Problems 7001 to 7100

Table 2.143: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

7001	$y^{'} - 2 x y = e^{x}$	[_linear]	✓	1.283

7002	$x^{2} y^{''} + (x^{2} - x) y^{'} + (1 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.709

7003	$y^{''} + y = e^{x^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.944

7004	$y^{'} x + y = \frac{1}{y^{2}}$	[_separable]	✓	3.341

7005	$1 + {y^{'}}^{2} = \frac{1}{y^{2}}$	[_quadrature]	✓	0.514

7006	$y^{''} = 2 y {y^{'}}^{3}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.464

7007	$(1 - x y) y^{'} = y^{2}$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.367

7008	$y^{''} + 9 y = 5$	[[_2nd_order, _missing_x]]	✓	1.557

7009	$2 y + y^{'} = 3 x$	[[_linear, ‘class A‘]]	✓	0.959

7010	$y^{''} - 2 y^{'} - 3 y = 6 x + 4$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.662

7011	$y^{''} - 2 y^{'} - 3 y = 6 x + 4$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.659

7012	$y^{''} - 2 y^{'} - 3 y = 6 x + 4$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.715

7013	$y^{''} - 2 y^{'} - 3 y = 6 x + 4$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.686

7014	$y^{'} = x^{2} - y^{2}$ i.c.	[_Riccati]	✓	2.401

7015	$y^{'} = x^{2} - y^{2}$ i.c.	[_Riccati]	✓	2.653

7016	$y^{'} = x^{2} - y^{2}$ i.c.	[_Riccati]	✗	2.280

7017	$y^{'} = x^{2} - y^{2}$ i.c.	[_Riccati]	✓	1.843

7018	$y^{'} = e^{- \frac{x y^{2}}{100}}$ i.c.	[‘y=_G(x,y’)‘]	✗	1.147

7019	$y^{'} = e^{- \frac{x y^{2}}{100}}$ i.c.	[‘y=_G(x,y’)‘]	✗	1.137

7020	$y^{'} = e^{- \frac{x y^{2}}{100}}$ i.c.	[‘y=_G(x,y’)‘]	✗	1.100

7021	$y^{'} = e^{- \frac{x y^{2}}{100}}$ i.c.	[‘y=_G(x,y’)‘]	✗	1.117

7022	$y^{'} = 1 - x y$ i.c.	[_linear]	✓	1.293

7023	$y^{'} = 1 - x y$ i.c.	[_linear]	✓	1.263

7024	$y^{'} = 1 - x y$ i.c.	[_linear]	✓	1.390

7025	$y^{'} = 1 - x y$ i.c.	[_linear]	✓	1.155

7026	$y^{'} = \sin (x) \cos (y)$ i.c.	[_separable]	✓	19.050

7027	$y^{'} = \sin (x) \cos (y)$ i.c.	[_separable]	✓	2.708

7028	$y^{'} = \sin (x) \cos (y)$ i.c.	[_separable]	✓	24.344

7029	$y^{'} = \sin (x) \cos (y)$ i.c.	[_separable]	✓	18.526

7030	$y^{'} = x$ i.c.	[_quadrature]	✓	0.520

7031	$y^{'} = x$ i.c.	[_quadrature]	✓	0.484

7032	$y^{'} = x + y$ i.c.	[[_linear, ‘class A‘]]	✓	1.222

7033	$y^{'} = x + y$ i.c.	[[_linear, ‘class A‘]]	✓	1.256

7034	$y y^{'} = - x$ i.c.	[_separable]	✓	3.219

7035	$y y^{'} = - x$ i.c.	[_separable]	✓	6.882

7036	$y^{'} = \frac{1}{y}$ i.c.	[_quadrature]	✓	0.886

7037	$y^{'} = \frac{1}{y}$ i.c.	[_quadrature]	✓	0.868

7038	$y^{'} = \frac{x^{2}}{5} + y$ i.c.	[[_linear, ‘class A‘]]	✓	1.307

7039	$y^{'} = \frac{x^{2}}{5} + y$ i.c.	[[_linear, ‘class A‘]]	✓	1.278

7040	$y^{'} = x e^{y}$ i.c.	[_separable]	✓	2.462

7041	$y^{'} = x e^{y}$ i.c.	[_separable]	✓	2.558

7042	$y^{'} = y - \cos (\frac{π x}{2})$ i.c.	[[_linear, ‘class A‘]]	✓	2.030

7043	$y^{'} = y - \cos (\frac{π x}{2})$ i.c.	[[_linear, ‘class A‘]]	✓	1.818

7044	$y^{'} = 1 - \frac{y}{x}$ i.c.	[_linear]	✓	2.153

7045	$y^{'} = 1 - \frac{y}{x}$ i.c.	[_linear]	✓	2.227

7046	$y^{'} = x + y$	[[_linear, ‘class A‘]]	✓	0.956

7047	$y^{'} = x^{2} + y^{2}$	[[_Riccati, _special]]	✓	1.258

7048	$y^{'} = x {(y - 4)}^{2} - 2$	[_Riccati]	✓	2.336

7049	$y^{'} = x^{2} - 2 y$	[[_linear, ‘class A‘]]	✓	1.087

7050	$y^{'} = y - y^{3}$	[_quadrature]	✓	2.892

7051	$y^{'} = y^{2} - y^{4}$	[_quadrature]	✓	0.900

7052	$y^{'} = y^{2} - 3 y$	[_quadrature]	✓	1.026

7053	$y^{'} = y^{2} - y^{3}$	[_quadrature]	✓	15.567

7054	$y^{'} = {(- 2 + y)}^{4}$	[_quadrature]	✓	1.322

7055	$y^{'} = 10 + 3 y - y^{2}$	[_quadrature]	✓	0.921

7056	$y^{'} = y^{2} (4 - y^{2})$	[_quadrature]	✓	0.968

7057	$y^{'} = y (2 - y) (4 - y)$	[_quadrature]	✓	2.802

7058	$y^{'} = y \ln (y + 2)$	[_quadrature]	✓	2.148

7059	$y^{'} = (e^{y} y - 9 y) e^{- y}$	[_quadrature]	✓	1.626

7060	$y^{'} = \frac{2 y}{π} - \sin (y)$	[_quadrature]	✓	1.541

7061	$y^{'} = y^{2} - y - 6$	[_quadrature]	✓	0.865

7062	$m v^{'} = m g - k v^{2}$	[_quadrature]	✓	2.341

7063	$y^{'} = \sin (5 x)$	[_quadrature]	✓	0.425

7064	$y^{'} = {(x + 1)}^{2}$	[_quadrature]	✓	0.307

7065	$1 + e^{3 x} y^{'} = 0$	[_quadrature]	✓	0.400

7066	$y^{'} - {(- 1 + y)}^{2} = 0$	[_quadrature]	✓	0.417

7067	$y^{'} x = 4 y$	[_separable]	✓	1.569

7068	$y^{'} + 2 x y^{2} = 0$	[_separable]	✓	1.614

7069	$y^{'} = e^{3 x + 2 y}$	[_separable]	✓	2.310

7070	$y e^{x} y^{'} = e^{- y} + e^{- 2 x - y}$	[_separable]	✓	2.118

7071	$y \ln (x) y^{'} = \frac{{(1 + y)}^{2}}{x^{2}}$	[_separable]	✓	2.106

7072	$y^{'} = \frac{{(3 + 2 y)}^{2}}{{(5 + 4 x)}^{2}}$	[_separable]	✓	2.313

7073	$\csc (y) + \sec {(x)}^{2} y^{'} = 0$	[_separable]	✓	2.675

7074	$\sin (3 x) + 2 y \cos {(3 x)}^{3} y^{'} = 0$	[_separable]	✓	45.542

7075	${(1 + e^{y})}^{2} e^{- y} + {(e^{x} + 1)}^{3} e^{- x} y^{'} = 0$	[_separable]	✓	3.576

7076	$x \sqrt{1 + y^{2}} = y y^{'} \sqrt{x^{2} + 1}$	[_separable]	✓	2.669

7077	$s^{'} = k s$	[_quadrature]	✓	0.693

7078	$q^{'} = k (q - 70)$	[_quadrature]	✓	0.654

7079	$p^{'} = p - p^{2}$	[_quadrature]	✓	0.969

7080	$n^{'} + n = n t e^{t + 2}$	[_separable]	✓	1.486

7081	$y^{'} = \frac{x y + 3 x - y - 3}{x y - 2 x + 4 y - 8}$	[_separable]	✓	1.835

7082	$y^{'} = \frac{x y + 2 y - x - 2}{x y - 3 y + x - 3}$	[_separable]	✓	1.840

7083	$y^{'} = x \sqrt{1 - y^{2}}$	[_separable]	✓	35.541

7084	$(e^{x} + e^{- x}) y^{'} = y^{2}$	[_separable]	✓	2.195

7085	$x^{'} = 4 x^{2} + 4$ i.c.	[_quadrature]	✓	32.997

7086	$y^{'} = \frac{- 1 + y^{2}}{x^{2} - 1}$ i.c.	[_separable]	✓	2.037

7087	$x^{2} y^{'} = y - x y$ i.c.	[_separable]	✓	1.898

7088	$y^{'} + 2 y = 1$ i.c.	[_quadrature]	✓	1.001

7089	$\sqrt{1 - y^{2}} - y^{'} \sqrt{- x^{2} + 1} = 0$ i.c.	[_separable]	✓	7.231

7090	$(x^{4} + 1) y^{'} + x (1 + 4 y^{2}) = 0$ i.c.	[_separable]	✓	2.731

7091	$y^{'} = - y \ln (y)$ i.c.	[_quadrature]	✓	1.120

7092	$x \sinh (y) y^{'} = \cosh (y)$ i.c.	[_separable]	✓	2.040

7093	$y^{'} = e^{- x^{2}} y$ i.c.	[_separable]	✓	1.753

7094	$y^{'} = y^{2} \sin (x^{2})$ i.c.	[_separable]	✓	3.170

7095	$y^{'} = (1 + y^{2}) \sqrt{1 + \cos (x^{3})}$ i.c.	[_separable]	✓	79.166

7096	$y^{'} = \frac{e^{- 2 y} \sin (x)}{x^{2} + 1}$ i.c.	[_separable]	✓	2.882

7097	$y^{'} = \frac{3 x + 1}{2 y}$ i.c.	[_separable]	✓	3.076

7098	$(- 2 + 2 y) y^{'} = 3 x^{2} + 4 x + 2$ i.c.	[_separable]	✓	2.038

7099	$e^{y} - e^{- x} y^{'} = 0$ i.c.	[_separable]	✓	2.491

7100	$\sin (x) + y y^{'} = 0$ i.c.	[_separable]	✓	2.108

2.2.71 Problems 7001 to 7100