Problems 3101 to 3200

Table 2.65: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

3101	$y^{''''} + y^{''} - 20 y = 0$	[[_high_order, _missing_x]]	✓	0.087

3102	$y^{''''} + 5 y^{''} + 6 y = 0$	[[_high_order, _missing_x]]	✓	0.090

3103	$y^{''''} - 4 y^{'''} + 6 y^{''} - 8 y^{'} + 8 y = 0$	[[_high_order, _missing_x]]	✓	0.085

3104	$y^{''''} - 2 y^{'''} - 6 y^{'} + 2 y = 0$	[[_high_order, _missing_x]]	✓	0.112

3105	$y^{''''} + y^{'''} - 3 y^{''} - 4 y^{'} - 4 y = 0$	[[_high_order, _missing_x]]	✓	0.093

3106	$2 y^{'''} - 3 y^{''} + 10 y^{'} - 15 y = 0$	[[_3rd_order, _missing_x]]	✓	0.092

3107	$2 y^{'''} - 3 y^{''} + 11 y^{'} - 40 y = 0$	[[_3rd_order, _missing_x]]	✓	0.093

3108	$y^{''''} - 3 y^{'''} + 4 y^{''} - 12 y^{'} + 16 y = 0$	[[_high_order, _missing_x]]	✓	0.120

3109	$4 y^{'''} + 12 y^{''} - 3 y^{'} + 14 y = 0$	[[_3rd_order, _missing_x]]	✓	0.107

3110	$y^{(5)} - y^{''''} + 6 y^{'''} - 6 y^{''} + 8 y^{'} - 8 y = 0$	[[_high_order, _missing_x]]	✓	0.105

3111	$y^{''} - 4 y = 3 \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.679

3112	$y^{''} + y = \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.690

3113	$y^{''} + y^{'} - 2 y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.602

3114	$y^{''} + 3 y^{'} + 2 y = e^{- 2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.481

3115	$y^{''} + y^{'} + y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.672

3116	$y^{''} + y^{'} + y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.694

3117	$y^{''} + 3 y^{'} + 2 y = x e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.497

3118	$y^{''''} - y = e^{x}$	[[_high_order, _with_linear_symmetries]]	✓	0.158

3119	$y^{''} - 4 y = x + e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.687

3120	$y^{''} - 9 y = e^{3 x} + \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.057

3121	$y^{''} - y^{'} - 6 y = x^{3}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.453

3122	$- 2 y^{''} + 3 y = x e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.721

3123	$y^{''} + 4 y = x \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.833

3124	$y^{'''} - 4 y^{''} = x^{2} + 8$	[[_3rd_order, _missing_y]]	✓	0.153

3125	$y^{''} + y^{'} + y = e^{x} \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.833

3126	$y^{'''} - 3 y^{''} + 4 y^{'} - 12 y = x + e^{2 x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.189

3127	$y^{'''} - 4 y^{''} + y^{'} - 4 y = e^{4 x} \sin (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.212

3128	$y^{''} + 4 y^{'} + 4 y = x^{3} e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.658

3129	$y^{'''} - 2 y^{''} + y^{'} - 2 y = x e^{2 x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.183

3130	$y^{''''} + 2 n^{2} y^{''} + n^{4} y = \sin (k x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.208

3131	$y^{''} + 2 n y^{'} + n^{2} y = 5 \cos (6 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.845

3132	$y^{''} + 9 y = (1 + \sin (3 x)) \cos (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.935

3133	$y^{''} + 4 y^{'} + 5 y = 2 x - e^{- 4 x} + \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.982

3134	$y^{'''} + 2 y^{''} = (2 x^{2} + x) e^{- 2 x} + 5 \cos (3 x)$	[[_3rd_order, _missing_y]]	✓	1.338

3135	$y^{''} + 4 y = 8 \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.824

3136	$y^{''''} + 4 y = 5 e^{2 x} \sin (3 x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.263

3137	$y^{''} - 5 y^{'} - 6 y = e^{3 x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.688

3138	$y^{''} + 4 y = 12 \cos {(x)}^{2}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.207

3139	$y^{''} - 3 y^{'} + 2 y = x e^{- x}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.747

3140	$y^{''} + y = e^{x} \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.099

3141	$2 y^{''} + y^{'} = 8 \sin (2 x) + e^{- x}$ i.c.	[[_2nd_order, _missing_y]]	✓	2.006

3142	$y^{''} + y = 3 x \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.076

3143	$2 y^{''} + 5 y^{'} - 3 y = \sin (x) - 8 x$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.971

3144	$8 y^{''} - y = x e^{- \frac{x}{2}}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.941

3145	$y^{''} + y = \sec (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.682

3146	$y^{''} + 4 y^{'} + 4 y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.543

3147	$y^{''} + 4 y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.622

3148	$y^{''} - 2 y^{'} + y = e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.574

3149	$y^{''} + y = 4 \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.712

3150	$y^{''} + 4 y = 2 x - 2 \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.897

3151	$y^{''} - y = 3 x + 5 e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.645

3152	$y^{''} + 9 y = e^{x} + \sin (4 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.963

3153	$y^{'''} + 3 y^{''} - 4 y^{'} = \cos (2 x)$	[[_3rd_order, _missing_y]]	✓	0.204

3154	$y^{'''} + 4 y^{''} - 5 y^{'} = e^{3 x}$	[[_3rd_order, _missing_y]]	✓	0.136

3155	$y^{''} + y = \tan (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.768

3156	$y^{''} + a^{2} y = \sec (a x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.146

3157	$y^{'''} - 2 y^{''} + y^{'} = e^{2 x}$	[[_3rd_order, _missing_y]]	✓	0.153

3158	$y^{''''} - 2 y^{'''} + y^{''} = x^{2}$	[[_high_order, _missing_y]]	✓	0.165

3159	$y^{'''} - 3 y^{''} - 4 y^{'} = e^{2 x} + \sin (x)$	[[_3rd_order, _missing_y]]	✓	0.223

3160	$y^{''} - 2 y^{'} + y = \frac{e^{x}}{{(1 - x)}^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.619

3161	$y^{''} - 3 y^{'} + 2 y = \sin (e^{- x})$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.759

3162	$y^{''} + 4 y = \sec (x) \tan (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.053

3163	$y^{''} - 2 y = e^{- x} \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.934

3164	$y^{''} + 9 y = \sec (x) \csc (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.349

3165	$y^{''} + 9 y = \csc (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.356

3166	$y^{''} + y = \tan {(\frac{x}{3})}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.121

3167	$y^{'''} + y^{'} = \tan (x)$	[[_3rd_order, _missing_y]]	✓	0.692

3168	$4 y^{''} - 4 y^{'} + y = e^{\frac{x}{2}} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.707

3169	$y^{'} + P (x) y = Q (x)$	[_linear]	✓	1.119

3170	$y^{''} - 6 y^{'} + 9 y = e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.566

3171	$y^{'''} - 3 y^{''} + 3 y^{'} - y = e^{x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.162

3172	$y^{''} - 5 y^{'} + 6 y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.543

3173	$y^{''} + 4 y = 2 e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.697

3174	$y^{''} + 3 y = 3 e^{- 4 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.757

3175	$y^{''} + 4 y^{'} + 4 y = \frac{e^{x}}{2} + \frac{e^{- x}}{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.014

3176	$y^{''} + y^{'} - 2 y = e^{- 2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.523

3177	$y^{''} + 2 y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.792

3178	$y^{''} + 4 y^{'} + 4 y = \frac{e^{3 x}}{2} - \frac{e^{- 3 x}}{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.952

3179	$y^{''} + 3 y^{'} - 2 y = \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.707

3180	$y^{''} + 3 y^{'} + 2 y = e^{x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.587

3181	$y^{'''} - y = e^{x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.159

3182	$y^{'''} - 4 y^{''} + y^{'} - 4 y = \sin (x) - e^{4 x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.933

3183	$y^{''''} + 3 y^{''} - 4 y = 4 e^{x} + 3 \cos (2 x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.849

3184	$y^{''} + y = e^{3 x} (1 + \sin (2 x))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.159

3185	$y^{''} + 2 n^{2} y^{'} + n^{4} y = \sin (k x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.750

3186	$y^{''} + 4 y^{'} + 5 y = \frac{e^{x}}{2} + \frac{e^{- x}}{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.992

3187	$y^{''} + y^{'} - 2 y = x e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.464

3188	$y^{''} + 4 y = x e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.684

3189	$y^{''} + 2 y = x^{2} e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.757

3190	$y^{''} - y^{'} - 2 y = x^{2} - 8$	[[_2nd_order, _with_linear_symmetries]]	✓	0.448

3191	$y^{'''} - y = x^{2}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.145

3192	$y^{'''} + 4 y^{''} - 5 y^{'} = x^{2} e^{- x}$	[[_3rd_order, _missing_y]]	✓	0.174

3193	$y^{''''} - 2 y^{'''} + y^{''} = x^{2}$	[[_high_order, _missing_y]]	✓	0.161

3194	$y^{'''} - y^{'} = e^{x} (\sin (x) - x^{2})$	[[_3rd_order, _missing_y]]	✓	0.269

3195	$y^{'''} - 4 y^{''} = e^{2 x} (x - 3)$	[[_3rd_order, _missing_y]]	✓	0.175

3196	$y^{''''} - 6 y^{'''} + 9 y^{''} = \sin (3 x) + x e^{x}$	[[_high_order, _missing_y]]	✓	0.494

3197	$y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = x^{2} e^{2 x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.169

3198	$y^{'''} + 2 y^{'} = x^{2} + \cos (x)$	[[_3rd_order, _missing_y]]	✓	0.241

3199	$y^{''''} + 3 y^{''} - y^{'} + 2 y = \sin (2 x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.225

3200	$y^{''''} + 2 y^{''} + y^{'} = x^{3} - \frac{\cos (2 x)}{2}$	[[_high_order, _missing_y]]	✓	0.423

2.2.32 Problems 3101 to 3200