Problems 8001 to 8100

Table 2.163: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

8001	$(x^{2} + x) y^{''} + (- x^{2} + 2) y^{'} - (x + 2) y = x {(x + 1)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.852

8002	$(1 - x) y^{''} + y^{'} x - y = {(1 - x)}^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.846

8003	$x y^{''} - (x + 1) y^{'} + y = x^{2} e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.717

8004	$x^{2} y^{''} - 2 y^{'} x + 2 y = x e^{- x}$	[[_2nd_order, _with_linear_symmetries]]	✓	2.014

8005	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.181

8006	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	0.165

8007	$x y^{''} + 3 y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.124

8008	$x^{2} y^{''} + y^{'} x - 4 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.130

8009	$(- x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[_Gegenbauer]	✓	0.148

8010	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.135

8011	$y^{''} - \frac{x y^{'}}{x - 1} + \frac{y}{x - 1} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.164

8012	$x^{2} y^{''} + 2 y^{'} x - 2 y = 0$	[[_Emden, _Fowler]]	✓	0.133

8013	$x^{2} y^{''} - x (x + 2) y^{'} + (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.153

8014	$y^{''} - x f (x) y^{'} + f (x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.808

8015	$x y^{''} - (2 x + 1) y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.164

8016	$y^{'''} - 3 y^{''} + 2 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.073

8017	$y^{'''} - 3 y^{''} + 4 y^{'} - 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.081

8018	$y^{'''} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.087

8019	$y^{'''} + y = 0$	[[_3rd_order, _missing_x]]	✓	0.090

8020	$y^{'''} + 3 y^{''} + 3 y^{'} + y = 0$	[[_3rd_order, _missing_x]]	✓	0.076

8021	$y^{''''} + 4 y^{'''} + 6 y^{''} + 4 y^{'} + y = 0$	[[_high_order, _missing_x]]	✓	0.085

8022	$y^{''''} - y = 0$	[[_high_order, _missing_x]]	✓	0.080

8023	$y^{''''} + 5 y^{''} + 4 y = 0$	[[_high_order, _missing_x]]	✓	0.083

8024	$y^{''''} - 2 a^{2} y^{''} + a^{4} y = 0$	[[_high_order, _missing_x]]	✓	0.088

8025	$y^{''''} + 2 a^{2} y^{''} + a^{4} y = 0$	[[_high_order, _missing_x]]	✓	0.102

8026	$y^{''''} + 2 y^{'''} + 2 y^{''} + 2 y^{'} + y = 0$	[[_high_order, _missing_x]]	✓	0.088

8027	$y^{''''} + 2 y^{'''} - 2 y^{''} - 6 y^{'} + 5 y = 0$	[[_high_order, _missing_x]]	✓	0.086

8028	$y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = 0$	[[_3rd_order, _missing_x]]	✓	0.071

8029	$y^{''''} + y^{'''} - 3 y^{''} - 5 y^{'} - 2 y = 0$	[[_high_order, _missing_x]]	✓	0.080

8030	$y^{(5)} - 6 y^{''''} - 8 y^{'''} + 48 y^{''} + 16 y^{'} - 96 y = 0$	[[_high_order, _missing_x]]	✓	0.092

8031	$y^{''''} = 0$	[[_high_order, _quadrature]]	✓	0.075

8032	$y^{''''} = \sin (x) + 24$	[[_high_order, _quadrature]]	✓	0.195

8033	$y^{'''} - 3 y^{''} + 2 y^{'} = 10 + 42 e^{3 x}$	[[_3rd_order, _missing_y]]	✓	0.189

8034	$y^{'''} - y^{'} = 1$ i.c.	[[_3rd_order, _missing_x]]	✓	0.172

8035	$x^{3} y^{'''} + 3 x^{2} y^{''} = 0$	[[_3rd_order, _missing_y]]	✓	0.130

8036	$x^{3} y^{'''} + x^{2} y^{''} - 2 y^{'} x + 2 y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	0.129

8037	$x^{3} y^{'''} + 2 x^{2} y^{''} + y^{'} x - y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.133

8038	$x^{3} y^{''''} + 8 x^{2} y^{'''} + 8 x y^{''} - 8 y^{'} = 0$	[[_high_order, _missing_y]]	✓	0.263

8039	$y^{''} - 3 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.460

8040	$y^{''} + y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.531

8041	$y^{''} + 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.420

8042	$y^{''} - y^{'} + 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.553

8043	$y^{''} - 2 y^{'} - 5 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.549

8044	$y^{''} + y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.613

8045	$y^{''} + y^{'} + y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.665

8046	$y^{''} - y = e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.540

8047	$y^{''} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.783

8048	$y^{''} - y^{'} + 4 y = x$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	1.092

8049	$y^{''} + 2 y^{'} + 5 y = e^{x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.904

8050	$y^{''} + 3 y^{'} + 4 y = \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.227

8051	$y^{''} + y = e^{- x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.976

8052	$y^{''} - y = \cos (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.961

8053	$y^{''} = \tan (x)$ i.c.	[[_2nd_order, _quadrature]]	✓	4.746

8054	$y^{''} - 2 y^{'} = \ln (x)$ i.c.	[[_2nd_order, _missing_y]]	✓	2.208

8055	$y^{''} + 3 y^{'} + 2 y = 2 x - 1$	[[_2nd_order, _with_linear_symmetries]]	✓	0.481

8056	$y^{''} - 3 y^{'} + 2 y = e^{- x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.496

8057	$y^{''} - y^{'} - 2 y = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.464

8058	$y^{''} + 2 y^{'} - y = x e^{x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.712

8059	$y^{''} + 9 y = \sec (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.252

8060	$y^{''} + 4 y^{'} + 4 y = x \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.795

8061	$x^{2} y^{''} + 3 y^{'} x + y = \frac{2}{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.737

8062	$y^{''} + 4 y = \tan {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.912

8063	$y^{''} - y = 3 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.246

8064	$y^{''} + y = - 8 \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.297

8065	$y^{''} + y^{'} + y = x^{2} + 2 x + 2$	[[_2nd_order, _with_linear_symmetries]]	✓	0.277

8066	$y^{''} + y^{'} = \frac{x - 1}{x}$	[[_2nd_order, _missing_y]]	✓	0.390

8067	$x^{2} y^{''} - 2 y^{'} x + 2 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.294

8068	$y^{''} + 9 y = - 3 \cos (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.669

8069	$y^{'} + y = \cos (x)$	[[_linear, ‘class A‘]]	✓	1.330

8070	$y^{''} = - 3 y$ i.c.	[[_2nd_order, _missing_x]]	✓	1.621

8071	$y^{''} + \sin (y) = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	152.823

8072	$y^{'} = 2 x y$	[_separable]	✓	0.404

8073	$y^{'} = 2 x y$	[_separable]	✓	1.128

8074	$y^{'} + y = 1$	[_quadrature]	✓	0.319

8075	$y^{'} + y = 1$	[_quadrature]	✓	0.596

8076	$y^{'} - y = 2$	[_quadrature]	✓	0.314

8077	$y^{'} - y = 2$	[_quadrature]	✓	0.547

8078	$y^{'} + y = 0$	[_quadrature]	✓	0.256

8079	$y^{'} + y = 0$	[_quadrature]	✓	0.734

8080	$y^{'} - y = 0$	[_quadrature]	✓	0.338

8081	$y^{'} - y = 0$	[_quadrature]	✓	0.693

8082	$y^{'} - y = x^{2}$	[[_linear, ‘class A‘]]	✓	0.295

8083	$y^{'} - y = x^{2}$	[[_linear, ‘class A‘]]	✓	0.968

8084	$y^{'} x = y$	[_separable]	✓	0.242

8085	$y^{'} x = y$	[_separable]	✓	1.292

8086	$x^{2} y^{'} = y$	[_separable]	✗	0.105

8087	$x^{2} y^{'} = y$	[_separable]	✓	1.335

8088	$y^{'} - \frac{y}{x} = x^{2}$	[_linear]	✓	0.293

8089	$y^{'} - \frac{y}{x} = x^{2}$	[_linear]	✓	1.304

8090	$y^{'} + \frac{y}{x} = x$	[_linear]	✓	1.082

8091	$y^{'} = \frac{1}{\sqrt{- x^{2} + 1}}$	[_quadrature]	✓	0.450

8092	$y^{'} = 1 + y$	[_quadrature]	✓	0.289

8093	$y^{'} = x - y$ i.c.	[[_linear, ‘class A‘]]	✓	0.399

8094	$y^{'} = x - y$ i.c.	[[_linear, ‘class A‘]]	✓	1.176

8095	$y^{''} + y^{'} x + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.433

8096	$y^{''} - y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.509

8097	$y^{''} + 2 y^{'} x - y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.503

8098	$y^{''} + y^{'} - x^{2} y = 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.585

8099	$(x^{2} + 1) y^{''} + y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.594

8100	$y^{''} + (x + 1) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.532

2.2.81 Problems 8001 to 8100