[\begin{matrix} x^{'} = x + 2 y \\ y^{'} = 2 x + 2 y \end{matrix}]$	system_of_ODEs	✓	0.598

14216	$[\begin{matrix} x^{'} = 4 x - 2 y \\ y^{'} = 3 x - y \end{matrix}]$	system_of_ODEs	✓	0.457

14217	$[\begin{matrix} x^{'} = 2 x + y \\ y^{'} = y - x \end{matrix}]$	system_of_ODEs	✓	0.775

14218	$[\begin{matrix} x^{'} = 3 x - y \\ y^{'} = x + y \end{matrix}]$	system_of_ODEs	✓	0.439

14219	$[\begin{matrix} x^{'} = x - y \\ y^{'} = 2 x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.456

14220	$[\begin{matrix} x^{'} = x \\ y^{'} = 2 x - 3 y \end{matrix}]$	system_of_ODEs	✓	0.444

14221	$[\begin{matrix} x^{'} = x \\ y^{'} = x + 3 y \end{matrix}]$	system_of_ODEs	✓	0.440

14222	$[\begin{matrix} x^{'} = - y \\ y^{'} = 2 x - 4 y \end{matrix}]$	system_of_ODEs	✓	0.594

14223	$[\begin{matrix} x^{'} = x \\ y^{'} = y \end{matrix}]$	system_of_ODEs	✓	0.297

14224	$[\begin{matrix} x^{'} = 0 \\ y^{'} = x \end{matrix}]$	system_of_ODEs	✓	0.302

14225	$x^{''} + x - x^{3} = 0$	[[_2nd_order, _missing_x], _Duﬃng, [_2nd_order, _reducible, _mu_x_y1]]	✓	4.732

14226	$x^{''} + x + x^{3} = 0$	[[_2nd_order, _missing_x], _Duﬃng, [_2nd_order, _reducible, _mu_x_y1]]	✓	5.082

14227	$x^{''} + x^{'} + x - x^{3} = 0$	[[_2nd_order, _missing_x]]	✗	1.933

14228	$x^{''} + x^{'} + x + x^{3} = 0$	[[_2nd_order, _missing_x]]	✗	1.914

14229	$x^{''} = (2 \cos (x) - 1) \sin (x)$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	4.000

14230	$[\begin{matrix} x^{'} = x - 5 y \\ y^{'} = x - y \end{matrix}]$	system_of_ODEs	✓	0.538

14231	$x^{2} y^{''} + x y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.233

14232	$- y + x y^{'} = 0$	[_separable]	✓	1.667

14233	$2 x^{2} y^{''} + 3 x y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.994

14234	$y^{''} - 3 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.846

14235	$x^{2} y^{''} - 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.669

14236	$y^{'} + \frac{1}{2 y} = 0$	[_quadrature]	✓	1.857

14237	$y^{'} - \frac{y}{x} = 1$	[_linear]	✓	1.557

14238	$y^{'} - 2 \sqrt{\| y \|} = 0$	[_quadrature]	✓	2.973

14239	$x^{2} y^{'} + 2 x y = 0$	[_separable]	✓	2.262

14240	$y^{'} - y^{2} = 1$	[_quadrature]	✓	3.381

14241	$2 x^{2} y^{''} + x y^{'} - y = 0$	[[_Emden, _Fowler]]	✓	0.934

14242	$x y^{'} - \sin (x) = 0$	[_quadrature]	✓	0.584

14243	$y^{'} + 3 y = 0$	[_quadrature]	✓	1.753

14244	$y^{''} - 3 y^{'} - 10 y = 0$	[[_2nd_order, _missing_x]]	✓	0.880

14245	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.970

14246	$y^{'''} - 7 y^{''} + 12 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.050

14247	$2 x y^{'} - y = 0$	[_separable]	✓	2.242

14248	$x^{2} y^{''} - x y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.514

14249	$x^{2} y^{''} + 6 x y^{'} + 4 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.189

14250	$x^{2} y^{''} - 5 x y^{'} + 9 y = 0$	[[_Emden, _Fowler]]	✓	0.879

14251	${y^{'}}^{2} - 4 y = 0$	[_quadrature]	✓	0.378

14252	${y^{'}}^{2} - 9 x y = 0$	[[_homogeneous, ‘class G‘]]	✓	0.654

14253	${y^{'}}^{2} = x^{6}$	[_quadrature]	✓	0.558

14254	$y^{'} - 2 x y = 0$	[_separable]	✓	1.652

14255	$y^{'} + y = x^{2} + 2 x - 1$	[[_linear, ‘class A‘]]	✓	1.354

14256	$y^{''} - y^{'} - 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.838

14257	$y^{'} = x \sqrt{y}$	[_separable]	✓	4.438

14258	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	2.050

14259	$y^{'} = 3 y^{2 / 3}$	[_quadrature]	✓	2.115

14260	$x \ln (x) y^{'} - (1 + \ln (x)) y = 0$	[_separable]	✓	1.821

14261	$y^{''} - y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.370

14262	$y^{''} - y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.450

14263	$y^{''} - y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.967

14264	$y^{''} - y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.961

14265	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 x y^{'} - 6 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.109

14266	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.752

14267	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.833

14268	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.733

14269	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.760

14270	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.272

14271	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✗	0.989

14272	$y^{'} = 1 - x$	[_quadrature]	✓	0.449

14273	$y^{'} = - 1 + x$	[_quadrature]	✓	0.444

14274	$y^{'} = 1 - y$	[_quadrature]	✓	1.427

14275	$y^{'} = y + 1$	[_quadrature]	✓	1.386

14276	$y^{'} = y^{2} - 4$	[_quadrature]	✓	3.904

14277	$y^{'} = 4 - y^{2}$	[_quadrature]	✓	3.749

14278	$y^{'} = x y$	[_separable]	✓	1.645

14279	$y^{'} = - x y$	[_separable]	✓	1.687

14280	$y^{'} = x^{2} - y^{2}$	[_Riccati]	✓	1.173

14281	$y^{'} = y^{2} - x^{2}$	[_Riccati]	✓	1.165

14282	$y^{'} = x + y$	[[_linear, ‘class A‘]]	✓	1.287

14283	$y^{'} = x y$	[_separable]	✓	1.661

14284	$y^{'} = \frac{x}{y}$	[_separable]	✓	4.490

14285	$y^{'} = \frac{y}{x}$	[_separable]	✓	1.683

14286	$y^{'} = 1 + y^{2}$	[_quadrature]	✓	3.300

14287	$y^{'} = y^{2} - 3 y$	[_quadrature]	✓	2.017

14288	$y^{'} = x^{3} + y^{3}$	[_Abel]	✗	0.757

14289	$y^{'} = \| y \|$	[_quadrature]	✓	1.481

14290	$y^{'} = e^{x - y}$	[_separable]	✓	2.422

14291	$y^{'} = \ln (x + y)$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	1.178

14292	$y^{'} = \frac{2 x - y}{x + 3 y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.386

14293	$y^{'} = \frac{1}{\sqrt{15 - x^{2} - y^{2}}}$	[‘y=_G(x,y’)‘]	✗	1.530

14294	$y^{'} = \frac{3 y}{(x - 5) (x + 3)} + e^{- x}$	[_linear]	✓	2.224

14295	$y^{'} = \frac{x y}{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	15.597

14296	$y^{'} = \frac{1}{x y}$	[_separable]	✓	2.480

14297	$y^{'} = \ln (y - 1)$	[_quadrature]	✓	1.332

14298	$y^{'} = \sqrt{(y + 2) (y - 1)}$	[_quadrature]	✓	54.013

14299	$y^{'} = \frac{y}{y - x}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.275

14300	$y^{'} = \frac{x}{y^{2}}$	[_separable]	✓	2.495

2.2.143 Problems 14201 to 14300