Problems 16801 to 16900

Table 2.339: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

16801	$3 x y^{2} - x^{2} + (3 x^{2} y - 6 y^{2} - 1) y^{'} = 0$	[_exact, _rational]	✓	1.630

16802	$y - x y^{2} \ln (x) + y^{'} x = 0$	[_Bernoulli]	✓	2.216

16803	$2 x y e^{x^{2}} - x \sin (x) + e^{x^{2}} y^{'} = 0$	[_linear]	✓	2.505

16804	$y^{'} = \frac{1}{2 x - y^{2}}$	[[_1st_order, _with_exponential_symmetries]]	✓	1.002

16805	$x^{2} + y^{'} x = 3 x + y^{'}$	[_quadrature]	✓	0.396

16806	$x y^{'} y - y^{2} = x^{4}$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	3.161

16807	$\frac{1}{x^{2} - x y + y^{2}} = \frac{y^{'}}{2 y^{2} - x y}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	16.201

16808	$(2 x - 1) y^{'} - 2 y = \frac{1 - 4 x}{x^{2}}$	[_linear]	✓	1.039

16809	$x - y + 3 + (3 x + y + 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.368

16810	$y^{'} + \cos (\frac{x}{2} + \frac{y}{2}) = \cos (\frac{x}{2} - \frac{y}{2})$	[_separable]	✓	4.979

16811	$y^{'} (3 x^{2} - 2 x) - y (6 x - 2) = 0$	[_separable]	✓	1.158

16812	$x y^{2} y^{'} - y^{3} = \frac{x^{4}}{3}$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	2.676

16813	$1 + e^{\frac{x}{y}} + e^{\frac{x}{y}} (1 - \frac{x}{y}) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _exact, _dAlembert]	✓	5.042

16814	$x^{2} + y^{2} - x y^{'} y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	5.350

16815	$x - y + 2 + (x - y + 3) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.815

16816	$y + x y^{2} - y^{'} x = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	1.764

16817	$2 y y^{'} + 2 x + x^{2} + y^{2} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	2.316

16818	$(x - 1) (y^{2} - y + 1) = (- 1 + y) (x^{2} + x + 1) y^{'}$	[_separable]	✓	2.229

16819	$(x - 2 x y - y^{2}) y^{'} + y^{2} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.942

16820	$\cos (x) y + (2 y - \sin (x)) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.232

16821	$y^{'} - 1 = e^{x + 2 y}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.275

16822	$2 x^{5} + 4 x^{3} y - 2 x y^{2} + (y^{2} + 2 x^{2} y - x^{4}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	4.590

16823	$x^{2} y^{n} y^{'} = 2 y^{'} x - y$	[[_homogeneous, ‘class G‘], _rational]	✓	1.839

16824	$(3 x + 3 y + a^{2}) y^{'} = 4 x + 4 y + b^{2}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.003

16825	$x - y^{2} + 2 x y^{'} y = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.051

16826	$y^{'} x + y = y^{2} \ln (x)$ i.c.	[_Bernoulli]	✓	2.570

16827	$\sin (\ln (x)) - \cos (\ln (y)) y^{'} = 0$	[_separable]	✓	2.552

16828	$y^{'} = \sqrt{\frac{9 y^{2} - 6 y + 2}{x^{2} - 2 x + 5}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	2.299

16829	$(5 x - 7 y + 1) y^{'} + x + y - 1 = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.609

16830	$x + y + 1 + (2 x + 2 y - 1) y^{'} = 0$ i.c.	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.073

16831	$y^{3} + 2 (x^{2} - x y^{2}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.055

16832	$y^{'} = \frac{2 {(y + 2)}^{2}}{{(x + y - 1)}^{2}}$	[[_homogeneous, ‘class C‘], _rational]	✓	1.861

16833	$4 x^{2} {y^{'}}^{2} - y^{2} = x y^{3}$	[[_homogeneous, ‘class G‘]]	✓	2.454

16834	$y^{'} + x {y^{'}}^{2} - y = 0$	[_rational, _dAlembert]	✓	1.154

16835	$y^{''} + y = 2 \cos (x) + 2 \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.886

16836	$x y^{'''} = 2$	[[_3rd_order, _quadrature]]	✓	1.034

16837	$y^{''} = {y^{'}}^{2}$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]	✓	0.505

16838	$(x - 1) y^{''} = 1$	[[_2nd_order, _quadrature]]	✓	0.725

16839	${y^{'}}^{4} = 1$	[_quadrature]	✓	0.508

16840	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	1.267

16841	$y^{''} - 3 y^{'} + 2 y = 2$	[[_2nd_order, _missing_x]]	✓	0.477

16842	$y^{''} = {(1 + {y^{'}}^{2})}^{3 / 2}$	[[_2nd_order, _missing_x]]	✓	2.425

16843	$y y^{''} + {y^{'}}^{2} = 1$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	2.612

16844	$y^{''''} = x$	[[_high_order, _quadrature]]	✓	0.135

16845	$y^{'''} = x + \cos (x)$	[[_3rd_order, _quadrature]]	✓	0.186

16846	$y^{''} {(x + 2)}^{5} = 1$ i.c.	[[_2nd_order, _quadrature]]	✓	0.725

16847	$y^{''} = x e^{x}$ i.c.	[[_2nd_order, _quadrature]]	✓	1.324

16848	$y^{''} = 2 x \ln (x)$	[[_2nd_order, _quadrature]]	✓	1.030

16849	$x y^{''} = y^{'}$	[[_2nd_order, _missing_y]]	✓	1.000

16850	$x y^{''} + y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.827

16851	$x y^{''} = (2 x^{2} + 1) y^{'}$	[[_2nd_order, _missing_y]]	✓	0.819

16852	$x y^{''} = y^{'} + x^{2}$	[[_2nd_order, _missing_y]]	✓	0.941

16853	$x \ln (x) y^{''} = y^{'}$	[[_2nd_order, _missing_y]]	✓	0.536

16854	$x y = y^{'} \ln (\frac{y^{'}}{x})$	[_separable]	✓	2.619

16855	$2 y^{''} = \frac{y^{'}}{x} + \frac{x^{2}}{y^{'}}$ i.c.	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_poly_yn]]	✗	527.245

16856	$y^{'''} = \sqrt{1 - {y^{''}}^{2}}$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	✓	4.847

16857	$x y^{'''} - y^{''} = 0$	[[_3rd_order, _missing_y]]	✓	1.207

16858	$y^{''} = \sqrt{1 + {y^{'}}^{2}}$	[[_2nd_order, _missing_x]]	✓	3.559

16859	$y^{''} = {y^{'}}^{2}$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]	✓	0.544

16860	$y^{''} = \sqrt{1 - {y^{'}}^{2}}$	[[_2nd_order, _missing_x]]	✓	4.708

16861	$y^{''} = 1 + {y^{'}}^{2}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	✓	1.540

16862	$y^{''} = \sqrt{y^{'} + 1}$	[[_2nd_order, _missing_x]]	✓	1.368

16863	$y^{''} = y^{'} \ln (y^{'})$ i.c.	[[_2nd_order, _missing_x]]	✓	0.617

16864	$y^{''} + y^{'} + 2 = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.243

16865	$y^{''} = y^{'} (y^{'} + 1)$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]	✓	1.194

16866	$3 y^{''} = {(1 + {y^{'}}^{2})}^{3 / 2}$	[[_2nd_order, _missing_x]]	✓	1.900

16867	$y^{'''} + {y^{''}}^{2} = 0$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]	✓	0.646

16868	$y y^{''} = {y^{'}}^{2}$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.496

16869	$y^{''} = 2 y y^{'}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	15.761

16870	$3 y^{'} y^{''} = 2 y$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✗	3.446

16871	$2 y^{''} = 3 y^{2}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✗	3.495

16872	$y y^{''} + {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	1.248

16873	$y y^{''} = {y^{'}}^{2} + y^{'}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.523

16874	$y y^{''} = 1 + {y^{'}}^{2}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.694

16875	$2 y y^{''} = 1 + {y^{'}}^{2}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.389

16876	$y^{3} y^{''} = - 1$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.300

16877	$y y^{''} - {y^{'}}^{2} = y^{2} y^{'}$	[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	0.741

16878	$y^{''} = e^{2 y}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.603

16879	$2 y y^{''} - 3 {y^{'}}^{2} = 4 y^{2}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	✓	2.681

16880	$y^{'''} = 3 y y^{'}$ i.c.	[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	✗	0.082

16881	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	1.514

16882	$3 y^{''} - 2 y^{'} - 8 y = 0$	[[_2nd_order, _missing_x]]	✓	0.356

16883	$y^{'''} - 3 y^{''} + 3 y^{'} - y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.137

16884	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.374

16885	$y^{''} - 4 y^{'} + 3 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.591

16886	$y^{'''} + 6 y^{''} + 11 y^{'} + 6 y = 0$	[[_3rd_order, _missing_x]]	✓	0.078

16887	$y^{''} - 2 y^{'} - 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.422

16888	$y^{(6)} + 2 y^{(5)} + y^{''''} = 0$	[[_high_order, _missing_x]]	✓	0.088

16889	$4 y^{''} - 8 y^{'} + 5 y = 0$	[[_2nd_order, _missing_x]]	✓	0.453

16890	$y^{'''} - 8 y = 0$	[[_3rd_order, _missing_x]]	✓	0.089

16891	$y^{''''} + 4 y^{'''} + 10 y^{''} + 12 y^{'} + 5 y = 0$	[[_high_order, _missing_x]]	✓	0.083

16892	$y^{''} - 2 y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.728

16893	$y^{''} - 2 y^{'} + 3 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.868

16894	$y^{''''} + 2 y^{'''} + 4 y^{''} - 2 y^{'} - 5 y = 0$	[[_high_order, _missing_x]]	✓	0.085

16895	$y^{(5)} + 4 y^{''''} + 5 y^{'''} - 6 y^{'} - 4 y = 0$	[[_high_order, _missing_x]]	✓	0.096

16896	$y^{'''} + 2 y^{''} - y^{'} - 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.080

16897	$y^{'''} - 2 y^{''} + 2 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.087

16898	$y^{''''} - y = 0$	[[_high_order, _missing_x]]	✓	0.088

16899	$y^{(5)} = 0$	[[_high_order, _quadrature]]	✓	0.074

16900	$y^{'''} - 3 y^{'} - 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.086

2.2.169 Problems 16801 to 16900