Problems 19001 to 19100

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


#	ODE	CAS classiﬁcation	Solved?	time (sec)

19001	$(2 x - 2 y + 5) y^{'} - x + y - 3 = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.910

19002	$x + y + 1 - (2 x + 2 y + 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.012

19003	$y^{2} = (x y - x^{2}) y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	7.398

19004	$x \sin (\frac{y}{x}) y^{'} = y \sin (\frac{y}{x}) - x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	5.743

19005	$(x^{2} + y^{2}) y^{'} = x y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	15.869

19006	$x^{2} y^{'} + y (x + y) = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	3.541

19007	$2 y^{'} = \frac{y}{x} + \frac{y^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	3.421

19008	$(6 x - 5 y + 4) y^{'} + y - 2 x - 1 = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	81.902

19009	$(x - 3 y + 4) y^{'} + 7 y - 5 x = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	7.069

19010	$(2 x + 4 y + 3) y^{'} = 2 y + x + 1$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.948

19011	$- y + x y^{'} = \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	8.435

19012	$x (x^{2} + 3 y^{2}) + y (y^{2} + 3 x^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	26.245

19013	$x^{2} + 3 y^{2} - 2 x y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	7.155

19014	$y^{'} = \frac{2 x - y + 1}{x + 2 y - 3}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.276

19015	$(x - y) y^{'} = x + y + 1$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	37.393

19016	$x - y - 2 - (2 x - 2 y - 3) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.937

19017	$y^{'} + \cot (x) y = 2 \cos (x)$	[_linear]	✓	1.995

19018	$\cos {(x)}^{2} y^{'} + y = \tan (x)$	[_linear]	✓	4.470

19019	$x \cos (x) y^{'} + y (x \sin (x) + \cos (x)) = 1$	[_linear]	✓	6.336

19020	$y - x \sin (x^{2}) + x y^{'} = 0$	[_linear]	✓	1.689

19021	$x \ln (x) y^{'} + y = 2 \ln (x)$	[_linear]	✓	1.174

19022	$\sin (x) \cos (x) y^{'} = y + \sin (x)$	[_linear]	✓	3.543

19023	$(1 + x + x y^{2}) y^{'} + y + y^{3} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.408

19024	$y^{2} + (x - \frac{1}{y}) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	2.123

19025	$y^{'} + 3 x^{2} y = x^{5} e^{x^{3}}$	[_linear]	✓	1.522

19026	$y^{'} - \frac{\tan (y)}{x + 1} = (x + 1) e^{x} \sec (y)$	[‘y=_G(x,y’)‘]	✗	46.418

19027	$y^{'} + \frac{(1 - 2 x) y}{x^{2}} = 1$	[_linear]	✓	1.864

19028	$y^{'} + \frac{2 y}{x} = \sin (x)$	[_linear]	✓	1.584

19029	$1 + y^{2} = (\arctan (y) - x) y^{'}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	6.056

19030	$1 + y + x^{2} y + (x^{3} + x) y^{'} = 0$	[_linear]	✓	1.403

19031	$y^{'} + \frac{x y}{x^{2} + 1} = \frac{1}{2 x (x^{2} + 1)}$	[_linear]	✓	1.428

19032	$y^{'} + \frac{\tan (y)}{x} = \frac{\tan (y) \sin (y)}{x^{2}}$	[‘y=_G(x,y’)‘]	✗	46.005

19033	$y^{'} + \frac{y \ln (y)}{x} = \frac{y}{x^{2}} - \ln {(y)}^{2}$	[‘x=_G(y,y’)‘]	✗	1.824

19034	$y^{'} + x = x e^{(n - 1) y}$	[_separable]	✓	1.889

19035	$y (2 x y + e^{x}) - e^{x} y^{'} = 0$	[_Bernoulli]	✓	2.752

19036	$2 y^{'} - y \sec (x) = y^{3} \tan (x)$	[_Bernoulli]	✓	12.716

19037	$y^{'} + y \cos (x) = y^{n} \sin (2 x)$	[_Bernoulli]	✓	6.137

19038	$x + y y^{'} = \frac{a^{2} (- y + x y^{'})}{x^{2} + y^{2}}$	[[_1st_order, _with_linear_symmetries], _exact, _rational]	✓	1.571

19039	$1 + 4 x y + 2 y^{2} + (1 + 4 x y + 2 x^{2}) y^{'} = 0$	[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.729

19040	$x^{2} y - 2 x y^{2} - (x^{3} - 3 x^{2} y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	36.149

19041	$(x^{4} y^{4} + y^{2} x^{2} + x y) y + (x^{4} y^{4} - y^{2} x^{2} + x y) x y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.923

19042	$y (x y + 2 y^{2} x^{2}) + x (x y - y^{2} x^{2}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.092

19043	$y^{4} + 2 y + (x y^{3} + 2 y^{4} - 4 x) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	2.510

19044	$x^{2} + y^{2} - 2 x y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	7.693

19045	$(20 x^{2} + 8 x y + 4 y^{2} + 3 y^{3}) y + 4 (x^{2} + x y + y^{2} + y^{3}) x y^{'} = 0$	[_rational]	✓	1.822

19046	$y^{2} + 2 x^{2} y + (2 x^{3} - x y) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.089

19047	$2 y + 3 x y^{'} + 2 x y (3 y + 4 x y^{'}) = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	4.057

19048	$\frac{x + y y^{'}}{- y + x y^{'}} = \sqrt{\frac{a^{2} - x^{2} - y^{2}}{x^{2} + y^{2}}}$	[[_1st_order, _with_linear_symmetries]]	✓	508.325

19049	$\frac{(x + y - a) y^{'}}{x + y - b} = \frac{x + y + a}{x + y + b}$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	4.338

19050	${(x - y)}^{2} y^{'} = a^{2}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.962

19051	${(x + y)}^{2} y^{'} = a^{2}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	4.146

19052	$y^{'} = {(4 x + y + 1)}^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	6.028

19053	$- y + x y^{'} = x \sqrt{x^{2} + y^{2}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	3.707

19054	$x y^{'} + y \ln (y) = x y e^{x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	1.593

19055	$- y + x y^{'} = \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	8.220

19056	$x (x^{2} + y^{2} - a^{2}) + y (x^{2} - y^{2} - b^{2}) y^{'} = 0$	[_exact, _rational]	✓	1.897

19057	$y^{'} = \frac{1 + x^{2} + y^{2}}{2 x y}$	[_rational, _Bernoulli]	✓	2.351

19058	$x + y y^{'} = m (- y + x y^{'})$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.201

19059	$y + (a x^{2} y^{n} - 2 x) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	1.638

19060	$y (2 x^{2} y + e^{x}) - (e^{x} + y^{3}) y^{'} = 0$	[‘y=_G(x,y’)‘]	✓	1.918

19061	${x^{'}}^{2} = k^{2} (1 - e^{- \frac{2 g x}{k^{2}}})$ i.c.	[_quadrature]	✓	1.048

19062	$y y^{'} + b y^{2} = a \cos (x)$	[_Bernoulli]	✓	2.931

19063	$y^{'} = e^{- 2 y + 3 x} + x^{2} e^{- 2 y}$	[_separable]	✓	1.572

19064	$x^{2} + y^{2} + x - (2 x^{2} + 2 y^{2} - y) y^{'} = 0$	[_rational]	✓	1.483

19065	$2 y + 3 x y^{'} + 2 x y (3 y + 4 x y^{'}) = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	4.025

19066	$y (1 + \frac{1}{x}) + \cos (y) + (x + \ln (x) - x \sin (y)) y^{'} = 0$	[_exact]	✓	38.715

19067	$(2 x + 2 y + 3) y^{'} = x + y + 1$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.994

19068	$y^{'} = \frac{x (2 \ln (x) + 1)}{\sin (y) + y \cos (y)}$	[_separable]	✓	35.228

19069	$s^{'} + x^{2} = x^{2} e^{3 s}$	[_separable]	✓	2.046

19070	$y^{'} = e^{x - y} (e^{x} - e^{y})$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✗	2.497

19071	$y^{'} = \sin (x + y) + \cos (x + y)$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	74.459

19072	$y^{'} + \frac{\tan (y)}{x} = \frac{\tan (y) \sin (y)}{x^{2}}$	[‘y=_G(x,y’)‘]	✗	45.026

19073	$x^{2} - a y = (a x - y^{2}) y^{'}$	[_exact, _rational]	✓	1.110

19074	$y (2 x y + e^{x}) - e^{x} y^{'} = 0$	[_Bernoulli]	✓	2.704

19075	$y^{2} + x^{2} y^{'} = x y y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	72.090

19076	$y^{'} + \frac{y}{{(- x^{2} + 1)}^{3 / 2}} = \frac{x + \sqrt{- x^{2} + 1}}{{(- x^{2} + 1)}^{2}}$	[_linear]	✓	4.029

19077	$y - x y^{'} + x^{2} + 1 + x^{2} \sin (y) y^{'} = 0$	[‘x=_G(y,y’)‘]	✓	2.126

19078	$\sec {(y)}^{2} y^{'} + 2 x \tan (y) = x^{3}$	[‘y=_G(x,y’)‘]	✓	3.744

19079	$y^{'} + \frac{a x + b y + c}{b x + f y + e} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.094

19080	$y^{''} - n^{2} y = 0$	[[_2nd_order, _missing_x]]	✓	1.637

19081	$y^{'''} - 2 y^{''} - y^{'} + 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.051

19082	$2 x^{''} + 5 x^{'} - 12 x = 0$	[[_2nd_order, _missing_x]]	✓	0.873

19083	$y^{''} + 3 y^{'} - 54 y = 0$	[[_2nd_order, _missing_x]]	✓	0.842

19084	$9 x^{''} + 18 x^{'} - 16 x = 0$	[[_2nd_order, _missing_x]]	✓	0.862

19085	$y^{'''} + y^{''} - 5 y^{'} + 3 y = 0$	[[_3rd_order, _missing_x]]	✓	0.054

19086	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.953

19087	$y^{'''} - 3 y^{''} + 3 y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.052

19088	$y^{''''} - 2 y^{''} + y = 0$	[[_high_order, _missing_x]]	✓	0.053

19089	$y^{''''} + 8 y^{''} + 16 y = 0$	[[_high_order, _missing_x]]	✓	0.068

19090	$y^{'''} + 3 y^{''} + y^{'} - 5 y = 0$	[[_3rd_order, _missing_x]]	✓	0.059

19091	$2 y^{'''} - 3 y^{''} + 2 y^{'} + 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.057

19092	$y^{''''} - y = 0$	[[_high_order, _missing_x]]	✓	0.055

19093	$y^{''''} + 2 y^{''} + y = 0$	[[_high_order, _missing_x]]	✓	0.066

19094	$y^{''} - 5 y^{'} + 6 y = e^{4 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.000

19095	$y^{''} - y = 2 + 5 x$	[[_2nd_order, _with_linear_symmetries]]	✓	1.125

19096	$y^{''} + 2 y^{'} - 15 y = 15 x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.198

19097	$y^{''} + y = \sec {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.967

19098	$y^{''} - 2 y^{'} + y = 2 e^{\frac{5 x}{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.237

19099	$y^{''} + y^{'} + y = e^{- x}$	[[_2nd_order, _with_linear_symmetries]]	✓	21.846

19100	$y^{''} + 2 p y^{'} + (p^{2} + q^{2}) y = e^{k x}$	[[_2nd_order, _with_linear_symmetries]]	✓	44.007

2.2.191 Problems 19001 to 19100