Problems 19001 to 19100

Table 2.383: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

19001	$y - y^{'} x = a (y^{'} + y^{2})$	[_separable]	✓	1.600

19002	$(x + y - 1) y^{'} = x + y + 1$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.783

19003	$(2 x + 2 y + 1) y^{'} = x + y + 1$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.033

19004	$2 x + 3 y - 1 + (2 x + 3 y - 5) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.881

19005	$(x^{2} + y^{2}) y^{'} = x^{2} + x y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	6.269

19006	$(x \cos (\frac{y}{x}) + y \sin (\frac{y}{x})) y - (y \sin (\frac{y}{x}) - x \cos (\frac{y}{x})) x y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	7.155

19007	$x^{2} - y^{2} + 2 x y^{'} y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	9.345

19008	$y^{'} = \frac{y}{x} + \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.846

19009	$(2 x - 2 y + 5) y^{'} - x + y - 3 = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.043

19010	$x + y + 1 - (2 x + 2 y + 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.096

19011	$y^{2} = (x y - x^{2}) y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	35.840

19012	$x \sin (\frac{y}{x}) y^{'} = y \sin (\frac{y}{x}) - x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	5.625

19013	$(x^{2} + y^{2}) y^{'} = x y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	3.575

19014	$x^{2} y^{'} + y (x + y) = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.758

19015	$2 y^{'} = \frac{y}{x} + \frac{y^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.843

19016	$(6 x - 5 y + 4) y^{'} + y - 2 x - 1 = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	8.397

19017	$(x - 3 y + 4) y^{'} + 7 y - 5 x = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	7.753

19018	$(3 + 2 x + 4 y) y^{'} = x + 2 y + 1$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.005

19019	$y^{'} x - y = \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.351

19020	$(3 x^{2} + y^{2}) y y^{'} + x (x^{2} + 3 y^{2}) = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	10.571

19021	$x^{2} + 3 y^{2} - 2 x y^{'} y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	4.414

19022	$y^{'} = \frac{1 + 2 x - y}{x + 2 y - 3}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.859

19023	$(x - y) y^{'} = x + y + 1$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.510

19024	$x - y - 2 - (2 x - 2 y - 3) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.951

19025	$y^{'} + \cot (x) y = 2 \cos (x)$	[_linear]	✓	1.914

19026	$\cos {(x)}^{2} y^{'} + y = \tan (x)$	[_linear]	✓	4.159

19027	$x \cos (x) y^{'} + y (x \sin (x) + \cos (x)) = 1$	[_linear]	✓	5.795

19028	$y - x \sin (x^{2}) + y^{'} x = 0$	[_linear]	✓	1.382

19029	$x \ln (x) y^{'} + y = 2 \ln (x)$	[_linear]	✓	1.266

19030	$\cos (x) \sin (x) y^{'} = \sin (x) + y$	[_linear]	✓	3.483

19031	$(x y^{2} + 1 + x) y^{'} + y + y^{3} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.392

19032	$y^{2} + (x - \frac{1}{y}) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	1.985

19033	$y^{'} + 3 x^{2} y = x^{5} e^{x^{3}}$	[_linear]	✓	1.352

19034	$y^{'} - \frac{\tan (y)}{x + 1} = (x + 1) e^{x} \sec (y)$	[‘y=_G(x,y’)‘]	✗	31.380

19035	$y^{'} + \frac{(- 2 x + 1) y}{x^{2}} = 1$	[_linear]	✓	1.554

19036	$y^{'} + \frac{2 y}{x} = \sin (x)$	[_linear]	✓	1.485

19037	$1 + y^{2} = (\arctan (y) - x) y^{'}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	8.149

19038	$1 + y + x^{2} y + (x^{3} + x) y^{'} = 0$	[_linear]	✓	1.279

19039	$y^{'} + \frac{x y}{x^{2} + 1} = \frac{1}{2 x (x^{2} + 1)}$	[_linear]	✓	1.333

19040	$y^{'} + \frac{\tan (y)}{x} = \frac{\tan (y) \sin (y)}{x^{2}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	29.180

19041	$y^{'} + \frac{y \ln (y)}{x} = \frac{y}{x^{2}} - \ln {(y)}^{2}$	[‘x=_G(y,y’)‘]	✗	1.805

19042	$x + y^{'} = x e^{(n - 1) y}$	[_separable]	✓	2.267

19043	$y (e^{x} + 2 x y) - e^{x} y^{'} = 0$	[_Bernoulli]	✓	2.362

19044	$2 y^{'} - y \sec (x) = y^{3} \tan (x)$	[_Bernoulli]	✓	12.279

19045	$y^{'} + \cos (x) y = y^{n} \sin (2 x)$	[_Bernoulli]	✓	5.286

19046	$y y^{'} + x = \frac{a^{2} (y^{'} x - y)}{x^{2} + y^{2}}$	[[_1st_order, _with_linear_symmetries], _exact, _rational]	✓	1.619

19047	$1 + 4 x y + 2 y^{2} + (1 + 4 x y + 2 x^{2}) y^{'} = 0$	[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.748

19048	$x^{2} y - 2 x y^{2} - (x^{3} - 3 x^{2} y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	4.922

19049	$(x^{4} y^{4} + x^{2} y^{2} + x y) y + (x^{4} y^{4} - x^{2} y^{2} + x y) x y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.579

19050	$y (x y + 2 x^{2} y^{2}) + x (x y - x^{2} y^{2}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.987

19051	$y^{4} + 2 y + (x y^{3} + 2 y^{4} - 4 x) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	2.282

19052	$x^{2} + y^{2} - 2 x y^{'} y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	7.496

19053	$(20 x^{2} + 8 x y + 4 y^{2} + 3 y^{3}) y + 4 (x^{2} + x y + y^{2} + y^{3}) x y^{'} = 0$	[_rational]	✓	1.734

19054	$y^{2} + 2 x^{2} y + (2 x^{3} - x y) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.747

19055	$2 y + 3 y^{'} x + 2 x y (3 y + 4 y^{'} x) = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	4.361

19056	$\frac{y y^{'} + x}{y^{'} x - y} = \sqrt{\frac{a^{2} - x^{2} - y^{2}}{x^{2} + y^{2}}}$	[[_1st_order, _with_linear_symmetries]]	✓	288.048

19057	$\frac{(x + y - a) y^{'}}{x + y - b} = \frac{x + y + a}{x + y + b}$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	3.989

19058	${(x - y)}^{2} y^{'} = a^{2}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	4.369

19059	${(x + y)}^{2} y^{'} = a^{2}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	12.540

19060	$y^{'} = {(4 x + y + 1)}^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	13.765

19061	$y^{'} x - y = x \sqrt{x^{2} + y^{2}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	4.086

19062	$y \ln (y) + y^{'} x = y x e^{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	1.666

19063	$y^{'} x - y = \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.232

19064	$x (x^{2} + y^{2} - a^{2}) + y (x^{2} - y^{2} - b^{2}) y^{'} = 0$	[_exact, _rational]	✓	2.328

19065	$y^{'} = \frac{x^{2} + y^{2} + 1}{2 x y}$	[_rational, _Bernoulli]	✓	2.076

19066	$y y^{'} + x = m (y^{'} x - y)$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.523

19067	$y + (a x^{2} y^{n} - 2 x) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	1.760

19068	$y (2 x^{2} y + e^{x}) - (e^{x} + y^{3}) y^{'} = 0$	[‘y=_G(x,y’)‘]	✓	1.977

19069	${x^{'}}^{2} = k^{2} (1 - e^{- \frac{2 g x}{k^{2}}})$ i.c.	[_quadrature]	✓	1.264

19070	$y y^{'} + b y^{2} = a \cos (x)$	[_Bernoulli]	✓	3.805

19071	$y^{'} = e^{3 x - 2 y} + x^{2} e^{- 2 y}$	[_separable]	✓	1.761

19072	$x^{2} + y^{2} + x - (2 x^{2} + 2 y^{2} - y) y^{'} = 0$	[_rational]	✓	1.422

19073	$2 y + 3 y^{'} x + 2 x y (3 y + 4 y^{'} x) = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	4.671

19074	$y (1 + \frac{1}{x}) + \cos (y) + (x + \ln (x) - x \sin (y)) y^{'} = 0$	[_exact]	✓	42.455

19075	$(2 x + 2 y + 3) y^{'} = x + y + 1$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.119

19076	$y^{'} = \frac{x (2 \ln (x) + 1)}{\sin (y) + y \cos (y)}$	[_separable]	✓	36.162

19077	$s^{'} + x^{2} = x^{2} e^{3 s}$	[_separable]	✓	1.896

19078	$y^{'} = e^{x - y} (e^{x} - e^{y})$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	3.058

19079	$y^{'} = \sin (x + y) + \cos (x + y)$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	104.457

19080	$y^{'} + \frac{\tan (y)}{x} = \frac{\tan (y) \sin (y)}{x^{2}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	28.919

19081	$x^{2} - a y = (a x - y^{2}) y^{'}$	[_exact, _rational]	✓	1.271

19082	$y (e^{x} + 2 x y) - e^{x} y^{'} = 0$	[_Bernoulli]	✓	2.339

19083	$x^{2} y^{'} + y^{2} = x y^{'} y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	8.431

19084	$y^{'} + \frac{y}{{(- x^{2} + 1)}^{3 / 2}} = \frac{x + \sqrt{- x^{2} + 1}}{{(- x^{2} + 1)}^{2}}$	[_linear]	✓	3.559

19085	$y - y^{'} x + x^{2} + 1 + x^{2} \sin (y) y^{'} = 0$	[‘x=_G(y,y’)‘]	✓	1.994

19086	$\sec {(y)}^{2} y^{'} + 2 x \tan (y) = x^{3}$	[‘y=_G(x,y’)‘]	✓	3.605

19087	$y^{'} + \frac{a x + b y + c}{b x + f y + e} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.849

19088	$y^{''} - n^{2} y = 0$	[[_2nd_order, _missing_x]]	✓	1.509

19089	$y^{'''} - 2 y^{''} - y^{'} + 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.075

19090	$2 x^{''} + 5 x^{'} - 12 x = 0$	[[_2nd_order, _missing_x]]	✓	0.383

19091	$y^{''} + 3 y^{'} - 54 y = 0$	[[_2nd_order, _missing_x]]	✓	0.326

19092	$9 x^{''} + 18 x^{'} - 16 x = 0$	[[_2nd_order, _missing_x]]	✓	0.340

19093	$y^{'''} + y^{''} - 5 y^{'} + 3 y = 0$	[[_3rd_order, _missing_x]]	✓	0.071

19094	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.345

19095	$y^{'''} - 3 y^{''} + 3 y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.079

19096	$y^{''''} - 2 y^{''} + y = 0$	[[_high_order, _missing_x]]	✓	0.075

19097	$y^{''''} + 8 y^{''} + 16 y = 0$	[[_high_order, _missing_x]]	✓	0.093

19098	$y^{'''} + 3 y^{''} + y^{'} - 5 y = 0$	[[_3rd_order, _missing_x]]	✓	0.088

19099	$2 y^{'''} - 3 y^{''} + 2 y^{'} + 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.085

19100	$y^{''''} - y = 0$	[[_high_order, _missing_x]]	✓	0.087

2.2.191 Problems 19001 to 19100