Problems 14001 to 14100

Table 2.283: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

14001	$y^{''} + y = {\begin{array}{cc} t & 0 \leq t < π \\ - t & π \leq t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.069

14002	$y^{''} + 4 y = {\begin{array}{cc} 8 t & 0 \leq t < \frac{π}{2} \\ 8 π & \frac{π}{2} \leq t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.835

14003	$y^{''} + 4 π^{2} y = 3 δ (t - \frac{1}{3}) - δ (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.559

14004	$y^{''} + 2 y^{'} + 2 y = 3 δ (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.834

14005	$y^{''} + 4 y^{'} + 29 y = 5 δ (t - π) - 5 δ (t - 2 π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.667

14006	$y^{''} + 3 y^{'} + 2 y = 1 - δ (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.197

14007	$4 y^{''} + 4 y^{'} + y = e^{- \frac{t}{2}} δ (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.653

14008	$y^{''} - 7 y^{'} + 6 y = δ (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.767

14009	$10 Q^{'} + 100 Q = Heaviside (t - 1) - Heaviside (t - 2)$ i.c.	[[_linear, ‘class A‘]]	✓	0.770

14010	$y^{'''} + y^{''} + 4 y^{'} + 4 y = 8$ i.c.	[[_3rd_order, _missing_x]]	✓	0.483

14011	$y^{'''} - 2 y^{''} - y^{'} + 2 y = 4 t$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓	0.359

14012	$y^{'''} - y^{''} + 4 y^{'} - 4 y = 8 e^{2 t} - 5 e^{t}$ i.c.	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.521

14013	$y^{'''} - 5 y^{''} + y^{'} - y = - t^{2} + 2 t - 10$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓	1.886

14014	$y^{''''} - 5 y^{''} + 4 y = 12 Heaviside (t) - 12 Heaviside (t - 1)$ i.c.	[[_high_order, _linear, _nonhomogeneous]]	✓	5.644

14015	$y^{''''} - 16 y = 32 Heaviside (t) - 32 Heaviside (t - π)$ i.c.	[[_high_order, _linear, _nonhomogeneous]]	✓	4.186

14016	$t^{2} y^{''} + 3 y^{'} t + y = t^{7}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.698

14017	$t^{2} y^{''} - 6 y^{'} t + \sin (2 t) y = \ln (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	1.358

14018	$y^{''} + 3 y^{'} + \frac{y}{t} = t$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.720

14019	$y^{''} + y^{'} t - \ln (t) y = \cos (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.795

14020	$t^{3} y^{''} - 2 y^{'} t + y = t^{4}$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.789

14021	$y^{''} + 2 y^{'} + y = 1$	[[_2nd_order, _missing_x]]	✓	0.532

14022	$y^{''} - 2 y^{'} + 5 y = e^{t}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.591

14023	$y^{''} - 3 y^{'} - 7 y = 4$	[[_2nd_order, _missing_x]]	✓	0.541

14024	$y^{'''} + 3 y^{''} + 3 y^{'} + y = 5$	[[_3rd_order, _missing_x]]	✓	0.123

14025	$3 y^{''} + 5 y^{'} - 2 y = 3 t^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.462

14026	$y^{'''} = 2 y^{''} - 4 y^{'} + \sin (t)$	[[_3rd_order, _missing_y]]	✓	0.164

14027	$[\begin{matrix} x^{'} = x - 2 y \\ y^{'} = 3 x - 4 y \end{matrix}]$	system_of_ODEs	✓	0.330

14028	$[\begin{matrix} x^{'} = \frac{5 x}{4} + \frac{3 y}{4} \\ y^{'} = \frac{x}{2} - \frac{3 y}{2} \end{matrix}]$	system_of_ODEs	✓	0.659

14029	$[\begin{matrix} x^{'} - x + 2 y = 0 \\ y^{'} + y - x = 0 \end{matrix}]$	system_of_ODEs	✓	0.378

14030	$[\begin{matrix} x^{'} + 5 x - 2 y = 0 \\ 2 x + y^{'} - y = 0 \end{matrix}]$	system_of_ODEs	✓	0.569

14031	$[\begin{matrix} x^{'} - 3 x + 2 y = 0 \\ y^{'} - x + 3 y = 0 \end{matrix}]$	system_of_ODEs	✓	0.526

14032	$[\begin{matrix} x^{'} + x - z = 0 \\ x + y^{'} - y = 0 \\ z^{'} + x + 2 y - 3 z = 0 \end{matrix}]$	system_of_ODEs	✓	0.410

14033	$[\begin{matrix} x^{'} = - \frac{x}{2} + 2 y - 3 z \\ y^{'} = y - \frac{z}{2} \\ z^{'} = - 2 x + z \end{matrix}]$	system_of_ODEs	✓	1.137

14034	$[\begin{matrix} x^{'} + y^{'} = y \\ x^{'} - y^{'} = x \end{matrix}]$	system_of_ODEs	✓	0.467

14035	$[\begin{matrix} x^{'} + 2 y^{'} = t \\ x^{'} - y^{'} = x + y \end{matrix}]$	system_of_ODEs	✓	0.532

14036	$[\begin{matrix} x^{'} - y^{'} = x + y - t \\ 2 x^{'} + 3 y^{'} = 2 x + 6 \end{matrix}]$	system_of_ODEs	✓	0.690

14037	$[\begin{matrix} 2 x^{'} - y^{'} = t \\ 3 x^{'} + 2 y^{'} = y \end{matrix}]$	system_of_ODEs	✓	0.452

14038	$[\begin{matrix} 5 x^{'} - 3 y^{'} = x + y \\ 3 x^{'} - y^{'} = t \end{matrix}]$	system_of_ODEs	✓	0.489

14039	$[\begin{matrix} x^{'} - 4 y^{'} = 0 \\ 2 x^{'} - 3 y^{'} = t + y \end{matrix}]$	system_of_ODEs	✓	0.534

14040	$[\begin{matrix} 3 x^{'} + 2 y^{'} = \sin (t) \\ x^{'} - 2 y^{'} = x + y + t \end{matrix}]$	system_of_ODEs	✓	0.767

14041	$[\begin{matrix} x^{'} = - 4 x + 9 y + 12 e^{- t} \\ y^{'} = - 5 x + 2 y \end{matrix}]$	system_of_ODEs	✓	0.821

14042	$[\begin{matrix} x^{'} = - 7 x + 6 y + 6 e^{- t} \\ y^{'} = - 12 x + 5 y + 37 \end{matrix}]$	system_of_ODEs	✓	0.999

14043	$[\begin{matrix} x^{'} = - 7 x + 10 y + 18 e^{t} \\ y^{'} = - 10 x + 9 y + 37 \end{matrix}]$	system_of_ODEs	✓	1.257

14044	$[\begin{matrix} x^{'} = - 14 x + 39 y + 78 \sinh (t) \\ y^{'} = - 6 x + 16 y + 6 \cosh (t) \end{matrix}]$	system_of_ODEs	✓	1.555

14045	$[\begin{matrix} x^{'} = 2 x + 4 y - 2 z - 2 \sinh (t) \\ y^{'} = 4 x + 2 y - 2 z + 10 \cosh (t) \\ z^{'} = - x + 3 y + z + 5 \end{matrix}]$	system_of_ODEs	✓	1.900

14046	$[\begin{matrix} x^{'} = 2 x + 6 y - 2 z + 50 e^{t} \\ y^{'} = 6 x + 2 y - 2 z + 21 e^{- t} \\ z^{'} = - x + 6 y + z + 9 \end{matrix}]$	system_of_ODEs	✓	1.554

14047	$[\begin{matrix} x^{'} = - 2 x - 2 y + 4 z \\ y^{'} = - 2 x + y + 2 z \\ z^{'} = - 4 x - 2 y + 6 z + e^{2 t} \end{matrix}]$	system_of_ODEs	✓	0.799

14048	$[\begin{matrix} x^{'} = 3 x - 2 y + 3 z \\ y^{'} = x - y + 2 z + 2 e^{- t} \\ z^{'} = - 2 x + 2 y - 2 z \end{matrix}]$	system_of_ODEs	✓	0.946

14049	$[\begin{matrix} x^{'} = 7 x + y - 1 - 6 e^{t} \\ y^{'} = - 4 x + 3 y + 4 e^{t} - 3 \end{matrix}]$ i.c.	system_of_ODEs	✓	0.736

14050	$[\begin{matrix} x^{'} = 3 x - 2 y + 24 \sin (t) \\ y^{'} = 9 x - 3 y + 12 \cos (t) \end{matrix}]$ i.c.	system_of_ODEs	✓	1.088

14051	$[\begin{matrix} x^{'} = 7 x - 4 y + 10 e^{t} \\ y^{'} = 3 x + 14 y + 6 e^{2 t} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.766

14052	$[\begin{matrix} x^{'} = - 7 x + 4 y + 6 e^{3 t} \\ y^{'} = - 5 x + 2 y + 6 e^{2 t} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.777

14053	$[\begin{matrix} x^{'} = - 3 x - 3 y + z \\ y^{'} = 2 y + 2 z + 29 e^{- t} \\ z^{'} = 5 x + y + z + 39 e^{t} \end{matrix}]$ i.c.	system_of_ODEs	✓	31.404

14054	$[\begin{matrix} x^{'} = 2 x + y - z + 5 \sin (t) \\ y^{'} = y + z - 10 \cos (t) \\ z^{'} = x + z + 2 \end{matrix}]$ i.c.	system_of_ODEs	✓	2.683

14055	$[\begin{matrix} x^{'} = - 3 x + 3 y + z + 5 \sin (2 t) \\ y^{'} = x - 5 y - 3 z + 5 \cos (2 t) \\ z^{'} = - 3 x + 7 y + 3 z + 23 e^{t} \end{matrix}]$ i.c.	system_of_ODEs	✓	3.239

14056	$[\begin{matrix} x^{'} = - 3 x + y - 3 z + 2 e^{t} \\ y^{'} = 4 x - y + 2 z + 4 e^{t} \\ z^{'} = 4 x - 2 y + 3 z + 4 e^{t} \end{matrix}]$ i.c.	system_of_ODEs	✓	1.894

14057	$[\begin{matrix} x^{'} = x + 5 y + 10 \sinh (t) \\ y^{'} = 19 x - 13 y + 24 \sinh (t) \end{matrix}]$	system_of_ODEs	✓	1.715

14058	$[\begin{matrix} x^{'} = 9 x - 3 y - 6 t \\ y^{'} = - x + 11 y + 10 t \end{matrix}]$	system_of_ODEs	✓	1.820

14059	$(x - 1) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.176

14060	$x y^{''} + 2 y^{'} + x y = 0$	[_Lienard]	✓	0.133

14061	$y^{''} - 2 y^{'} + y = x^{3 / 2} e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.682

14062	$y^{''} + 4 y = 2 \sec (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.157

14063	$y^{''} + \frac{y^{'}}{x} + (1 - \frac{1}{4 x^{2}}) y = x$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.180

14064	$y^{''} + y = f (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.841

14065	$x^{2} y^{''} + x (x - \frac{1}{2}) y^{'} + \frac{y}{2} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.606

14066	$x^{2} y^{''} + x (x + 1) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.516

14067	$x (1 - x) y^{''} + (1 - 5 x) y^{'} - 4 y = 0$	[_Jacobi]	✓	0.668

14068	${(x^{2} - 1)}^{2} y^{''} + (x + 1) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.550

14069	$x y^{''} + 4 y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.648

14070	$2 x y^{''} + (x + 1) y^{'} - k y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.862

14071	$x^{3} y^{''} + x^{2} y^{'} + y = 0$	[[_Emden, _Fowler]]	✗	0.167

14072	$x^{2} y^{''} + y^{'} - 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✗	0.232

14073	$2 x^{2} y^{''} + x (1 - x) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.717

14074	$x (x - 1) y^{''} + 3 y^{'} x + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.505

14075	$y^{''} - x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.500

14076	$x y^{''} + y^{'} + y = 0$	[[_Emden, _Fowler]]	✓	0.356

14077	$x y^{''} + x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.296

14078	$y^{''} + α^{2} y = 0$	[[_2nd_order, _missing_x]]	✓	1.400

14079	$y^{''} - α^{2} y = 0$	[[_2nd_order, _missing_x]]	✓	1.633

14080	$y^{''} + β y^{'} + γ y = 0$	[[_2nd_order, _missing_x]]	✓	1.433

14081	$(- x^{2} + 1) y^{''} - 2 y^{'} x + n (n + 1) y = 0$	[_Gegenbauer]	✗	1.276

14082	$x^{2} y^{''} + y^{'} x + (- ν^{2} + x^{2}) y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.925

14083	$y^{'} + \cos (x) y = \frac{\sin (2 x)}{2}$	[_linear]	✓	2.261

14084	${y^{'}}^{2} - y^{'} - y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.515

14085	$y {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.828

14086	$x y (1 - {y^{'}}^{2}) = (x^{2} - y^{2} - a^{2}) y^{'}$	[_rational]	✓	26.782

14087	$y^{'''} + \frac{3 y^{''}}{x} = 0$	[[_3rd_order, _missing_y]]	✓	0.742

14088	$y^{''} - 2 k y^{'} + k^{2} y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.528

14089	$(- x^{2} + 1) y^{''} - y^{'} x - a^{2} y = 0$	[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.254

14090	$y^{''} + \frac{2 y^{'}}{x} = 0$	[[_2nd_order, _missing_y]]	✓	0.534

14091	$y - y^{'} x = 0$	[_separable]	✓	1.359

14092	$(1 + u) v + (1 - v) u v^{'} = 0$	[_separable]	✓	1.562

14093	$1 + y - (1 - x) y^{'} = 0$	[_separable]	✓	1.671

14094	$(t^{2} + x t^{2}) x^{'} + x^{2} + t x^{2} = 0$	[_separable]	✓	1.948

14095	$y - a + x^{2} y^{'} = 0$	[_separable]	✓	1.199

14096	$z - (- a^{2} + t^{2}) z^{'} = 0$	[_separable]	✓	1.884

14097	$y^{'} = \frac{1 + y^{2}}{x^{2} + 1}$	[_separable]	✓	1.895

14098	$1 + s^{2} - \sqrt{t} s^{'} = 0$	[_separable]	✓	2.268

14099	$r^{'} + r \tan (t) = 0$	[_separable]	✓	1.372

14100	$(x^{2} + 1) y^{'} - \sqrt{1 - y^{2}} = 0$	[_separable]	✓	2.175

2.2.141 Problems 14001 to 14100