Problems 7101 to 7200

Table 2.145: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

7101	$y^{'} = y^{2} - 4$ i.c.	[_quadrature]	✓	2.717

7102	$y^{'} = y^{2} - 4$ i.c.	[_quadrature]	✓	3.415

7103	$y^{'} = y^{2} - 4$ i.c.	[_quadrature]	✓	2.921

7104	$y^{'} x = y^{2} - y$ i.c.	[_separable]	✓	1.737

7105	$y^{'} x = y^{2} - y$ i.c.	[_separable]	✓	2.072

7106	$y^{'} x = y^{2} - y$ i.c.	[_separable]	✓	1.904

7107	$y^{'} x = y^{2} - y$ i.c.	[_separable]	✓	1.958

7108	$2 x \sin {(y)}^{2} - (x^{2} + 10) \cos (y) y^{'} = 0$	[_separable]	✓	3.300

7109	$y^{'} = {(- 1 + y)}^{2}$ i.c.	[_quadrature]	✓	0.660

7110	$y^{'} = {(- 1 + y)}^{2}$ i.c.	[_quadrature]	✓	0.634

7111	$y^{'} = {(- 1 + y)}^{2} + \frac{1}{100}$ i.c.	[_quadrature]	✓	0.677

7112	$y^{'} = {(- 1 + y)}^{2} - \frac{1}{100}$ i.c.	[_quadrature]	✓	1.311

7113	$y^{'} = y - y^{3}$ i.c.	[_quadrature]	✓	3.234

7114	$y^{'} = y - y^{3}$ i.c.	[_quadrature]	✓	3.098

7115	$y^{'} = y - y^{3}$ i.c.	[_quadrature]	✓	3.029

7116	$y^{'} = y - y^{3}$ i.c.	[_quadrature]	✓	3.206

7117	$y^{'} = \frac{1}{y - 3}$ i.c.	[_quadrature]	✓	0.974

7118	$y^{'} = \frac{1}{y - 3}$ i.c.	[_quadrature]	✓	0.855

7119	$y^{'} = \frac{1}{y - 3}$ i.c.	[_quadrature]	✓	0.835

7120	$y^{'} = \frac{1}{y - 3}$ i.c.	[_quadrature]	✓	0.877

7121	$y^{'} = \frac{1}{1 + \sin (x)}$	[_quadrature]	✓	0.560

7122	$y^{'} = \frac{\sin (\sqrt{x})}{\sqrt{y}}$	[_separable]	✓	8.115

7123	$(\sqrt{x} + x) y^{'} = \sqrt{y} + y$	[_separable]	✓	7.048

7124	$y^{'} = y^{2 / 3} - y$	[_quadrature]	✓	254.464

7125	$y^{'} = \frac{e^{\sqrt{x}}}{y}$ i.c.	[_separable]	✓	3.008

7126	$y^{'} = \frac{x \arctan (x)}{y}$ i.c.	[_separable]	✓	3.095

7127	$y^{'} = - \frac{x}{y}$ i.c.	[_separable]	✓	2.946

7128	$y^{'} = x \sqrt{y}$	[_separable]	✓	4.826

7129	$y^{'} = \sqrt{1 + y^{2}} \sin {(y)}^{2}$ i.c.	[_quadrature]	✓	3.819

7130	$y^{'} = y$ i.c.	[_quadrature]	✓	1.684

7131	$y^{'} = y + \frac{y}{x \ln (x)}$ i.c.	[_separable]	✓	2.204

7132	${y^{'}}^{2} + y^{2} = 1$	[_quadrature]	✓	0.885

7133	$y^{'} = \sqrt{\frac{1 - y^{2}}{- x^{2} + 1}}$ i.c.	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	3.482

7134	$m^{'} = - \frac{k}{m^{2}}$ i.c.	[_quadrature]	✓	1.362

7135	$u^{'} = a \sqrt{1 + u^{2}}$ i.c.	[_quadrature]	✓	2.081

7136	$x^{'} = k {(A - x)}^{2}$ i.c.	[_quadrature]	✓	1.419

7137	$1 + {x^{'}}^{2} = \frac{a}{y}$	[_quadrature]	✓	0.488

7138	$y^{'} = - \frac{8 x + 5}{3 y^{2} + 1}$ i.c.	[_separable]	✓	2.600

7139	$y^{'} = - \frac{8 x + 5}{3 y^{2} + 1}$ i.c.	[_separable]	✓	2.472

7140	$y^{'} = - \frac{8 x + 5}{3 y^{2} + 1}$ i.c.	[_separable]	✓	2.690

7141	$y^{'} = - \frac{8 x + 5}{3 y^{2} + 1}$ i.c.	[_separable]	✓	2.580

7142	$(2 y + 2) y^{'} - 4 x^{3} - 6 x = 0$ i.c.	[_separable]	✓	1.827

7143	$y^{'} = \frac{x (1 - x)}{y (- 2 + y)}$ i.c.	[_separable]	✓	3.197

7144	$y^{'} = \frac{x (1 - x)}{y (- 2 + y)}$ i.c.	[_separable]	✓	2.408

7145	$y^{'} = 5 y$	[_quadrature]	✓	0.761

7146	$2 y + y^{'} = 0$	[_quadrature]	✓	0.800

7147	$y^{'} + y = e^{3 x}$	[[_linear, ‘class A‘]]	✓	1.058

7148	$3 y^{'} + 12 y = 4$	[_quadrature]	✓	0.986

7149	$y^{'} + 3 x^{2} y = x^{2}$	[_separable]	✓	1.192

7150	$y^{'} + 2 x y = x^{3}$	[_linear]	✓	1.313

7151	$x y + x^{2} y^{'} = 1$	[_linear]	✓	0.939

7152	$y^{'} = 2 y + x^{2} + 5$	[[_linear, ‘class A‘]]	✓	1.039

7153	$y^{'} x - y = x^{2} \sin (x)$	[_linear]	✓	1.238

7154	$y^{'} x + 2 y = 3$	[_separable]	✓	1.883

7155	$4 y + y^{'} x = x^{3} - x$	[_linear]	✓	1.278

7156	$(x + 1) y^{'} - x y = x^{2} + x$	[_linear]	✓	1.398

7157	$x^{2} y^{'} + x (x + 2) y = e^{x}$	[_linear]	✓	1.442

7158	$y^{'} x + (x + 1) y = e^{- x} \sin (2 x)$	[_linear]	✓	3.190

7159	$y - 4 (x + y^{6}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.546

7160	$y = (e^{y} y - 2 x) y^{'}$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.409

7161	$\cos (x) y^{'} + y \sin (x) = 1$	[_linear]	✓	1.984

7162	$\cos {(x)}^{2} \sin (x) y^{'} + \cos {(x)}^{3} y = 1$	[_linear]	✓	4.492

7163	$(x + 1) y^{'} + (x + 2) y = 2 x e^{- x}$	[_linear]	✓	1.763

7164	${(x + 2)}^{2} y^{'} = 5 - 8 y - 4 x y$	[_linear]	✓	1.670

7165	$r^{'} + r \sec (t) = \cos (t)$	[_linear]	✓	2.060

7166	$p^{'} + 2 t p = p + 4 t - 2$	[_separable]	✓	1.372

7167	$y^{'} x + (3 x + 1) y = e^{- 3 x}$	[_linear]	✓	1.752

7168	$(x^{2} - 1) y^{'} + 2 y = {(x + 1)}^{2}$	[_linear]	✓	1.180

7169	$y^{'} = x + 5 y$ i.c.	[[_linear, ‘class A‘]]	✓	1.192

7170	$y^{'} = 2 x - 3 y$ i.c.	[[_linear, ‘class A‘]]	✓	1.242

7171	$y^{'} x + y = e^{x}$ i.c.	[_linear]	✓	1.326

7172	$y y^{'} - x = 2 y^{2}$ i.c.	[_rational, _Bernoulli]	✓	2.239

7173	$L i^{'} + R i = E$ i.c.	[_quadrature]	✓	1.091

7174	$T^{'} = k (T - T_{m})$ i.c.	[_quadrature]	✓	0.871

7175	$y^{'} x + y = 1 + 4 x$ i.c.	[_linear]	✓	1.740

7176	$y^{'} + 4 x y = x^{3} e^{x^{2}}$ i.c.	[_linear]	✓	1.645

7177	$(x + 1) y^{'} + y = \ln (x)$ i.c.	[_linear]	✓	1.544

7178	$x (x + 1) y^{'} + x y = 1$ i.c.	[_linear]	✓	1.407

7179	$y^{'} - y \sin (x) = 2 \sin (x)$ i.c.	[_separable]	✓	1.837

7180	$y^{'} + y \tan (x) = \cos {(x)}^{2}$ i.c.	[_linear]	✓	2.096

7181	$2 y + y^{'} = {\begin{array}{cc} 1 & 0 \leq x \leq 3 \\ 0 & 3 < x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	0.899

7182	$y^{'} + y = {\begin{array}{cc} 1 & 0 \leq x \leq 1 \\ - 1 & 1 < x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	0.858

7183	$y^{'} + 2 x y = {\begin{array}{cc} x & 0 \leq x < 1 \\ 0 & 1 \leq x \end{array}$ i.c.	[_linear]	✓	0.981

7184	$(x^{2} + 1) y^{'} + 2 x y = {\begin{array}{cc} x & 0 \leq x < 1 \\ - x & 1 \leq x \end{array}$ i.c.	[_linear]	✓	0.818

7185	$y^{'} + ({\begin{array}{cc} 2 & 0 \leq x \leq 1 \\ - \frac{2}{x} & 1 < x \end{array}) y = 4 x$ i.c.	[_linear]	✓	1.779

7186	$y^{'} + ({\begin{array}{cc} 1 & 0 \leq x \leq 2 \\ 5 & 2 < x \end{array}) y = 0$ i.c.	[_separable]	✓	1.669

7187	$y^{'} - 2 x y = 1$ i.c.	[_linear]	✓	1.266

7188	$y^{'} - 2 x y = - 1$ i.c.	[_linear]	✓	1.216

7189	$y^{'} + y e^{x} = 1$ i.c.	[_linear]	✓	1.637

7190	$x^{2} y^{'} - y = x^{3}$ i.c.	[_linear]	✓	1.585

7191	$2 x^{2} y + x^{3} y^{'} = 10 \sin (x)$ i.c.	[_linear]	✓	1.740

7192	$y^{'} - \sin (x^{2}) y = 0$ i.c.	[_separable]	✓	4.267

7193	$1 = (x + y^{2}) y^{'}$	[[_1st_order, _with_exponential_symmetries]]	✓	1.003

7194	$y + (2 x + x y - 3) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.249

7195	$y^{'} x - 4 y = x^{6} e^{x}$ i.c.	[_linear]	✓	1.608

7196	$y^{'} x - 4 y = x^{6} e^{x}$ i.c.	[_linear]	✗	1.629

7197	$y^{'} x - 4 y = x^{6} e^{x}$ i.c.	[_linear]	✓	1.399

7198	$[\begin{matrix} x^{'} = - λ_{1} x \\ y^{'} = λ_{1} x - λ_{2} y \end{matrix}]$	system_of_ODEs	✓	0.323

7199	$e^{'} = - \frac{e}{r c}$ i.c.	[_quadrature]	✓	1.186

7200	$2 x - 1 + (3 y + 7) y^{'} = 0$	[_separable]	✓	2.701

2.2.72 Problems 7101 to 7200