Problems 1001 to 1100

Table 2.23: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

1001	$[\begin{matrix} x_{1}^{'} = 47 x_{1} - 8 x_{2} + 5 x_{3} - 5 x_{4} \\ x_{2}^{'} = - 10 x_{1} + 32 x_{2} + 18 x_{3} - 2 x_{4} \\ x_{3}^{'} = 139 x_{1} - 40 x_{2} - 167 x_{3} - 121 x_{4} \\ x_{4}^{'} = - 232 x_{1} + 64 x_{2} + 360 x_{3} + 248 x_{4} \end{matrix}]$	system_of_ODEs	✓	2.595

1002	$[\begin{matrix} x_{1}^{'} = 139 x_{1} - 14 x_{2} - 52 x_{3} - 14 x_{4} + 28 x_{5} \\ x_{2}^{'} = - 22 x_{1} + 5 x_{2} + 7 x_{3} + 8 x_{4} - 7 x_{5} \\ x_{3}^{'} = 370 x_{1} - 38 x_{2} - 139 x_{3} - 38 x_{4} + 76 x_{5} \\ x_{4}^{'} = 152 x_{1} - 16 x_{2} - 59 x_{3} - 13 x_{4} + 35 x_{5} \\ x_{5}^{'} = 95 x_{1} - 10 x_{2} - 38 x_{3} - 7 x_{4} + 23 x_{5} \end{matrix}]$	system_of_ODEs	✓	4.131

1003	$[\begin{matrix} x_{1}^{'} = 9 x_{1} + 13 x_{2} - 13 x_{6} \\ x_{2}^{'} = - 14 x_{1} + 19 x_{2} - 10 x_{3} - 20 x_{4} + 10 x_{5} + 4 x_{6} \\ x_{3}^{'} = - 30 x_{1} + 12 x_{2} - 7 x_{3} - 30 x_{4} + 12 x_{5} + 18 x_{6} \\ x_{4}^{'} = - 12 x_{1} + 10 x_{2} - 10 x_{3} - 9 x_{4} + 10 x_{5} + 2 x_{6} \\ x_{5}^{'} = 6 x_{1} + 9 x_{2} + 6 x_{4} + 5 x_{5} - 15 x_{6} \\ x_{6}^{'} = - 14 x_{1} + 23 x_{2} - 10 x_{3} - 20 x_{4} + 10 x_{5} \end{matrix}]$	system_of_ODEs	✓	3.490

1004	$[\begin{matrix} x_{1}^{'} = 9 x_{1} + 4 x_{2} \\ x_{2}^{'} = - 6 x_{1} - x_{2} \\ x_{3}^{'} = 6 x_{1} + 4 x_{2} + 3 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.495

1005	$[\begin{matrix} x_{1}^{'} = x_{1} - 3 x_{2} \\ x_{2}^{'} = 3 x_{1} + 7 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.334

1006	$[\begin{matrix} x_{1}^{'} = x_{2} + 2 x_{3} \\ x_{2}^{'} = - 5 x_{1} - 3 x_{2} - 7 x_{3} \\ x_{3}^{'} = x_{1} \end{matrix}]$	system_of_ODEs	✓	0.493

1007	$[\begin{matrix} x_{1}^{'} = x_{3} \\ x_{2}^{'} = x_{4} \\ x_{3}^{'} = - 2 x_{1} + 2 x_{2} - 3 x_{3} + x_{4} \\ x_{4}^{'} = 2 x_{1} - 2 x_{2} + x_{3} - 3 x_{4} \end{matrix}]$	system_of_ODEs	✓	0.644

1008	$[\begin{matrix} x_{1}^{'} = - 2 x_{1} + x_{2} \\ x_{2}^{'} = - x_{1} - 4 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.393

1009	$[\begin{matrix} x_{1}^{'} = 3 x_{1} - x_{2} \\ x_{2}^{'} = x_{1} + x_{2} \end{matrix}]$	system_of_ODEs	✓	0.328

1010	$[\begin{matrix} x_{1}^{'} = x_{1} - 2 x_{2} \\ x_{2}^{'} = 2 x_{1} + 5 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.338

1011	$[\begin{matrix} x_{1}^{'} = 3 x_{1} - x_{2} \\ x_{2}^{'} = x_{1} + 5 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.314

1012	$[\begin{matrix} x_{1}^{'} = 7 x_{1} + x_{2} \\ x_{2}^{'} = - 4 x_{1} + 3 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.389

1013	$[\begin{matrix} x_{1}^{'} = x_{1} - 4 x_{2} \\ x_{2}^{'} = 4 x_{1} + 9 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.347

1014	$[\begin{matrix} x_{1}^{'} = 2 x_{1} \\ x_{2}^{'} = - 7 x_{1} + 9 x_{2} + 7 x_{3} \\ x_{3}^{'} = 2 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.485

1015	$[\begin{matrix} x_{1}^{'} = 25 x_{1} + 12 x_{2} \\ x_{2}^{'} = - 18 x_{1} - 5 x_{2} \\ x_{3}^{'} = 6 x_{1} + 6 x_{2} + 13 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.542

1016	$[\begin{matrix} x_{1}^{'} = - 19 x_{1} + 12 x_{2} + 84 x_{3} \\ x_{2}^{'} = 5 x_{2} \\ x_{3}^{'} = - 8 x_{1} + 4 x_{2} + 33 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.575

1017	$[\begin{matrix} x_{1}^{'} = - 13 x_{1} + 40 x_{2} - 48 x_{3} \\ x_{2}^{'} = - 8 x_{1} + 23 x_{2} - 24 x_{3} \\ x_{3}^{'} = 3 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.550

1018	$[\begin{matrix} x_{1}^{'} = - 3 x_{1} - 4 x_{3} \\ x_{2}^{'} = - x_{1} - x_{2} - x_{3} \\ x_{3}^{'} = x_{1} + x_{3} \end{matrix}]$	system_of_ODEs	✓	0.446

1019	$[\begin{matrix} x_{1}^{'} = - x_{1} + x_{3} \\ x_{2}^{'} = - x_{2} + x_{3} \\ x_{3}^{'} = x_{1} - x_{2} - x_{3} \end{matrix}]$	system_of_ODEs	✓	0.407

1020	$[\begin{matrix} x_{1}^{'} = - x_{1} + x_{3} \\ x_{2}^{'} = x_{2} - 4 x_{3} \\ x_{3}^{'} = x_{2} - 3 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.444

1021	$[\begin{matrix} x_{1}^{'} = x_{3} \\ x_{2}^{'} = - 5 x_{1} - x_{2} - 5 x_{3} \\ x_{3}^{'} = 4 x_{1} + x_{2} - 2 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.480

1022	$[\begin{matrix} x_{1}^{'} = - 2 x_{1} - 9 x_{2} \\ x_{2}^{'} = x_{1} + 4 x_{2} \\ x_{3}^{'} = x_{1} + 3 x_{2} + x_{3} \end{matrix}]$	system_of_ODEs	✓	0.435

1023	$[\begin{matrix} x_{1}^{'} = x_{1} \\ x_{2}^{'} = - 2 x_{1} - 2 x_{2} - 3 x_{3} \\ x_{3}^{'} = 2 x_{1} + 3 x_{2} + 4 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.459

1024	$[\begin{matrix} x_{1}^{'} = x_{1} \\ x_{2}^{'} = 18 x_{1} + 7 x_{2} + 4 x_{3} \\ x_{3}^{'} = - 27 x_{1} - 9 x_{2} - 5 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.490

1025	$[\begin{matrix} x_{1}^{'} = x_{1} \\ x_{2}^{'} = x_{1} + 3 x_{2} + x_{3} \\ x_{3}^{'} = - 2 x_{1} - 4 x_{2} - x_{3} \end{matrix}]$	system_of_ODEs	✓	0.445

1026	$[\begin{matrix} x_{1}^{'} = x_{1} - 4 x_{2} - 2 x_{4} \\ x_{2}^{'} = x_{2} \\ x_{3}^{'} = 6 x_{1} - 12 x_{2} - x_{3} - 6 x_{4} \\ x_{4}^{'} = - 4 x_{2} - x_{4} \end{matrix}]$	system_of_ODEs	✓	0.586

1027	$[\begin{matrix} x_{1}^{'} = 2 x_{1} + x_{2} + x_{4} \\ x_{2}^{'} = 2 x_{2} + x_{3} \\ x_{3}^{'} = 2 x_{3} + x_{4} \\ x_{4}^{'} = 2 x_{4} \end{matrix}]$	system_of_ODEs	✓	0.472

1028	$[\begin{matrix} x_{1}^{'} = - x_{1} - 4 x_{2} \\ x_{2}^{'} = x_{1} + 3 x_{2} \\ x_{3}^{'} = x_{1} + 2 x_{2} + x_{3} \\ x_{4}^{'} = x_{2} + x_{4} \end{matrix}]$	system_of_ODEs	✓	0.469

1029	$[\begin{matrix} x_{1}^{'} = x_{1} + 3 x_{2} + 7 x_{3} \\ x_{2}^{'} = - x_{2} - 4 x_{3} \\ x_{3}^{'} = x_{2} + 3 x_{3} \\ x_{4}^{'} = - 6 x_{2} - 14 x_{3} + x_{4} \end{matrix}]$	system_of_ODEs	✓	0.591

1030	$[\begin{matrix} x_{1}^{'} = 39 x_{1} + 8 x_{2} - 16 x_{3} \\ x_{2}^{'} = - 36 x_{1} - 5 x_{2} + 16 x_{3} \\ x_{3}^{'} = 72 x_{1} + 16 x_{2} - 29 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.554

1031	$[\begin{matrix} x_{1}^{'} = 28 x_{1} + 50 x_{2} + 100 x_{3} \\ x_{2}^{'} = 15 x_{1} + 33 x_{2} + 60 x_{3} \\ x_{3}^{'} = - 15 x_{1} - 30 x_{2} - 57 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.591

1032	$[\begin{matrix} x_{1}^{'} = - 2 x_{1} + 17 x_{2} + 4 x_{3} \\ x_{2}^{'} = - x_{1} + 6 x_{2} + x_{3} \\ x_{3}^{'} = x_{2} + 2 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.518

1033	$[\begin{matrix} x_{1}^{'} = 5 x_{1} - x_{2} + x_{3} \\ x_{2}^{'} = x_{1} + 3 x_{2} \\ x_{3}^{'} = - 3 x_{1} + 2 x_{2} + x_{3} \end{matrix}]$	system_of_ODEs	✓	0.503

1034	$[\begin{matrix} x_{1}^{'} = - 3 x_{1} + 5 x_{2} - 5 x_{3} \\ x_{2}^{'} = 3 x_{1} - x_{2} + 3 x_{3} \\ x_{3}^{'} = 8 x_{1} - 8 x_{2} + 10 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.509

1035	$[\begin{matrix} x_{1}^{'} = - 15 x_{1} - 7 x_{2} + 4 x_{3} \\ x_{2}^{'} = 34 x_{1} + 16 x_{2} - 11 x_{3} \\ x_{3}^{'} = 17 x_{1} + 7 x_{2} + 5 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.522

1036	$[\begin{matrix} x_{1}^{'} = - x_{1} + x_{2} + x_{3} - 2 x_{4} \\ x_{2}^{'} = 7 x_{1} - 4 x_{2} - 6 x_{3} + 11 x_{4} \\ x_{3}^{'} = 5 x_{1} - x_{2} + x_{3} + 3 x_{4} \\ x_{4}^{'} = 6 x_{1} - 2 x_{2} - 2 x_{3} + 6 x_{4} \end{matrix}]$	system_of_ODEs	✓	0.912

1037	$[\begin{matrix} x_{1}^{'} = 2 x_{1} + x_{2} - 2 x_{3} + x_{4} \\ x_{2}^{'} = 3 x_{2} - 5 x_{3} + 3 x_{4} \\ x_{3}^{'} = - 13 x_{2} + 22 x_{3} - 12 x_{4} \\ x_{4}^{'} = - 27 x_{2} + 45 x_{3} - 25 x_{4} \end{matrix}]$	system_of_ODEs	✓	0.868

1038	$[\begin{matrix} x_{1}^{'} = 35 x_{1} - 12 x_{2} + 4 x_{3} + 30 x_{4} \\ x_{2}^{'} = 22 x_{1} - 8 x_{2} + 3 x_{3} + 19 x_{4} \\ x_{3}^{'} = - 10 x_{1} + 3 x_{2} - 9 x_{4} \\ x_{4}^{'} = - 27 x_{1} + 9 x_{2} - 3 x_{3} - 23 x_{4} \end{matrix}]$	system_of_ODEs	✓	0.826

1039	$[\begin{matrix} x_{1}^{'} = 11 x_{1} - x_{2} + 26 x_{3} + 6 x_{4} - 3 x_{5} \\ x_{2}^{'} = 3 x_{2} \\ x_{3}^{'} = - 9 x_{1} - 24 x_{3} - 6 x_{4} + 3 x_{5} \\ x_{4}^{'} = 3 x_{1} + 9 x_{3} + 5 x_{4} - x_{5} \\ x_{5}^{'} = - 48 x_{1} - 3 x_{2} - 138 x_{3} - 30 x_{4} + 18 x_{5} \end{matrix}]$	system_of_ODEs	✓	1.206

1040	$[\begin{matrix} x_{1}^{'} = 3 x_{1} - 4 x_{2} + x_{3} \\ x_{2}^{'} = 4 x_{1} + 3 x_{2} + x_{4} \\ x_{3}^{'} = 3 x_{3} - 4 x_{4} \\ x_{4}^{'} = 4 x_{3} + 3 x_{4} \end{matrix}]$	system_of_ODEs	✓	0.615

1041	$[\begin{matrix} x_{1}^{'} = 2 x_{1} - 8 x_{3} - 3 x_{4} \\ x_{2}^{'} = - 18 x_{1} - x_{2} \\ x_{3}^{'} = - 9 x_{1} - 3 x_{2} - 25 x_{3} - 9 x_{4} \\ x_{4}^{'} = 33 x_{1} + 10 x_{2} + 90 x_{3} + 32 x_{4} \end{matrix}]$	system_of_ODEs	✓	1.391

1042	$y^{'} = y$	[_quadrature]	✓	0.266

1043	$y^{'} = 4 y$	[_quadrature]	✓	0.299

1044	$2 y^{'} + 3 y = 0$	[_quadrature]	✓	0.293

1045	$y^{'} + 2 x y = 0$	[_separable]	✓	0.321

1046	$y^{'} = x^{2} y$	[_separable]	✓	0.364

1047	$(x - 2) y^{'} + y = 0$	[_separable]	✓	0.336

1048	$(2 x - 1) y^{'} + 2 y = 0$	[_separable]	✓	0.393

1049	$2 (x + 1) y^{'} = y$	[_separable]	✓	0.316

1050	$(x - 1) y^{'} + 2 y = 0$	[_separable]	✓	0.329

1051	$2 (x - 1) y^{'} = 3 y$	[_separable]	✓	0.343

1052	$y^{''} = y$	[[_2nd_order, _missing_x]]	✓	0.340

1053	$y^{''} = 4 y$	[[_2nd_order, _missing_x]]	✓	0.325

1054	$y^{''} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.396

1055	$y^{''} + y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.422

1056	$y^{'} x + y = 0$	[_separable]	✓	0.255

1057	$2 y^{'} x = y$	[_separable]	✓	0.249

1058	$x^{2} y^{'} + y = 0$	[_separable]	✗	0.129

1059	$x^{3} y^{'} = 2 y$	[_separable]	✗	0.122

1060	$y^{''} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.456

1061	$y^{''} - 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.457

1062	$y^{''} - 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.497

1063	$y^{''} + y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.537

1064	$x^{2} y^{''} + x^{2} y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.750

1065	$y^{'} = 1 + y^{2}$ i.c.	[_quadrature]	✓	1.608

1066	$(x^{2} - 1) y^{''} + 4 y^{'} x + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.471

1067	$(x^{2} + 2) y^{''} + 4 y^{'} x + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.478

1068	$y^{''} + y^{'} x + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.399

1069	$(x^{2} + 1) y^{''} + 6 y^{'} x + 4 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.461

1070	$(x^{2} + 1) y^{''} + 2 y^{'} x = 0$	[[_2nd_order, _missing_y]]	✓	0.452

1071	$(x^{2} - 1) y^{''} - 6 y^{'} x + 12 y = 0$	[_Gegenbauer]	✓	0.402

1072	$(x^{2} + 3) y^{''} - 7 y^{'} x + 16 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.500

1073	$(- x^{2} + 2) y^{''} - y^{'} x + 16 y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.465

1074	$(x^{2} - 1) y^{''} + 8 y^{'} x + 12 y = 0$	[_Gegenbauer]	✓	0.473

1075	$3 y^{''} + y^{'} x - 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.423

1076	$5 y^{''} - 2 y^{'} x + 10 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.426

1077	$y^{''} - x^{2} y^{'} - 3 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.385

1078	$y^{''} + x^{2} y^{'} + 2 x y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.408

1079	$y^{''} + x y = 0$	[[_Emden, _Fowler]]	✓	0.296

1080	$y^{''} + x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.297

1081	$(x^{2} + 1) y^{''} + 2 y^{'} x - 2 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.454

1082	$y^{''} + y^{'} x - 2 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.399

1083	$y^{''} + (x - 1) y^{'} + y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.444

1084	$(- x^{2} + 2 x) y^{''} - 6 (x - 1) y^{'} - 4 y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.542

1085	$(x^{2} - 6 x + 10) y^{''} - 4 (x - 3) y^{'} + 6 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.449

1086	$(4 x^{2} + 16 x + 17) y^{''} = 8 y$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.462

1087	$(x^{2} + 6 x) y^{''} + (3 x + 9) y^{'} - 3 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.525

1088	$y^{''} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.399

1089	$(x^{2} - 1) y^{''} + 2 y^{'} x + 2 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.533

1090	$y^{''} + x^{2} y^{'} + x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.424

1091	$(x^{3} + 1) y^{''} + y x^{4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.480

1092	$y^{''} + y^{'} x + (2 x^{2} + 1) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.493

1093	$y^{''} + e^{- x} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.628

1094	$\cos (x) y^{''} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.778

1095	$x y^{''} + y^{'} \sin (x) + x y = 0$	[_Lienard]	✓	1.516

1096	$y^{''} - 2 y^{'} x + 2 α y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.482

1097	$y^{''} = x y$	[[_Emden, _Fowler]]	✓	0.313

1098	$3 y + y^{'} = e^{- 2 t} + t$	[[_linear, ‘class A‘]]	✓	1.194

1099	$- 2 y + y^{'} = e^{2 t} t^{2}$	[[_linear, ‘class A‘]]	✓	1.502

1100	$y + y^{'} = 1 + t e^{- t}$	[[_linear, ‘class A‘]]	✓	1.586

2.2.11 Problems 1001 to 1100