Problems 13501 to 13600

Table 2.273: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

13501	$(x^{4} - 2 x^{3} + x^{2}) y^{''} + 2 (- 1 + x) y^{'} + x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.156

13502	$(x^{5} + x^{4} - 6 x^{3}) y^{''} + x^{2} y^{'} + (- 2 + x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.112

13503	$2 x^{2} y^{''} + x y^{'} + (x^{2} - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.639

13504	$2 x^{2} y^{''} + x y^{'} + (2 x^{2} - 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.623

13505	$x^{2} y^{''} - x y^{'} + (x^{2} + \frac{8}{9}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.631

13506	$x^{2} y^{''} - x y^{'} + (2 x^{2} + \frac{5}{9}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.635

13507	$x^{2} y^{''} + x y^{'} + (x^{2} - \frac{1}{9}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.613

13508	$2 x y^{''} + y^{'} + 2 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.652

13509	$3 x y^{''} - (- 2 + x) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.683

13510	$x y^{''} + 2 y^{'} + x y = 0$	[_Lienard]	✓	0.577

13511	$x^{2} y^{''} + x y^{'} + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.653

13512	$x^{2} y^{''} + (x^{4} + x) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.622

13513	$x y^{''} - (x^{2} + 2) y^{'} + x y = 0$	[_Lienard]	✓	0.608

13514	$x^{2} y^{''} + x^{2} y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.710

13515	$(2 x^{2} - x) y^{''} + (2 x - 2) y^{'} + (- 2 x^{2} + 3 x - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.739

13516	$x^{2} y^{''} - x y^{'} + \frac{3 y}{4} = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.613

13517	$x^{2} y^{''} + x y^{'} + (- 1 + x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.250

13518	$x^{2} y^{''} + (x^{3} - x) y^{'} - 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.286

13519	$x^{2} y^{''} - x y^{'} + 8 (x^{2} - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.293

13520	$x^{2} y^{''} + x^{2} y^{'} - \frac{3 y}{4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.390

13521	$x y^{''} + y^{'} + 2 y = 0$	[[_Emden, _Fowler]]	✓	0.505

13522	$2 x y^{''} + 6 y^{'} + y = 0$	[[_Emden, _Fowler]]	✓	1.203

13523	$x^{2} y^{''} - x y^{'} + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.507

13524	$x^{2} y^{''} - x y^{'} + (x^{2} - 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.235

13525	$[\begin{matrix} x^{'} + y^{'} - 2 x - 4 y = e^{t} \\ x^{'} + y^{'} - y = e^{4 t} \end{matrix}]$	system_of_ODEs	✓	0.277

13526	$[\begin{matrix} x^{'} + y^{'} - x = - 2 t \\ x^{'} + y^{'} - 3 x - y = t^{2} \end{matrix}]$	system_of_ODEs	✓	0.175

13527	$[\begin{matrix} x^{'} + y^{'} - x - 3 y = e^{t} \\ x^{'} + y^{'} + x = e^{3 t} \end{matrix}]$	system_of_ODEs	✓	0.176

13528	$[\begin{matrix} x^{'} + y^{'} - x - 2 y = 2 e^{t} \\ x^{'} + y^{'} - 3 x - 4 y = e^{2 t} \end{matrix}]$	system_of_ODEs	✓	0.103

13529	$[\begin{matrix} 2 x^{'} + y^{'} - x - y = e^{- t} \\ x^{'} + 2 x + y^{'} + y = e^{t} \end{matrix}]$	system_of_ODEs	✓	0.767

13530	$[\begin{matrix} 2 x^{'} + y^{'} - 3 x - y = t \\ x^{'} + y^{'} - 4 x - y = e^{t} \end{matrix}]$	system_of_ODEs	✓	0.476

13531	$[\begin{matrix} x^{'} + y^{'} - x - 6 y = e^{3 t} \\ x^{'} + 2 y^{'} - 2 x - 6 y = t \end{matrix}]$	system_of_ODEs	✓	0.713

13532	$[\begin{matrix} x^{'} + y^{'} - x - 3 y = 3 t \\ x^{'} + 2 y^{'} - 2 x - 3 y = 1 \end{matrix}]$	system_of_ODEs	✓	0.710

13533	$[\begin{matrix} x^{'} + y^{'} + 2 y = \sin (t) \\ x^{'} + y^{'} - x - y = 0 \end{matrix}]$	system_of_ODEs	✓	0.305

13534	$[\begin{matrix} x^{'} - y^{'} - 2 x + 4 y = t \\ x^{'} + y^{'} - x - y = 1 \end{matrix}]$	system_of_ODEs	✓	0.486

13535	$[\begin{matrix} 2 x^{'} + y^{'} + x + 5 y = 4 t \\ x^{'} + y^{'} + 2 x + 2 y = 2 \end{matrix}]$	system_of_ODEs	✓	0.459

13536	$[\begin{matrix} x^{'} + y^{'} - x + 5 y = t^{2} \\ x^{'} + 2 y^{'} - 2 x + 4 y = 2 t + 1 \end{matrix}]$	system_of_ODEs	✓	1.559

13537	$[\begin{matrix} 2 x^{'} + y^{'} + x + y = t^{2} + 4 t \\ x^{'} + y^{'} + 2 x + 2 y = 2 t^{2} - 2 t \end{matrix}]$	system_of_ODEs	✓	0.479

13538	$[\begin{matrix} 3 x^{'} + 2 y^{'} - x + y = t - 1 \\ x^{'} + y^{'} - x = t + 2 \end{matrix}]$	system_of_ODEs	✓	0.718

13539	$[\begin{matrix} 2 x^{'} + 4 y^{'} + x - y = 3 e^{t} \\ x^{'} + y^{'} + 2 x + 2 y = e^{t} \end{matrix}]$	system_of_ODEs	✓	0.520

13540	$[\begin{matrix} 2 x^{'} + y^{'} - x - y = - 2 t \\ x^{'} + y^{'} + x - y = t^{2} \end{matrix}]$	system_of_ODEs	✓	0.467

13541	$[\begin{matrix} 2 x^{'} + y^{'} - x - y = 1 \\ x^{'} + y^{'} + 2 x - y = t \end{matrix}]$	system_of_ODEs	✓	0.468

13542	$[\begin{matrix} x^{'} = 3 x + 4 y \\ y^{'} = 2 x + y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.567

13543	$[\begin{matrix} x^{'} = 5 x + 3 y \\ y^{'} = 4 x + y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.585

13544	$[\begin{matrix} x^{'} = 5 x + 2 y + 5 t \\ y^{'} = 3 x + 4 y + 17 t \end{matrix}]$	system_of_ODEs	✓	0.504

13545	$[\begin{matrix} x^{'} = 5 x - 2 y \\ y^{'} = 4 x - y \end{matrix}]$	system_of_ODEs	✓	0.439

13546	$[\begin{matrix} x^{'} = 5 x - y \\ y^{'} = 3 x + y \end{matrix}]$	system_of_ODEs	✓	0.447

13547	$[\begin{matrix} x^{'} = - 2 x + 7 y \\ y^{'} = 3 x + 2 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.604

13548	$[\begin{matrix} x^{'} = - 2 x + y \\ y^{'} = 7 x + 4 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.605

13549	$[\begin{array}{cc} 1 & 2 \\ 3 & 2 \end{array}]$	Eigenvectors	✓	0.116

13550	$[\begin{array}{cc} 3 & 2 \\ 6 & - 1 \end{array}]$	Eigenvectors	✓	0.119

13551	$[\begin{array}{cc} 3 & 1 \\ 12 & 2 \end{array}]$	Eigenvectors	✓	0.122

13552	$[\begin{array}{cc} - 2 & 7 \\ 3 & 2 \end{array}]$	Eigenvectors	✓	0.131

13553	$[\begin{array}{cc} 3 & 4 \\ 5 & 2 \end{array}]$	Eigenvectors	✓	0.117

13554	$[\begin{array}{cc} 3 & - 5 \\ - 4 & 2 \end{array}]$	Eigenvectors	✓	0.132

13555	$[\begin{array}{ccc} 1 & 1 & - 1 \\ 2 & 3 & - 4 \\ 4 & 1 & - 4 \end{array}]$	Eigenvectors	✓	0.275

13556	$[\begin{array}{ccc} 1 & - 1 & - 1 \\ 1 & 3 & 1 \\ - 3 & - 6 & 6 \end{array}]$	Eigenvectors	✓	0.287

13557	$[\begin{array}{ccc} 1 & - 1 & - 1 \\ 1 & 3 & 1 \\ - 3 & 1 & - 1 \end{array}]$	Eigenvectors	✓	0.268

13558	$[\begin{array}{ccc} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end{array}]$	Eigenvectors	✓	0.256

13559	$[\begin{array}{ccc} 1 & 3 & - 6 \\ 0 & 2 & 2 \\ 0 & - 1 & 5 \end{array}]$	Eigenvectors	✓	0.256

13560	$[\begin{array}{ccc} - 5 & - 12 & 6 \\ 1 & 5 & - 1 \\ - 7 & - 10 & 8 \end{array}]$	Eigenvectors	✓	0.284

13561	$[\begin{array}{ccc} - 2 & 5 & 5 \\ - 1 & 4 & 5 \\ 3 & - 3 & 2 \end{array}]$	Eigenvectors	✓	0.283

13562	$[\begin{array}{ccc} - 2 & 6 & - 18 \\ 12 & - 23 & 66 \\ 5 & - 10 & 29 \end{array}]$	Eigenvectors	✓	0.284

13563	$[\begin{matrix} x^{'} = x + y - z \\ y^{'} = 2 x + 3 y - 4 z \\ z^{'} = 4 x + y - 4 z \end{matrix}]$	system_of_ODEs	✓	0.533

13564	$[\begin{matrix} x^{'} = x - y - z \\ y^{'} = x + 3 y + z \\ z^{'} = - 3 x - 6 y + 6 z \end{matrix}]$	system_of_ODEs	✓	0.501

13565	$y^{'} - y = e^{3 t}$ i.c.	[[_linear, ‘class A‘]]	✓	0.479

13566	$y^{'} + y = 2 \sin (t)$ i.c.	[[_linear, ‘class A‘]]	✓	0.485

13567	$y^{''} - 5 y^{'} + 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.200

13568	$y^{''} + y^{'} - 12 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.299

13569	$y^{''} + 4 y = 8$ i.c.	[[_2nd_order, _missing_x]]	✓	0.355

13570	$y^{''} + 2 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.374

13571	$y^{''} - y^{'} - 2 y = 18 e^{- t} \sin (3 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.507

13572	$y^{''} + 2 y^{'} + y = t e^{- 2 t}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.338

13573	$y^{''} + 7 y^{'} + 10 y = 4 t e^{- 3 t}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.333

13574	$y^{''} - 8 y^{'} + 15 y = 9 t e^{2 t}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.328

13575	$y^{'''} - 5 y^{''} + 7 y^{'} - 3 y = 20 \sin (t)$ i.c.	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.440

13576	$y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = 36 t e^{4 t}$ i.c.	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.399

13577	$y^{''} - 3 y^{'} + 2 y = {\begin{array}{cc} 2 & 0 < t < 4 \\ 0 & 4 < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.920

13578	$y^{''} + 5 y^{'} + 6 y = {\begin{array}{cc} 6 & 0 < t < 2 \\ 0 & 2 < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.089

13579	$y^{''} + 4 y^{'} + 5 y = {\begin{array}{cc} 1 & 0 < t < \frac{π}{2} \\ 0 & \frac{π}{2} < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.651

13580	$y^{''} + 6 y^{'} + 8 y = {\begin{array}{cc} 3 & 0 < t < 2 π \\ 0 & 2 π < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.859

13581	$y^{''} + 4 y = {\begin{array}{cc} - 4 t + 8 π & 0 < t < 2 π \\ 0 & 2 < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.156

13582	$y^{''} + y = {\begin{array}{cc} t & 0 < t < π \\ π & π < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.753

13583	$t x^{''} - 2 x^{'} + 9 t^{5} x = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.253

13584	$t^{3} x^{'''} - 3 t^{2} x^{''} + 6 t x^{'} - 6 x = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.114

13585	$(t^{3} - 2 t^{2}) x^{''} - (t^{3} + 2 t^{2} - 6 t) x^{'} + (3 t^{2} - 6) x = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.436

13586	$t^{3} x^{'''} - (3 + t) t^{2} x^{''} + 2 t (3 + t) x^{'} - 2 (3 + t) x = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.042

13587	$t^{2} x^{''} + 3 t x^{'} + 3 x = 0$	[[_Emden, _Fowler]]	✓	2.262

13588	$(2 t + 1) x^{''} + t^{3} x^{'} + x = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.007

13589	$t^{2} x^{''} + (2 t^{3} + 7 t) x^{'} + (8 t^{2} + 8) x = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.182

13590	$t^{3} x^{''} - (t^{3} + 2 t^{2} - t) x^{'} + (t^{2} + t - 1) x = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.260

13591	$t^{3} x^{''} + 3 t^{2} x^{'} + x = 0$	[[_Emden, _Fowler]]	✓	0.745

13592	$\sin (t) x^{''} + \cos (t) x^{'} + 2 x = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.853

13593	$\frac{(t + 1) x^{''}}{t} - \frac{x^{'}}{t^{2}} + \frac{x}{t^{3}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.013

13594	$t^{2} x^{''} + t x^{'} + x = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.145

13595	$(t^{4} + t^{2}) x^{''} + 2 t^{3} x^{'} + 3 x = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.974

13596	$x^{''} - \tan (t) x^{'} + x = 0$	[_Lienard]	✗	1.252

13597	$f (t) x^{''} + x g (t) = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.433

13598	$x^{''} + (t + 1) x = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.418

13599	$y^{''} + λ y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.071

13600	$y^{''} + λ y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.020

2.2.136 Problems 13501 to 13600