Problems 14401 to 14500

Table 2.291: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

14401	$y^{'} = x \sqrt{1 - y^{2}}$ i.c.	[_separable]	✓	10.640

14402	$y^{'} = x \sqrt{1 - y^{2}}$ i.c.	[_separable]	✓	4.978

14403	$y^{'} = x \sqrt{1 - y^{2}}$ i.c.	[_separable]	✓	4.291

14404	$y^{'} = - \frac{x}{2} + \frac{\sqrt{x^{2} + 4 y}}{2}$ i.c.	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	2.475

14405	$y^{'} = - \frac{x}{2} + \frac{\sqrt{x^{2} + 4 y}}{2}$ i.c.	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	3.147

14406	$y^{'} = - \frac{x}{2} + \frac{\sqrt{x^{2} + 4 y}}{2}$ i.c.	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	2.526

14407	$y^{'} = - \frac{x}{2} + \frac{\sqrt{x^{2} + 4 y}}{2}$ i.c.	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	3.545

14408	$y^{'} = - \frac{x}{2} + \frac{\sqrt{x^{2} + 4 y}}{2}$ i.c.	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	2.306

14409	$3 y^{''} - 2 y^{'} + 4 y = x$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	1.111

14410	$x y^{'''} + y^{'} x = 4$ i.c.	[[_3rd_order, _missing_y]]	✓	1.079

14411	$x (x - 3) y^{''} + 3 y^{'} = x^{2}$ i.c.	[[_2nd_order, _missing_y]]	✓	1.130

14412	$x (x - 3) y^{''} + 3 y^{'} = x^{2}$ i.c.	[[_2nd_order, _missing_y]]	✓	1.357

14413	$\sqrt{1 - x} y^{''} - 4 y = \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✗	1.080

14414	$(x^{2} - 4) y^{''} + y \ln (x) = x e^{x}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.665

14415	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	1.612

14416	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	1.421

14417	$x^{2} y^{''} + 2 y^{'} x - 2 y = 0$	[[_Emden, _Fowler]]	✓	0.817

14418	$2 y y^{''} - {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.552

14419	$y^{''} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.623

14420	$y^{'''} + y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.095

14421	$x^{2} y^{''} - y^{'} x + y = 0$ i.c.	[[_Emden, _Fowler]]	✓	1.804

14422	$y^{''} - 4 y = 31$ i.c.	[[_2nd_order, _missing_x]]	✓	1.589

14423	$y^{''} + 9 y = 27 x + 18$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.916

14424	$x^{2} y^{''} + y^{'} x - 4 y = - 3 x - \frac{3}{x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	4.719

14425	$4 y^{''} + 4 y^{'} - 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.344

14426	$y^{'''} - 4 y^{''} + 6 y^{'} - 4 y = 0$	[[_3rd_order, _missing_x]]	✓	0.087

14427	$y^{''''} - 16 y = 0$	[[_high_order, _missing_x]]	✓	0.090

14428	$y^{''''} + 16 y = 0$	[[_high_order, _missing_x]]	✓	0.098

14429	$y^{''''} - 4 y^{'''} + 8 y^{''} - 8 y^{'} + 4 y = 0$	[[_high_order, _missing_x]]	✓	0.104

14430	$y^{''''} - 8 y^{'} = 0$	[[_high_order, _missing_x]]	✓	0.093

14431	$36 y^{''''} - 12 y^{'''} - 11 y^{''} + 2 y^{'} + y = 0$	[[_high_order, _missing_x]]	✓	0.096

14432	$y^{(5)} - 3 y^{''''} + 3 y^{'''} - 3 y^{''} + 2 y^{'} = 0$	[[_high_order, _missing_x]]	✓	0.096

14433	$y^{(5)} - y^{''''} + y^{'''} + 35 y^{''} + 16 y^{'} - 52 y = 0$	[[_high_order, _missing_x]]	✓	0.099

14434	$y^{(8)} + 8 y^{''''} + 16 y = 0$	[[_high_order, _missing_x]]	✓	0.132

14435	$y^{''} + α y = 0$	[[_2nd_order, _missing_x]]	✓	1.798

14436	$y^{'''} + (- 3 - 4 i) y^{''} + (- 4 + 12 i) y^{'} + 12 y = 0$	[[_3rd_order, _missing_x]]	✓	0.122

14437	$y^{''''} + (- 3 - i) y^{'''} + (4 + 3 i) y^{''} = 0$	[[_high_order, _missing_x]]	✓	0.090

14438	$y^{'} - i y = 0$ i.c.	[_quadrature]	✓	1.596

14439	$y^{''''} - 6 y^{'''} + 13 y^{''} - 12 y^{'} + 4 y = 2 e^{x} - 4 e^{2 x}$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.225

14440	$y^{''''} + 4 y^{''} = 24 x^{2} - 6 x + 14 + 32 \cos (2 x)$	[[_high_order, _missing_y]]	✓	0.846

14441	$y^{''''} + 2 y^{''} + y = 3 + \cos (2 x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.232

14442	$y^{''''} - 3 y^{'''} + 3 y^{''} - y^{'} = 6 x - 20 - 120 x^{2} e^{x}$	[[_high_order, _missing_y]]	✓	0.232

14443	$y^{'''} - 6 y^{''} + 21 y^{'} - 26 y = 36 e^{2 x} \sin (3 x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.671

14444	$y^{'''} + y^{''} - y^{'} - y = (2 x^{2} + 4 x + 8) \cos (x) + (6 x^{2} + 8 x + 12) \sin (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.369

14445	$y^{(6)} - 12 y^{(5)} + 63 y^{''''} - 18 y^{'''} + 315 y^{''} - 300 y^{'} + 125 y = e^{x} (48 \cos (x) + 96 \sin (x))$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.338

14446	$y^{'''} - 3 y^{''} - 4 y^{'} + 12 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.154

14447	$y^{''''} - 2 y^{'''} + 2 y^{'} - y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.149

14448	$y^{'''} - y^{''} + y^{'} - y = 2 e^{x}$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓	0.184

14449	$y^{''''} + 2 y^{''} + y = 3 x + 4$ i.c.	[[_high_order, _with_linear_symmetries]]	✓	0.179

14450	$y^{'} - y = 0$	[_quadrature]	✓	0.193

14451	$y^{''} - 2 y^{'} + 5 y = 0$	[[_2nd_order, _missing_x]]	✓	0.296

14452	$2 y + y^{'} = 4$	[_quadrature]	✓	0.254

14453	$y^{''} - 9 y = 2 \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.328

14454	$y^{''} + 9 y = 2 \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.327

14455	$y^{''} + y^{'} - 2 y = x e^{x} - 3 x^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.295

14456	$y^{''''} - 2 y^{'''} + y^{''} = x e^{x} - 3 x^{2}$	[[_high_order, _missing_y]]	✓	0.308

14457	$y^{'} = e^{x}$ i.c.	[_quadrature]	✓	0.306

14458	$y^{'} - y = 2 e^{x}$ i.c.	[[_linear, ‘class A‘]]	✓	0.313

14459	$y^{''} - 9 y = x + 2$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.372

14460	$y^{''} + 9 y = x + 2$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.482

14461	$y^{''} - y^{'} + 6 y = - 2 \sin (3 x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.586

14462	$y^{''} - 2 y^{'} + 2 y = - x^{2} + 1$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.377

14463	$y^{'''} + 3 y^{''} + 2 y^{'} = x + \cos (x)$ i.c.	[[_3rd_order, _missing_y]]	✓	0.529

14464	$y^{'} - 2 y = 6$ i.c.	[_quadrature]	✓	0.366

14465	$y^{'} + y = e^{x}$ i.c.	[[_linear, ‘class A‘]]	✓	0.399

14466	$y^{''} + 9 y = 1$ i.c.	[[_2nd_order, _missing_x]]	✓	0.361

14467	$y^{''} + 9 y = 18 e^{3 x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.423

14468	$y^{''} - y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.302

14469	$y^{''} - y^{'} - 2 y = x^{2}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.352

14470	$y^{''} - 2 y^{'} + y = 2 \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.521

14471	$y^{'''} - y^{''} + 4 y^{'} - 4 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.583

14472	$2 y + y^{'} = {\begin{array}{cc} 2 & 0 \leq x < 1 \\ 1 & 1 \leq x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	0.713

14473	$y^{''} - y^{'} - 2 y = {\begin{array}{cc} 1 & 2 \leq x < 4 \\ 0 & otherwise \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.210

14474	$y^{''} - 2 y^{'} = {\begin{array}{cc} 0 & 0 \leq x < 1 \\ {(x - 1)}^{2} & 1 \leq x \end{array}$ i.c.	[[_2nd_order, _missing_y]]	✓	1.017

14475	$y^{''} - 2 y^{'} + y = {\begin{array}{cc} 0 & 0 \leq x < 1 \\ x^{2} - 2 x + 3 & 1 \leq x \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.121

14476	$y^{''} + 4 y = {\begin{array}{cc} 0 & 0 \leq x < π \\ - \sin (3 x) & π \leq x \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.978

14477	$y^{''} - 4 y = {\begin{array}{cc} x & 0 \leq x < 1 \\ 1 & 1 \leq x \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.063

14478	$y^{''} - 4 y^{'} + 5 y = {\begin{array}{cc} x & 0 \leq x < 1 \\ 1 & 1 \leq x \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.542

14479	$y^{'} + 3 y = δ (x - 2)$ i.c.	[[_linear, ‘class A‘]]	✓	0.581

14480	$y^{'} - 3 y = δ (x - 1) + 2 Heaviside (x - 2)$ i.c.	[[_linear, ‘class A‘]]	✓	0.703

14481	$y^{''} + 9 y = δ (x - π) + δ (x - 3 π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.823

14482	$y^{''} - 2 y^{'} + y = 2 δ (x - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.711

14483	$y^{''} - 2 y^{'} + 5 y = \cos (x) + 2 δ (x - π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.396

14484	$y^{''} + 4 y = \cos (x) δ (x - π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.779

14485	$y^{''} + a^{2} y = δ (x - π) f (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.724

14486	$[\begin{matrix} y_{1}^{'} = 2 y_{1} - 3 y_{2} \\ y_{2}^{'} = y_{1} - 2 y_{2} \end{matrix}]$	system_of_ODEs	✓	0.335

14487	$[\begin{matrix} y_{1}^{'} = y_{1} - 2 y_{2} \\ y_{2}^{'} = y_{1} + 3 y_{2} \end{matrix}]$	system_of_ODEs	✓	0.515

14488	$[\begin{matrix} y_{1}^{'} = y_{1} + 2 y_{2} + x - 1 \\ y_{2}^{'} = 3 y_{1} + 2 y_{2} - 5 x - 2 \end{matrix}]$ i.c.	system_of_ODEs	✓	0.622

14489	$[\begin{matrix} y_{1}^{'} = \frac{2 y_{1}}{x} - \frac{y_{2}}{x^{2}} - 3 + \frac{1}{x} - \frac{1}{x^{2}} \\ y_{2}^{'} = 2 y_{1} + 1 - 6 x \end{matrix}]$ i.c.	system_of_ODEs	✓	0.065

14490	$[\begin{matrix} y_{1}^{'} = \frac{5 y_{1}}{x} + \frac{4 y_{2}}{x} - 2 x \\ y_{2}^{'} = - \frac{6 y_{1}}{x} - \frac{5 y_{2}}{x} + 5 x \end{matrix}]$ i.c.	system_of_ODEs	✓	0.067

14491	$[\begin{matrix} y_{1}^{'} = 3 y_{1} - 2 y_{2} \\ y_{2}^{'} = y_{2} - y_{1} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.650

14492	$[\begin{matrix} y_{1}^{'} = \sin (x) y_{1} + \sqrt{x} y_{2} + \ln (x) \\ y_{2}^{'} = \tan (x) y_{1} - e^{x} y_{2} + 1 \end{matrix}]$ i.c.	system_of_ODEs	✓	0.068

14493	$[\begin{matrix} y_{1}^{'} = \sin (x) y_{1} + \sqrt{x} y_{2} + \ln (x) \\ y_{2}^{'} = \tan (x) y_{1} - e^{x} y_{2} + 1 \end{matrix}]$ i.c.	system_of_ODEs	✓	0.073

14494	$[\begin{matrix} y_{1}^{'} = e^{- x} y_{1} - \sqrt{x + 1} y_{2} + x^{2} \\ y_{2}^{'} = \frac{y_{1}}{{(x - 2)}^{2}} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.077

14495	$[\begin{matrix} y_{1}^{'} = e^{- x} y_{1} - \sqrt{x + 1} y_{2} + x^{2} \\ y_{2}^{'} = \frac{y_{1}}{{(x - 2)}^{2}} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.076

14496	$[\begin{array}{cc} - 2 & - 4 \\ 1 & 3 \end{array}]$	Eigenvectors	✓	0.145

14497	$[\begin{array}{cc} - 3 & - 1 \\ 2 & - 1 \end{array}]$	Eigenvectors	✓	0.178

14498	$[\begin{array}{ccc} 1 & 0 & 1 \\ 0 & 1 & - 1 \\ - 2 & 0 & - 1 \end{array}]$	Eigenvectors	✓	0.323

14499	$[\begin{array}{ccc} 3 & 1 & - 1 \\ 1 & 3 & - 1 \\ 3 & 3 & - 1 \end{array}]$	Eigenvectors	✓	0.201

14500	$[\begin{array}{ccc} 7 & - 1 & 6 \\ - 10 & 4 & - 12 \\ - 2 & 1 & - 1 \end{array}]$	Eigenvectors	✓	0.296

2.2.145 Problems 14401 to 14500