Problems 2101 to 2200

Table 2.45: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

2101	$x^{2} (x^{2} + 1) y^{''} + x (11 x^{2} + 5) y^{'} + 24 x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.641

2102	$4 x^{2} (x^{2} + 1) y^{''} + 8 x y^{'} - (- x^{2} + 35) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.759

2103	$x^{2} (x^{2} + 1) y^{''} - x (- x^{2} + 5) y^{'} - (25 x^{2} + 7) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.843

2104	$x^{2} (x^{2} + 1) y^{''} + x (2 x^{2} + 5) y^{'} - 21 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.099

2105	$x^{2} (2 x^{2} + 1) y^{''} - x (x^{2} + 3) y^{'} - 2 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.457

2106	$4 x^{2} (x^{2} + 1) y^{''} + 4 x (x^{2} + 2) y^{'} - (x^{2} + 15) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.727

2107	$x^{3} y^{'''} - x^{2} y^{''} - 2 x y^{'} + 6 y = 0$ i.c.	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	0.210

2108	$y^{''''} + y^{'''} - 7 y^{''} - y^{'} + 6 y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.143

2109	$x^{3} y^{'''} - x^{2} y^{''} - 2 x y^{'} + 6 y = 0$ i.c.	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	0.276

2110	$x^{3} y^{'''} - x^{2} y^{''} - 2 x y^{'} + 6 y = 0$ i.c.	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	0.196

2111	$x^{3} y^{'''} - x^{2} y^{''} - 2 x y^{'} + 6 y = 0$ i.c.	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	0.203

2112	$x^{3} y^{'''} - x^{2} y^{''} - 2 x y^{'} + 6 y = 0$ i.c.	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	0.131

2113	$y^{'''} + y^{''} - y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.051

2114	$y^{'''} - 3 y^{''} + 7 y^{'} - 5 y = 0$	[[_3rd_order, _missing_x]]	✓	0.062

2115	$y^{'''} - 3 y^{''} + 3 y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.051

2116	$y^{''''} + 8 y^{''} - 9 y = 0$	[[_high_order, _missing_x]]	✓	0.060

2117	$y^{'''} - y^{''} + 16 y^{'} - 16 y = 0$	[[_3rd_order, _missing_x]]	✓	0.058

2118	$2 y^{'''} + 3 y^{''} - 2 y^{'} - 3 y = 0$	[[_3rd_order, _missing_x]]	✓	0.054

2119	$y^{'''} + 5 y^{''} + 9 y^{'} + 5 y = 0$	[[_3rd_order, _missing_x]]	✓	0.059

2120	$4 y^{'''} - 8 y^{''} + 5 y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.055

2121	$27 y^{'''} + 27 y^{''} + 9 y^{'} + y = 0$	[[_3rd_order, _missing_x]]	✓	0.054

2122	$y^{''''} + y^{''} = 0$	[[_high_order, _missing_x]]	✓	0.050

2123	$y^{''''} - 16 y = 0$	[[_high_order, _missing_x]]	✓	0.062

2124	$y^{''''} + 12 y^{''} + 36 y = 0$	[[_high_order, _missing_x]]	✓	0.072

2125	$16 y^{''''} - 72 y^{''} + 81 y = 0$	[[_high_order, _missing_x]]	✓	0.059

2126	$6 y^{''''} + 5 y^{'''} + 7 y^{''} + 5 y^{'} + y = 0$	[[_high_order, _missing_x]]	✓	0.064

2127	$4 y^{''''} + 12 y^{'''} + 3 y^{''} - 13 y^{'} - 6 y = 0$	[[_high_order, _missing_x]]	✓	0.063

2128	$y^{''''} - 4 y^{'''} + 7 y^{''} - 6 y^{'} + 2 y = 0$	[[_high_order, _missing_x]]	✓	0.065

2129	$y^{'''} - 2 y^{''} + 4 y^{'} - 8 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.073

2130	$y^{'''} + 3 y^{''} - y^{'} - 3 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.132

2131	$y^{'''} - y^{''} - y^{'} + y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.130

2132	$y^{'''} - 2 y^{'} - 4 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.073

2133	$3 y^{'''} - y^{''} - 7 y^{'} + 5 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.135

2134	$y^{'''} - 6 y^{''} + 12 y^{'} - 8 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.131

2135	$2 y^{'''} - 11 y^{''} + 12 y^{'} + 9 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.134

2136	$8 y^{'''} - 4 y^{''} - 2 y^{'} + y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.129

2137	$y^{''''} - 16 y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.081

2138	$y^{''''} - 6 y^{'''} + 7 y^{''} + 6 y^{'} - 8 y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.141

2139	$4 y^{''''} - 13 y^{''} + 9 y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.134

2140	$y^{''''} + 2 y^{'''} - 2 y^{''} - 8 y^{'} - 8 y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.089

2141	$4 y^{''''} + 8 y^{'''} + 19 y^{''} + 32 y^{'} + 12 y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.089

2142	$y^{''''} - y = 0$	[[_high_order, _missing_x]]	✓	0.054

2143	$y^{''''} + y = 0$	[[_high_order, _missing_x]]	✓	0.069

2144	$y^{''''} + 64 y = 0$	[[_high_order, _missing_x]]	✓	0.066

2145	$y^{(6)} - y = 0$	[[_high_order, _missing_x]]	✓	0.095

2146	$y^{''''} + 64 y = 0$	[[_high_order, _missing_x]]	✓	0.065

2147	$y^{(5)} + y^{''''} + y^{'''} + y^{''} + y^{'} + y = 0$	[[_high_order, _missing_x]]	✓	0.076

2148	$y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = - e^{x} (- 24 x^{2} + 76 x + 4)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.141

2149	$y^{'''} - 2 y^{''} - 5 y^{'} + 6 y = e^{- 3 x} (6 x^{2} - 23 x + 32)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.138

2150	$4 y^{'''} + 8 y^{''} - y^{'} - 2 y = - e^{x} (6 x^{2} + 45 x + 4)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.134

2151	$y^{'''} + 3 y^{''} - y^{'} - 3 y = e^{- 2 x} (3 x^{2} - 17 x + 2)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.135

2152	$y^{'''} + 3 y^{''} - y^{'} - 3 y = e^{x} (16 x^{3} + 24 x^{2} + 2 x - 1)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.150

2153	$y^{'''} + y^{''} - 2 y = e^{x} (15 x^{2} + 34 x + 14)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.137

2154	$4 y^{'''} + 8 y^{''} - y^{'} - 2 y = - e^{- 2 x} (1 - 15 x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.134

2155	$y^{'''} - y^{''} - y^{'} + y = - e^{x} (7 + 6 x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.124

2156	$2 y^{'''} - 7 y^{''} + 4 y^{'} + 4 y = e^{2 x} (17 + 30 x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.133

2157	$y^{'''} - 5 y^{''} + 3 y^{'} + 9 y = 2 e^{3 x} (11 - 24 x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.139

2158	$y^{'''} - 7 y^{''} + 8 y^{'} + 16 y = 2 e^{4 x} (13 + 15 x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.132

2159	$8 y^{'''} - 12 y^{''} + 6 y^{'} - y = e^{\frac{x}{2}} (1 + 4 x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.138

2160	$y^{''''} + 3 y^{'''} - 3 y^{''} - 7 y^{'} + 6 y = - 3 e^{- x} (- 8 x^{2} + 8 x + 12)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.151

2161	$y^{''''} + 3 y^{'''} + y^{''} - 3 y^{'} - 2 y = - 3 e^{2 x} (11 + 12 x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.134

2162	$y^{''''} + 8 y^{'''} + 24 y^{''} + 32 y^{'} = - 16 e^{- 2 x} (- x^{3} + x^{2} + x + 1)$	[[_high_order, _missing_y]]	✓	0.164

2163	$4 y^{''''} - 11 y^{''} - 9 y^{'} - 2 y = - e^{x} (1 - 6 x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.132

2164	$y^{''''} - 2 y^{'''} + 3 y^{'} - y = e^{x} (x^{2} + 4 x + 3)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.164

2165	$y^{''''} - 4 y^{'''} + 6 y^{''} - 4 y^{'} + 2 y = e^{2 x} (x^{4} + x + 24)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.179

2166	$2 y^{''''} + 5 y^{'''} - 5 y^{'} - 2 y = 18 e^{x} (5 + 2 x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.133

2167	$y^{''''} + y^{'''} - 2 y^{''} - 6 y^{'} - 4 y = - e^{2 x} (15 x^{2} + 28 x + 4)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.155

2168	$2 y^{''''} + y^{'''} - 2 y^{'} - y = 3 e^{- \frac{x}{2}} (1 - 6 x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.151

2169	$y^{''''} - 5 y^{''} + 4 y = e^{x} (- 3 x^{2} + x + 3)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.140

2170	$y^{''''} - 2 y^{'''} - 3 y^{''} + 4 y^{'} + 4 y = e^{2 x} (18 x^{2} + 33 x + 13)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.158

2171	$y^{''''} - 3 y^{'''} + 4 y^{'} = e^{2 x} (12 x^{2} + 26 x + 15)$	[[_high_order, _missing_y]]	✓	0.148

2172	$y^{''''} - 2 y^{'''} + 2 y^{'} - y = e^{x} (x + 1)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.133

2173	$2 y^{''''} - 5 y^{'''} + 3 y^{''} + y^{'} - y = e^{x} (11 + 12 x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.140

2174	$y^{''''} + 3 y^{'''} + 3 y^{''} + y^{'} = e^{- x} (10 x^{2} - 24 x + 5)$	[[_high_order, _missing_y]]	✓	0.151

2175	$y^{''''} - 7 y^{'''} + 18 y^{''} - 20 y^{'} + 8 y = e^{2 x} (- 5 x^{2} - 8 x + 3)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.164

2176	$y^{'''} - y^{''} - 4 y^{'} + 4 y = e^{- x} ((16 + 10 x) \cos (x) + (30 - 10 x) \sin (x))$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.199

2177	$y^{'''} + y^{''} - 4 y^{'} - 4 y = e^{- x} ((1 - 22 x) \cos (2 x) - (1 + 6 x) \sin (2 x))$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.371

2178	$y^{'''} - y^{''} + 2 y^{'} - 2 y = e^{2 x} ((- x^{2} + 5 x + 27) \cos (x) + (9 x^{2} + 13 x + 2) \sin (x))$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.354

2179	$y^{'''} - 2 y^{''} + y^{'} - 2 y = - e^{x} ((4 x^{2} + 5 x + 9) \cos (2 x) - (- 3 x^{2} - 5 x + 6) \sin (2 x))$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.636

2180	$y^{'''} + 3 y^{''} + 4 y^{'} + 12 y = 8 \cos (2 x) - 16 \sin (2 x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.668

2181	$y^{'''} - y^{''} + 2 y = e^{x} ((20 + 4 x) \cos (x) - (12 + 12 x) \sin (x))$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.984

2182	$y^{'''} - 7 y^{''} + 20 y^{'} - 24 y = - e^{2 x} ((13 - 8 x) \cos (2 x) - (8 - 4 x) \sin (2 x))$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.885

2183	$y^{'''} - 6 y^{''} + 18 y^{'} = - e^{3 x} ((2 - 3 x) \cos (3 x) - (3 + 3 x) \sin (3 x))$	[[_3rd_order, _missing_y]]	✓	0.812

2184	$y^{''''} + 2 y^{'''} - 2 y^{''} - 8 y^{'} - 8 y = e^{x} (8 \cos (x) + 16 \sin (x))$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.169

2185	$y^{''''} - 3 y^{'''} + 2 y^{''} + 2 y^{'} - 4 y = e^{x} (2 \cos (2 x) - \sin (2 x))$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.188

2186	$y^{''''} - 8 y^{'''} + 24 y^{''} - 32 y^{'} + 15 y = e^{2 x} (15 x \cos (2 x) + 32 \sin (2 x))$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.209

2187	$y^{''''} + 6 y^{'''} + 13 y^{''} + 12 y^{'} + 4 y = e^{- x} ((4 - x) \cos (x) - (5 + x) \sin (x))$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.206

2188	$y^{''''} + 3 y^{'''} + 2 y^{''} - 2 y^{'} - 4 y = - e^{- x} (\cos (x) - \sin (x))$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.858

2189	$y^{''''} - 5 y^{'''} + 13 y^{''} - 19 y^{'} + 10 y = e^{x} (\cos (2 x) + \sin (2 x))$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.766

2190	$y^{''''} + 8 y^{'''} + 32 y^{''} + 64 y^{'} + 39 y = e^{- 2 x} ((4 - 15 x) \cos (3 x) - (4 + 15 x) \sin (3 x))$	[[_high_order, _linear, _nonhomogeneous]]	✓	1.036

2191	$y^{''''} - 5 y^{'''} + 13 y^{''} - 19 y^{'} + 10 y = e^{x} ((7 + 8 x) \cos (2 x) + (8 - 4 x) \sin (2 x))$	[[_high_order, _linear, _nonhomogeneous]]	✓	1.198

2192	$y^{''''} + 4 y^{'''} + 8 y^{''} + 8 y^{'} + 4 y = - 2 e^{x} (\cos (x) - \sin (x))$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.181

2193	$y^{''''} - 8 y^{'''} + 32 y^{''} - 64 y^{'} + 64 y = e^{2 x} (\cos (2 x) - \sin (2 x))$	[[_high_order, _linear, _nonhomogeneous]]	✓	1.104

2194	$y^{''''} - 8 y^{'''} + 26 y^{''} - 40 y^{'} + 25 y = e^{2 x} (3 \cos (x) - (1 + 3 x) \sin (x))$	[[_high_order, _linear, _nonhomogeneous]]	✓	1.520

2195	$y^{'''} - 4 y^{''} + 5 y^{'} - 2 y = e^{2 x} - 4 e^{x} - 2 \cos (x) + 4 \sin (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.275

2196	$y^{'''} - y^{''} + y^{'} - y = 5 e^{2 x} + 2 e^{x} - 4 \cos (x) + 4 \sin (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	1.046

2197	$y^{'''} - y^{'} = - 2 x - 2 + 4 e^{x} - 6 e^{- x} + 96 e^{3 x}$	[[_3rd_order, _missing_y]]	✓	0.164

2198	$y^{'''} - 4 y^{''} + 9 y^{'} - 10 y = 10 e^{2 x} + 20 e^{x} \sin (2 x) - 10$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.865

2199	$y^{'''} + 3 y^{''} + 3 y^{'} + y = 12 e^{- x} + 9 \cos (2 x) - 13 \sin (2 x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.288

2200	$y^{'''} + y^{''} - y^{'} - y = 4 e^{- x} (1 - 6 x) - 2 x \cos (x) + 2 (x + 1) \sin (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.709

2.2.22 Problems 2101 to 2200