Problems 15001 to 15100

Table 2.303: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

15001	$y^{'} = \frac{2 + \sqrt{x}}{2 + \sqrt{y}}$	[_separable]	✓	1.646

15002	$y^{'} - 3 x^{2} y^{2} = - 3 x^{2}$	[_separable]	✓	2.276

15003	$y^{'} - 3 x^{2} y^{2} = 3 x^{2}$	[_separable]	✓	2.268

15004	$y^{'} = 200 y - 2 y^{2}$	[_quadrature]	✓	1.126

15005	$y^{'} - 2 y = - 10$ i.c.	[_quadrature]	✓	1.061

15006	$y y^{'} = \sin (x)$ i.c.	[_separable]	✓	2.093

15007	$y^{'} = 2 x - 1 + 2 x y - y$ i.c.	[_separable]	✓	1.436

15008	$y^{'} x = y^{2} - y$ i.c.	[_separable]	✓	1.962

15009	$y^{'} x = y^{2} - y$ i.c.	[_separable]	✓	1.859

15010	$y^{'} = \frac{- 1 + y^{2}}{x y}$ i.c.	[_separable]	✓	3.643

15011	$(- 1 + y^{2}) y^{'} = 4 x y$ i.c.	[_separable]	✓	2.530

15012	$x^{2} y^{'} + 3 x^{2} y = \sin (x)$	[[_linear, ‘class A‘]]	✓	1.873

15013	$y^{2} y^{'} + 3 x^{2} y = \sin (x)$	[‘y=_G(x,y’)‘]	✗	3.064

15014	$y^{'} - x y^{2} = \sqrt{x}$	[_Riccati]	✓	1.787

15015	$y^{'} = 1 + {(x y + 3 y)}^{2}$	[_Riccati]	✓	2.503

15016	$y^{'} = 1 + x y + 3 y$	[_linear]	✓	1.226

15017	$y^{'} = 4 y + 8$	[_quadrature]	✓	0.684

15018	$y^{'} - e^{2 x} = 0$	[_quadrature]	✓	0.398

15019	$y^{'} = y \sin (x)$	[_separable]	✓	1.492

15020	$y^{'} + 4 y = y^{3}$	[_quadrature]	✓	1.589

15021	$y^{'} x + \cos (x^{2}) = 827 y$	[_linear]	✓	22.600

15022	$2 y + y^{'} = 6$	[_quadrature]	✓	0.983

15023	$2 y + y^{'} = 20 e^{3 x}$	[[_linear, ‘class A‘]]	✓	1.153

15024	$y^{'} = 4 y + 16 x$	[[_linear, ‘class A‘]]	✓	0.931

15025	$y^{'} - 2 x y = x$	[_separable]	✓	1.141

15026	$y^{'} x + 3 y - 10 x^{2} = 0$	[_linear]	✓	1.362

15027	$x^{2} y^{'} + 2 x y = \sin (x)$	[_linear]	✓	1.318

15028	$y^{'} x = \sqrt{x} + 3 y$	[_linear]	✓	1.389

15029	$\cos (x) y^{'} + y \sin (x) = \cos {(x)}^{2}$	[_linear]	✓	2.475

15030	$y^{'} x + (5 x + 2) y = \frac{20}{x}$	[_linear]	✓	2.091

15031	$2 \sqrt{x} y^{'} + y = 2 x e^{- \sqrt{x}}$	[_linear]	✓	2.982

15032	$y^{'} - 3 y = 6$ i.c.	[_quadrature]	✓	1.109

15033	$y^{'} - 3 y = 6$ i.c.	[_quadrature]	✓	0.787

15034	$y^{'} + 5 y = e^{- 3 x}$ i.c.	[[_linear, ‘class A‘]]	✓	1.363

15035	$y^{'} x + 3 y = 20 x^{2}$ i.c.	[_linear]	✓	1.745

15036	$y^{'} x = y + x^{2} \cos (x)$ i.c.	[_linear]	✓	1.507

15037	$(x^{2} + 1) y^{'} = x (3 + 3 x^{2} - y)$ i.c.	[_linear]	✓	2.159

15038	$y^{'} + 6 x y = \sin (x)$ i.c.	[_linear]	✓	1.979

15039	$x y + x^{2} y^{'} = \sqrt{x} \sin (x)$ i.c.	[_linear]	✓	2.085

15040	$y^{'} x - y = x^{2} e^{- x^{2}}$ i.c.	[_linear]	✓	1.573

15041	$y^{'} = \frac{1}{{(3 x + 3 y + 2)}^{2}}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	11.403

15042	$y^{'} = \frac{{(3 x - 2 y)}^{2} + 1}{3 x - 2 y} + \frac{3}{2}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	14.028

15043	$\cos (- 4 y + 8 x - 3) y^{'} = 2 + 2 \cos (- 4 y + 8 x - 3)$	[[_homogeneous, ‘class C‘], _exact, _dAlembert]	✓	121.559

15044	$y^{'} = 1 + {(y - x)}^{2}$ i.c.	[[_homogeneous, ‘class C‘], _Riccati]	✓	1.772

15045	$x^{2} y^{'} - x y = y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	1.702

15046	$y^{'} = \frac{x}{y} + \frac{y}{x}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	5.563

15047	$\cos (\frac{y}{x}) (y^{'} - \frac{y}{x}) = 1 + \sin (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.351

15048	$y^{'} = \frac{x - y}{x + y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	9.673

15049	$y^{'} + 3 y = 3 y^{3}$	[_quadrature]	✓	1.395

15050	$y^{'} - \frac{3 y}{x} = \frac{y^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.790

15051	$y^{'} + 3 \cot (x) y = 6 \cos (x) y^{2 / 3}$	[_Bernoulli]	✓	4.043

15052	$y^{'} - \frac{y}{x} = \frac{1}{y}$ i.c.	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	2.554

15053	$y^{'} = \frac{y}{x} + \frac{x^{2}}{y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	10.677

15054	$3 y^{'} = - 2 + \sqrt{2 x + 3 y + 4}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	1.336

15055	$3 y^{'} + \frac{2 y}{x} = 4 \sqrt{y}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.718

15056	$y^{'} = 4 + \frac{1}{\sin (4 x - y)}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	40.087

15057	$(y - x) y^{'} = 1$	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	1.495

15058	$(x + y) y^{'} = y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.750

15059	$(2 x y + 2 x^{2}) y^{'} = x^{2} + 2 x y + 2 y^{2}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	139.245

15060	$y^{'} + \frac{y}{x} = x^{2} y^{3}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.007

15061	$y^{'} = 2 \sqrt{2 x + y - 3} - 2$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	1.407

15062	$y^{'} = 2 \sqrt{2 x + y - 3}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.439

15063	$y^{'} x - y = \sqrt{x^{2} + x y}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	6.571

15064	$y^{'} + 3 y = \frac{28 e^{2 x}}{y^{3}}$	[[_1st_order, _with_linear_symmetries], _Bernoulli]	✓	2.953

15065	$y^{'} = {(x - y + 3)}^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	3.180

15066	$y^{'} + 2 x = 2 \sqrt{y + x^{2}}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	2.045

15067	$y^{'} \cos (y) = e^{- x} - \sin (y)$	[‘y=_G(x,y’)‘]	✓	2.284

15068	$y^{'} = x (1 + \frac{2 y}{x^{2}} + \frac{y^{2}}{x^{4}})$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	1.382

15069	$y^{'} = \frac{1}{y} - \frac{y}{2 x}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.011

15070	$e^{x y^{2} - x^{2}} (y^{2} - 2 x) + 2 e^{x y^{2} - x^{2}} x y y^{'} = 0$	[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]	✓	2.451

15071	$2 x y + y^{2} + (x^{2} + 2 x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	5.020

15072	$2 x y^{3} + 4 x^{3} + 3 x^{2} y^{2} y^{'} = 0$	[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]	✓	2.515

15073	$2 - 2 x + 3 y^{2} y^{'} = 0$	[_separable]	✓	2.011

15074	$1 + 3 x^{2} y^{2} + (2 x^{3} y + 6 y) y^{'} = 0$	[_exact, _rational, _Bernoulli]	✓	2.149

15075	$4 x^{3} y + (x^{4} - y^{4}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	73.496

15076	$1 + \ln (x y) + \frac{x y^{'}}{y} = 0$	[[_homogeneous, ‘class G‘], _exact]	✓	2.133

15077	$1 + e^{y} + x e^{y} y^{'} = 0$	[_separable]	✓	1.494

15078	$e^{y} + (x e^{y} + 1) y^{'} = 0$	[[_1st_order, _with_exponential_symmetries], _exact]	✓	1.062

15079	$1 + y^{4} + x y^{3} y^{'} = 0$	[_separable]	✓	3.617

15080	$y + (y^{4} - 3 x) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.522

15081	$\frac{2 y}{x} + (4 x^{2} y - 3) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.872

15082	$1 + (1 - x \tan (y)) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.390

15083	$3 y + 3 y^{2} + (2 x + 4 x y) y^{'} = 0$	[_separable]	✓	4.234

15084	$2 x (1 + y) - y^{'} = 0$	[_separable]	✓	1.045

15085	$2 y^{3} + (4 x^{3} y^{3} - 3 x y^{2}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.930

15086	$4 x y + (3 x^{2} + 5 y) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.716

15087	$6 + 12 x^{2} y^{2} + (7 x^{3} y + \frac{x}{y}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.525

15088	$y^{'} x = 2 y - 6 x^{3}$	[_linear]	✓	1.479

15089	$y^{'} x = 2 y^{2} - 6 y$	[_separable]	✓	2.062

15090	$4 y^{2} - x^{2} y^{2} + y^{'} = 0$	[_separable]	✓	1.332

15091	$y^{'} = \sqrt{x + y}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	3.052

15092	$x^{2} y^{'} - \sqrt{x} = 3$	[_quadrature]	✓	0.394

15093	$x y^{'} y - y^{2} = \sqrt{x^{2} y^{2} + x^{4}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	31.472

15094	$y^{'} = x^{2} - 2 x y + y^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	1.828

15095	$4 x y - 6 + x^{2} y^{'} = 0$	[_linear]	✓	1.593

15096	$x y^{2} - 6 + x^{2} y y^{'} = 0$	[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]	✓	2.111

15097	$x^{3} + y^{3} + x y^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	15.105

15098	$3 y - x^{3} + y^{'} x = 0$	[_linear]	✓	1.243

15099	$1 + 2 x y^{2} + (2 x^{2} y + 2 y) y^{'} = 0$	[_exact, _rational, _Bernoulli]	✓	2.219

15100	$3 x y^{3} - y + y^{'} x = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	2.485

2.2.151 Problems 15001 to 15100