Problems 14201 to 14300

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


#	ODE	CAS classiﬁcation	Solved?	time (sec)

14201	$[\begin{matrix} x^{'} = 1 + y \\ y^{'} = 1 + x \end{matrix}]$ i.c.	system_of_ODEs	✓	0.651

14202	$[\begin{matrix} x^{'} = x - 2 y \\ y^{'} = x - y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.492

14203	$[\begin{matrix} 4 x^{'} - y^{'} + 3 x = \sin (t) \\ x^{'} + y = \cos (t) \end{matrix}]$	system_of_ODEs	✓	0.878

14204	$y y^{''} = 1 + {y^{'}}^{2}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.578

14205	$\frac{x^{2} y^{'}}{{(x - y)}^{2}} - \frac{y^{2}}{{(x - y)}^{2}} = 0$	[_separable]	✓	2.338

14206	$y = x {y^{'}}^{2} + {y^{'}}^{2}$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	0.602

14207	$y^{''} + y = \sec (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.712

14208	$(x^{2} + 1) y^{'} - x y - α = 0$	[_linear]	✓	2.619

14209	$x \cos (\frac{y}{x}) y^{'} = y \cos (\frac{y}{x}) - x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	5.937

14210	$y^{''} - 4 y = e^{2 x} \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.899

14211	$y^{'} x - y^{2} \ln (x) + y = 0$	[_Bernoulli]	✓	2.090

14212	$2 x + 2 y - 1 + (x + y - 2) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.838

14213	$3 e^{x} \tan (y) + (1 - e^{x}) \sec {(y)}^{2} y^{'} = 0$	[_separable]	✓	3.359

14214	$[\begin{matrix} x^{'} = 2 x - 3 y \\ y^{'} = 5 x + 6 y \end{matrix}]$	system_of_ODEs	✓	0.731

14215	$[\begin{matrix} x^{'} = - 4 x - 10 y \\ y^{'} = x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.507

14216	$[\begin{matrix} x^{'} = 12 x + 18 y \\ y^{'} = - 8 x - 12 y \end{matrix}]$	system_of_ODEs	✓	0.285

14217	$y^{'} = x + y^{2}$ i.c.	[[_Riccati, _special]]	✓	2.188

14218	$y^{'} + \frac{y}{x} = e^{x}$ i.c.	[_linear]	✓	1.351

14219	$[\begin{matrix} x^{'} = - x + y \\ y^{'} = - x - 3 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.487

14220	$[\begin{matrix} x^{'} = x - 5 y \\ y^{'} = x - y \end{matrix}]$	system_of_ODEs	✓	0.474

14221	$[\begin{matrix} x^{'} = x + y \\ y^{'} = x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.552

14222	$[\begin{matrix} x^{'} = - 4 x + 2 y \\ y^{'} = 3 x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.528

14223	$[\begin{matrix} x^{'} = x + 2 y \\ y^{'} = 2 x + 2 y \end{matrix}]$	system_of_ODEs	✓	0.495

14224	$[\begin{matrix} x^{'} = 4 x - 2 y \\ y^{'} = 3 x - y \end{matrix}]$	system_of_ODEs	✓	0.334

14225	$[\begin{matrix} x^{'} = 2 x + y \\ y^{'} = - x + y \end{matrix}]$	system_of_ODEs	✓	0.699

14226	$[\begin{matrix} x^{'} = 3 x - y \\ y^{'} = x + y \end{matrix}]$	system_of_ODEs	✓	0.373

14227	$[\begin{matrix} x^{'} = x - y \\ y^{'} = 2 x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.300

14228	$[\begin{matrix} x^{'} = x \\ y^{'} = 2 x - 3 y \end{matrix}]$	system_of_ODEs	✓	0.319

14229	$[\begin{matrix} x^{'} = x \\ y^{'} = x + 3 y \end{matrix}]$	system_of_ODEs	✓	0.371

14230	$[\begin{matrix} x^{'} = - y \\ y^{'} = 2 x - 4 y \end{matrix}]$	system_of_ODEs	✓	0.560

14231	$[\begin{matrix} x^{'} = x \\ y^{'} = y \end{matrix}]$	system_of_ODEs	✓	0.248

14232	$[\begin{matrix} x^{'} = 0 \\ y^{'} = x \end{matrix}]$	system_of_ODEs	✓	0.250

14233	$x^{''} + x - x^{3} = 0$	[[_2nd_order, _missing_x], _Duﬃng, [_2nd_order, _reducible, _mu_x_y1]]	✓	6.187

14234	$x^{''} + x + x^{3} = 0$	[[_2nd_order, _missing_x], _Duﬃng, [_2nd_order, _reducible, _mu_x_y1]]	✓	6.663

14235	$x^{''} + x^{'} + x - x^{3} = 0$	[[_2nd_order, _missing_x]]	✗	2.237

14236	$x^{''} + x^{'} + x + x^{3} = 0$	[[_2nd_order, _missing_x]]	✗	2.261

14237	$x^{''} = (2 \cos (x) - 1) \sin (x)$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	3.355

14238	$[\begin{matrix} x^{'} = x - 5 y \\ y^{'} = x - y \end{matrix}]$	system_of_ODEs	✓	0.469

14239	$x^{2} y^{''} + y^{'} x - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.135

14240	$y^{'} x - y = 0$	[_separable]	✓	1.260

14241	$2 x^{2} y^{''} + 3 y^{'} x - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.007

14242	$y^{''} - 3 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.321

14243	$x^{2} y^{''} - 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.667

14244	$y^{'} + \frac{1}{2 y} = 0$	[_quadrature]	✓	0.930

14245	$y^{'} - \frac{y}{x} = 1$	[_linear]	✓	1.307

14246	$y^{'} - 2 \sqrt{\| y \|} = 0$	[_quadrature]	✓	3.266

14247	$x^{2} y^{'} + 2 x y = 0$	[_separable]	✓	1.596

14248	$y^{'} - y^{2} = 1$	[_quadrature]	✓	3.899

14249	$2 x^{2} y^{''} + y^{'} x - y = 0$	[[_Emden, _Fowler]]	✓	0.918

14250	$y^{'} x - \sin (x) = 0$	[_quadrature]	✓	0.434

14251	$y^{'} + 3 y = 0$	[_quadrature]	✓	0.884

14252	$y^{''} - 3 y^{'} - 10 y = 0$	[[_2nd_order, _missing_x]]	✓	0.359

14253	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.357

14254	$y^{'''} - 7 y^{''} + 12 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.074

14255	$2 y^{'} x - y = 0$	[_separable]	✓	1.515

14256	$x^{2} y^{''} - y^{'} x = 0$	[[_2nd_order, _missing_y]]	✓	0.561

14257	$x^{2} y^{''} + 6 y^{'} x + 4 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.133

14258	$x^{2} y^{''} - 5 y^{'} x + 9 y = 0$	[[_Emden, _Fowler]]	✓	0.967

14259	${y^{'}}^{2} - 4 y = 0$	[_quadrature]	✓	0.471

14260	${y^{'}}^{2} - 9 x y = 0$	[[_homogeneous, ‘class G‘]]	✓	0.789

14261	${y^{'}}^{2} = x^{6}$	[_quadrature]	✓	0.429

14262	$y^{'} - 2 x y = 0$	[_separable]	✓	1.196

14263	$y^{'} + y = x^{2} + 2 x - 1$	[[_linear, ‘class A‘]]	✓	1.075

14264	$y^{''} - y^{'} - 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.354

14265	$y^{'} = x \sqrt{y}$	[_separable]	✓	5.329

14266	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	1.551

14267	$y^{'} = 3 y^{2 / 3}$	[_quadrature]	✓	1.369

14268	$x \ln (x) y^{'} - (1 + \ln (x)) y = 0$	[_separable]	✓	1.701

14269	$y^{''} - y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.577

14270	$y^{''} - y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.567

14271	$y^{''} - y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.564

14272	$y^{''} - y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.427

14273	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 y^{'} x - 6 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.149

14274	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.812

14275	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.792

14276	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.782

14277	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.697

14278	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.282

14279	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✗	1.381

14280	$y^{'} = 1 - x$	[_quadrature]	✓	0.341

14281	$y^{'} = x - 1$	[_quadrature]	✓	0.333

14282	$y^{'} = 1 - y$	[_quadrature]	✓	0.630

14283	$y^{'} = 1 + y$	[_quadrature]	✓	0.597

14284	$y^{'} = y^{2} - 4$	[_quadrature]	✓	4.192

14285	$y^{'} = 4 - y^{2}$	[_quadrature]	✓	4.320

14286	$y^{'} = x y$	[_separable]	✓	1.104

14287	$y^{'} = - x y$	[_separable]	✓	1.198

14288	$y^{'} = x^{2} - y^{2}$	[_Riccati]	✓	1.439

14289	$y^{'} = y^{2} - x^{2}$	[_Riccati]	✓	1.462

14290	$y^{'} = x + y$	[[_linear, ‘class A‘]]	✓	1.021

14291	$y^{'} = x y$	[_separable]	✓	1.166

14292	$y^{'} = \frac{x}{y}$	[_separable]	✓	3.725

14293	$y^{'} = \frac{y}{x}$	[_separable]	✓	1.309

14294	$y^{'} = 1 + y^{2}$	[_quadrature]	✓	3.987

14295	$y^{'} = y^{2} - 3 y$	[_quadrature]	✓	1.055

14296	$y^{'} = x^{3} + y^{3}$	[_Abel]	✗	0.846

14297	$y^{'} = \| y \|$	[_quadrature]	✓	1.340

14298	$y^{'} = e^{x - y}$	[_separable]	✓	1.914

14299	$y^{'} = \ln (x + y)$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	1.255

14300	$y^{'} = \frac{2 x - y}{x + 3 y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.883

2.2.143 Problems 14201 to 14300