Problems 16901 to 17000

Table 2.341: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

16901	$2 y^{'''} - 3 y^{''} + y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.074

16902	$y^{'''} + y^{''} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.118

16903	$y^{''} + 3 y^{'} = 3$	[[_2nd_order, _missing_x]]	✓	1.129

16904	$y^{''} - 7 y^{'} = {(x - 1)}^{2}$	[[_2nd_order, _missing_y]]	✓	1.161

16905	$y^{''} + 3 y^{'} = e^{x}$	[[_2nd_order, _missing_y]]	✓	1.024

16906	$y^{''} + 7 y^{'} = e^{- 7 x}$	[[_2nd_order, _missing_y]]	✓	1.060

16907	$y^{''} - 8 y^{'} + 16 y = (1 - x) e^{4 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.656

16908	$y^{''} - 10 y^{'} + 25 y = e^{5 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.555

16909	$4 y^{''} - 3 y^{'} = x e^{\frac{3 x}{4}}$	[[_2nd_order, _missing_y]]	✓	1.215

16910	$y^{''} - 4 y^{'} = x e^{4 x}$	[[_2nd_order, _missing_y]]	✓	1.173

16911	$y^{''} + 25 y = \cos (5 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.748

16912	$y^{''} + y = \sin (x) - \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.831

16913	$y^{''} + 16 y = \sin (4 x + α)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.010

16914	$y^{''} + 4 y^{'} + 8 y = e^{2 x} (\cos (2 x) + \sin (2 x))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.703

16915	$y^{''} - 4 y^{'} + 8 y = e^{2 x} (\sin (2 x) - \cos (2 x))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.734

16916	$y^{''} + 6 y^{'} + 13 y = e^{- 3 x} \cos (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.718

16917	$y^{''} + k^{2} y = k \sin (k x + α)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.266

16918	$y^{''} + k^{2} y = k$	[[_2nd_order, _missing_x]]	✓	1.736

16919	$y^{'''} + y = x$	[[_3rd_order, _with_linear_symmetries]]	✓	0.136

16920	$y^{'''} + 6 y^{''} + 11 y^{'} + 6 y = 1$	[[_3rd_order, _missing_x]]	✓	0.123

16921	$y^{'''} + y^{'} = 2$	[[_3rd_order, _missing_x]]	✓	0.119

16922	$y^{'''} + y^{''} = 3$	[[_3rd_order, _missing_x]]	✓	0.123

16923	$y^{''''} - y = 1$	[[_high_order, _missing_x]]	✓	0.128

16924	$y^{''''} - y^{'} = 2$	[[_high_order, _missing_x]]	✓	0.135

16925	$y^{''''} - y^{''} = 3$	[[_high_order, _missing_x]]	✓	0.117

16926	$y^{''''} - y^{'''} = 4$	[[_high_order, _missing_x]]	✓	0.131

16927	$y^{''''} + 4 y^{'''} + 4 y^{''} = 1$	[[_high_order, _missing_x]]	✓	0.118

16928	$y^{''''} + 2 y^{'''} + y^{''} = e^{4 x}$	[[_high_order, _missing_y]]	✓	0.170

16929	$y^{''''} + 2 y^{'''} + y^{''} = e^{- x}$	[[_high_order, _missing_y]]	✓	0.163

16930	$y^{''''} + 2 y^{'''} + y^{''} = x e^{- x}$	[[_high_order, _missing_y]]	✓	0.171

16931	$y^{''''} + 4 y^{''} + 4 y = \sin (2 x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.203

16932	$y^{''''} + 4 y^{''} + 4 y = \cos (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.183

16933	$y^{''''} + 4 y^{''} + 4 y = x \sin (2 x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.234

16934	$y^{''''} + 2 n^{2} y^{''} + n^{4} y = a \sin (n x + α)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.945

16935	$y^{''''} - 2 n^{2} y^{''} + n^{4} y = \cos (n x + α)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.217

16936	$y^{''''} + 4 y^{'''} + 6 y^{''} + 4 y^{'} + y = \sin (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.178

16937	$y^{''''} - 4 y^{'''} + 6 y^{''} - 4 y^{'} + y = e^{x}$	[[_high_order, _with_linear_symmetries]]	✓	0.158

16938	$y^{''''} - 4 y^{'''} + 6 y^{''} - 4 y^{'} + y = x e^{x}$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.194

16939	$y^{''} + 2 y^{'} + y = - 2$	[[_2nd_order, _missing_x]]	✓	0.480

16940	$y^{''} + 2 y^{'} = - 2$	[[_2nd_order, _missing_x]]	✓	1.223

16941	$y^{''} + 9 y = 9$	[[_2nd_order, _missing_x]]	✓	1.713

16942	$y^{'''} + y^{''} = 1$	[[_3rd_order, _missing_x]]	✓	0.135

16943	$5 y^{'''} - 7 y^{''} = 3$	[[_3rd_order, _missing_x]]	✓	0.133

16944	$y^{''''} - 6 y^{'''} = - 6$	[[_high_order, _missing_x]]	✓	0.126

16945	$3 y^{''''} + y^{'''} = 2$	[[_high_order, _missing_x]]	✓	0.132

16946	$y^{''''} - 2 y^{'''} + 2 y^{''} - 2 y^{'} + y = 1$	[[_high_order, _missing_x]]	✓	0.139

16947	$y^{''} - 4 y^{'} + 4 y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.566

16948	$y^{''} + 8 y^{'} = 8 x$	[[_2nd_order, _missing_y]]	✓	1.231

16949	$y^{''} - 2 k y^{'} + k^{2} y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.506

16950	$y^{''} + 4 y^{'} + 4 y = 8 e^{- 2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.611

16951	$y^{''} + 4 y^{'} + 3 y = 9 e^{- 3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.572

16952	$7 y^{''} - y^{'} = 14 x$	[[_2nd_order, _missing_y]]	✓	1.073

16953	$y^{''} + 3 y^{'} = 3 x e^{- 3 x}$	[[_2nd_order, _missing_y]]	✓	1.219

16954	$y^{''} + 5 y^{'} + 6 y = 10 (1 - x) e^{- 2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.553

16955	$y^{''} + 2 y^{'} + 2 y = x + 1$	[[_2nd_order, _with_linear_symmetries]]	✓	0.675

16956	$y^{''} + y^{'} + y = (x^{2} + x) e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.758

16957	$y^{''} + 4 y^{'} - 2 y = 8 \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.725

16958	$y^{''} + y = 4 x \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.813

16959	$y^{''} - 2 m y^{'} + m^{2} y = \sin (n x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.695

16960	$y^{''} + 2 y^{'} + 5 y = e^{- x} \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.789

16961	$y^{''} + a^{2} y = 2 \cos (m x) + 3 \sin (m x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.919

16962	$y^{''} - y^{'} = e^{x} \sin (x)$	[[_2nd_order, _missing_y]]	✓	1.548

16963	$y^{''} + 2 y^{'} = 4 e^{x} (\cos (x) + \sin (x))$	[[_2nd_order, _missing_y]]	✓	1.741

16964	$y^{''} + 4 y^{'} + 5 y = 10 e^{- 2 x} \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.734

16965	$4 y^{''} + 8 y^{'} = x \sin (x)$	[[_2nd_order, _missing_y]]	✓	1.731

16966	$y^{''} - 3 y^{'} + 2 y = x e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.512

16967	$y^{''} + y^{'} - 2 y = x^{2} e^{4 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.484

16968	$y^{''} - 3 y^{'} + 2 y = (x^{2} + x) e^{3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.590

16969	$y^{'''} - y^{''} + y^{'} - y = x^{2} + x$	[[_3rd_order, _with_linear_symmetries]]	✓	0.153

16970	$y^{''''} - 2 y^{'''} + 2 y^{''} - 2 y^{'} + y = e^{x}$	[[_high_order, _with_linear_symmetries]]	✓	0.180

16971	$y^{''} - 2 y^{'} + y = x^{3}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.569

16972	$y^{''''} + y^{''} = x^{2} + x$	[[_high_order, _missing_y]]	✓	0.163

16973	$y^{''} + y = x^{2} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.915

16974	$y^{''} + 2 y^{'} + y = x^{2} e^{- x} \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.847

16975	$y^{'''} - y = \sin (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.187

16976	$y^{''''} - 2 y^{''} + y = \cos (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.175

16977	$y^{'''} - 3 y^{''} + 3 y^{'} - y = e^{x} \cos (2 x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.209

16978	$y^{''} - 4 y^{'} + 5 y = e^{2 x} (\sin (x) + 2 \cos (x))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.749

16979	$y^{''} - y^{'} - 2 y = e^{x} + e^{- 2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.597

16980	$y^{''} + 4 y^{'} = x + e^{- 4 x}$	[[_2nd_order, _missing_y]]	✓	1.339

16981	$y^{''} - y = \sin (x) + x$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.747

16982	$y^{''} - 2 y^{'} + 2 y = (1 + \sin (x)) e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.710

16983	$y^{'''} - y^{''} = e^{x} + 1$	[[_3rd_order, _missing_y]]	✓	0.156

16984	$y^{'''} + 4 y^{'} = e^{2 x} + \sin (2 x)$	[[_3rd_order, _missing_y]]	✓	0.591

16985	$y^{''} + 4 y = \sin (2 x) \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.296

16986	$y^{''} - 4 y^{'} = 2 \cos {(4 x)}^{2}$	[[_2nd_order, _missing_y]]	✓	1.670

16987	$y^{''} - y^{'} - 2 y = 4 x - 2 e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.514

16988	$y^{''} - 3 y^{'} = 18 x - 10 \cos (x)$	[[_2nd_order, _missing_y]]	✓	1.561

16989	$y^{''} - 2 y^{'} + y = 2 + e^{x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.669

16990	$y^{''} + 2 y^{'} + 2 y = (5 x + 4) e^{x} + e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.707

16991	$y^{''} + 2 y^{'} + 5 y = 4 e^{- x} + 17 \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.863

16992	$2 y^{''} - 3 y^{'} - 2 y = 5 e^{x} \cosh (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.837

16993	$y^{''} + 4 y = x \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.049

16994	$y^{''''} + 2 y^{'''} + 2 y^{''} + 2 y^{'} + y = x e^{x} + \frac{\cos (x)}{2}$	[[_high_order, _linear, _nonhomogeneous]]	✓	1.169

16995	$y^{''} + y^{'} = \cos {(x)}^{2} + e^{x} + x^{2}$	[[_2nd_order, _missing_y]]	✓	1.897

16996	$y^{''''} + 4 y^{'''} = e^{x} + 3 \sin (2 x) + 1$	[[_high_order, _missing_y]]	✓	0.272

16997	$y^{''} - 2 y^{'} + 5 y = 10 \sin (x) + 17 \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.926

16998	$y^{''} + y^{'} = x^{2} - e^{- x} + e^{x}$	[[_2nd_order, _missing_y]]	✓	1.924

16999	$y^{''} - 2 y^{'} - 3 y = 2 x + e^{- x} - 2 e^{3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.741

17000	$y^{''} + 4 y = e^{x} + 4 \sin (2 x) + 2 \cos {(x)}^{2} - 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.200

2.2.170 Problems 16901 to 17000