Problems 17801 to 17900

Table 2.359: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

17801	$[\begin{matrix} x_{1}^{'} = 1 - x_{2} + x_{3} \\ x_{2}^{'} = 2 x_{2} + t \\ x_{3}^{'} = - 2 x_{1} - x_{2} + 3 x_{3} + e^{- t} \end{matrix}]$	system_of_ODEs	✓	0.814

17802	$[\begin{matrix} x_{1}^{'} = - \frac{x_{1}}{2} + \frac{x_{2}}{2} - \frac{x_{3}}{2} + 1 \\ x_{2}^{'} = - x_{1} - 2 x_{2} + x_{3} + t \\ x_{3}^{'} = \frac{x_{1}}{2} + \frac{x_{2}}{2} - \frac{3 x_{3}}{2} + 11 e^{- 3 t} \end{matrix}]$	system_of_ODEs	✓	0.908

17803	$[\begin{matrix} x_{1}^{'} = - 4 x_{1} + x_{2} + 3 x_{3} + 3 t \\ x_{2}^{'} = - 2 x_{2} \\ x_{3}^{'} = - 2 x_{1} + x_{2} + x_{3} + 3 \cos (t) \end{matrix}]$	system_of_ODEs	✓	1.018

17804	$[\begin{matrix} x_{1}^{'} = - \frac{x_{1}}{2} + x_{2} + \frac{x_{3}}{2} \\ x_{2}^{'} = x_{1} - x_{2} + x_{3} - \sin (t) \\ x_{3}^{'} = \frac{x_{1}}{2} + x_{2} - \frac{x_{3}}{2} \end{matrix}]$	system_of_ODEs	✓	1.026

17805	$[\begin{matrix} x_{1}^{'} = 2 x_{1} + x_{2} + 1 \\ x_{2}^{'} = x_{1} - 2 x_{2} + x_{3} \\ x_{3}^{'} = x_{2} - x_{3} \end{matrix}]$ i.c.	system_of_ODEs	✓	288.759

17806	$[\begin{matrix} x_{1}^{'} = 4 x_{1} - 9 x_{2} \\ x_{2}^{'} = x_{1} - 2 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.301

17807	$[\begin{matrix} x_{1}^{'} = 3 x_{1} - 9 x_{2} \\ x_{2}^{'} = x_{1} - 3 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.257

17808	$[\begin{matrix} x_{1}^{'} = x_{1} + x_{2} + x_{3} \\ x_{2}^{'} = 2 x_{1} + x_{2} - x_{3} \\ x_{3}^{'} = - 3 x_{1} + 2 x_{2} + 4 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.465

17809	$[\begin{matrix} x_{1}^{'} = 5 x_{1} - 3 x_{2} - 2 x_{3} \\ x_{2}^{'} = 8 x_{1} - 5 x_{2} - 4 x_{3} \\ x_{3}^{'} = - 4 x_{1} + 3 x_{2} + 3 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.464

17810	$[\begin{matrix} x_{1}^{'} = - 7 x_{1} + 9 x_{2} - 6 x_{3} \\ x_{2}^{'} = - 8 x_{1} + 11 x_{2} - 7 x_{3} \\ x_{3}^{'} = - 2 x_{1} + 3 x_{2} - x_{3} \end{matrix}]$	system_of_ODEs	✓	0.617

17811	$[\begin{matrix} x_{1}^{'} = 5 x_{1} + 6 x_{2} + 2 x_{3} \\ x_{2}^{'} = - 2 x_{1} - 2 x_{2} - x_{3} \\ x_{3}^{'} = - 2 x_{1} - 3 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.477

17812	$[\begin{matrix} x_{1}^{'} = - 8 x_{1} - 16 x_{2} - 16 x_{3} - 17 x_{4} \\ x_{2}^{'} = - 2 x_{1} - 10 x_{2} - 8 x_{3} - 7 x_{4} \\ x_{3}^{'} = - 2 x_{1} - 2 x_{3} - 3 x_{4} \\ x_{4}^{'} = 6 x_{1} + 14 x_{2} + 14 x_{3} + 14 x_{4} \end{matrix}]$	system_of_ODEs	✓	1.308

17813	$[\begin{matrix} x_{1}^{'} = x_{1} - x_{2} - 2 x_{3} + 3 x_{4} \\ x_{2}^{'} = 2 x_{1} - \frac{3 x_{2}}{2} - x_{3} + \frac{7 x_{4}}{2} \\ x_{3}^{'} = - x_{1} + \frac{x_{2}}{2} - \frac{3 x_{4}}{2} \\ x_{4}^{'} = - 2 x_{1} + \frac{3 x_{2}}{2} + 3 x_{3} - \frac{7 x_{4}}{2} \end{matrix}]$	system_of_ODEs	✓	0.725

17814	$[\begin{matrix} x_{1}^{'} = x_{1} - 4 x_{2} \\ x_{2}^{'} = 4 x_{1} - 7 x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.511

17815	$[\begin{matrix} x_{1}^{'} = 3 x_{1} - 4 x_{2} \\ x_{2}^{'} = x_{1} - x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.402

17816	$[\begin{matrix} x_{1}^{'} = 4 x_{1} + x_{2} + 3 x_{3} \\ x_{2}^{'} = 6 x_{1} + 4 x_{2} + 6 x_{3} \\ x_{3}^{'} = - 5 x_{1} - 2 x_{2} - 4 x_{3} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.541

17817	$[\begin{matrix} x_{1}^{'} = x_{1} + x_{2} \\ x_{2}^{'} = - 14 x_{1} - 5 x_{2} + x_{3} \\ x_{3}^{'} = 15 x_{1} + 5 x_{2} - 2 x_{3} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.537

17818	$[\begin{matrix} x^{'} = - 2 y + x y \\ y^{'} = x + 4 x y \end{matrix}]$	system_of_ODEs	✓	0.056

17819	$[\begin{matrix} x^{'} = 1 + 5 y \\ y^{'} = 1 - 6 x^{2} \end{matrix}]$	system_of_ODEs	✓	0.060

17820	$y^{'} = 2$	[_quadrature]	✓	0.649

17821	$y^{'} = - x^{3}$	[_quadrature]	✓	0.286

17822	$y^{''} = \sin (x)$	[[_2nd_order, _quadrature]]	✓	0.927

17823	$y y^{'} \sqrt{x^{2} + 1} + x \sqrt{1 + y^{2}} = 0$ i.c.	[_separable]	✓	3.544

17824	$\sec {(x)}^{2} \tan (y) + \sec {(y)}^{2} \tan (x) y^{'} = 0$	[_separable]	✓	39.476

17825	$y^{'} \sqrt{- x^{2} + 1} + \sqrt{1 - y^{2}} = 0$	[_separable]	✓	19.764

17826	$y^{'} = \frac{2 x y}{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.776

17827	$y^{'} = \frac{y (1 + \ln (y) - \ln (x))}{x}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.805

17828	$x^{2} y^{'} + y^{2} = x y^{'} y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	8.865

17829	$(x + y) y^{'} = y - x$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.438

17830	$x - y \cos (\frac{y}{x}) + x \cos (\frac{y}{x}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	6.155

17831	$3 y - 7 x + 7 = (3 x - 7 y - 3) y^{'}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.143

17832	$(x + 2 y + 1) y^{'} = 3 + 2 x + 4 y$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.020

17833	$y^{'} = \frac{2 {(y + 2)}^{2}}{{(x + y - 1)}^{2}}$	[[_homogeneous, ‘class C‘], _rational]	✓	2.022

17834	${(x + y)}^{2} y^{'} = a^{2}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	13.050

17835	$y^{'} x - 4 y = x^{2} \sqrt{y}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.100

17836	$\cos (x) y^{'} = y \sin (x) + \cos {(x)}^{2}$	[_linear]	✓	2.506

17837	$y^{'} = 2 x y - x^{3} + x$	[_linear]	✓	1.460

17838	$y^{'} + \frac{x y}{x^{2} + 1} = \frac{1}{x (x^{2} + 1)}$	[_linear]	✓	1.298

17839	$(x - 2 x y - y^{2}) y^{'} + y^{2} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	2.200

17840	$y^{'} x + y = x y^{2} \ln (x)$	[_Bernoulli]	✓	2.293

17841	$y^{'} - \frac{x y}{2 x^{2} - 2} - \frac{x}{2 y} = 0$	[_rational, _Bernoulli]	✓	2.133

17842	$(x^{2} y^{3} + x y) y^{'} = 1$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.658

17843	$x - y^{2} + 2 x y^{'} y = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.022

17844	$y^{'} = \frac{y^{2}}{3} + \frac{2}{3 x^{2}}$	[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]	✓	1.657

17845	$y^{'} + y^{2} + \frac{y}{x} - \frac{4}{x^{2}} = 0$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	1.991

17846	$y^{'} x - 3 y + y^{2} = 4 x^{2} - 4 x$	[_rational, _Riccati]	✓	1.842

17847	$y^{'} = y^{2} + \frac{1}{x^{4}}$	[_rational, [_Riccati, _special]]	✓	1.682

17848	$(y - x) \sqrt{x^{2} + 1} y^{'} = {(1 + y^{2})}^{3 / 2}$	[‘y=_G(x,y’)‘]	✓	4.246

17849	$y^{'} (x^{2} + y^{2} + 3) = 2 x (2 y - \frac{x^{2}}{y})$	[_rational]	✗	3.043

17850	$y^{'} = \frac{x - y^{2}}{2 y (x + y^{2})}$	[[_homogeneous, ‘class G‘], _rational]	✓	2.365

17851	$((x + y) x + a^{2}) y^{'} = y (x + y) + b^{2}$	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.826

17852	$y^{'} = k y + f (x)$	[[_linear, ‘class A‘]]	✓	1.260

17853	$y^{'} = y^{2} - x^{2}$	[_Riccati]	✓	1.447

17854	$\frac{y y^{'} + x}{\sqrt{x^{2} + y^{2} + 1}} + \frac{y - y^{'} x}{x^{2} + y^{2}} = 0$	[[_1st_order, _with_linear_symmetries], _exact]	✓	2.553

17855	$\frac{2 x}{y^{3}} + \frac{(y^{2} - 3 x^{2}) y^{'}}{y^{4}} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	3.768

17856	$\frac{\sin (\frac{x}{y})}{y} - \frac{y \cos (\frac{y}{x})}{x^{2}} + 1 + (\frac{\cos (\frac{y}{x})}{x} - \frac{x \sin (\frac{x}{y})}{y^{2}} + \frac{1}{y^{2}}) y^{'} = 0$	[_exact]	✓	39.044

17857	$\frac{1}{x} - \frac{y^{2}}{{(x - y)}^{2}} + (\frac{x^{2}}{{(x - y)}^{2}} - \frac{1}{y}) y^{'} = 0$	[_exact, _rational]	✓	2.048

17858	$y^{3} + 2 (x^{2} - x y^{2}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.056

17859	$(x^{2} y^{2} - 1) y^{'} + 2 x y^{3} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.856

17860	$a x y^{'} + b y + x^{m} y^{n} (α x y^{'} + β y) = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.904

17861	$2 x y^{2} - y + (y^{2} + x + y) y^{'} = 0$	[_rational]	✓	1.606

17862	$y^{'} = 2 x y - x^{3} + x$	[_linear]	✓	1.566

17863	$y - x y^{2} \ln (x) + y^{'} x = 0$	[_Bernoulli]	✓	2.179

17864	$(x^{2} - x^{3} + 3 x y^{2} + 2 y^{3}) y^{'} + 2 x^{3} + 3 x^{2} y + y^{2} - y^{3} = 0$	[_rational]	✗	2.799

17865	$y {y^{'}}^{2} + (x - y) y^{'} - x = 0$	[_quadrature]	✓	0.418

17866	$x^{2} {y^{'}}^{2} - 2 x y^{'} y + y^{2} = x^{2} y^{2} + x^{4}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	9.415

17867	${y^{'}}^{3} - (x^{2} + x y + y^{2}) {y^{'}}^{2} + (x y^{3} + x^{2} y^{2} + x^{3} y) y^{'} - x^{3} y^{3} = 0$	[_quadrature]	✓	0.572

17868	$x {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	36.625

17869	$x {y^{'}}^{3} = y^{'} + 1$	[_quadrature]	✓	0.678

17870	${y^{'}}^{3} - x^{3} (1 - y^{'}) = 0$	[_quadrature]	✓	0.672

17871	${y^{'}}^{3} + y^{3} - 3 y y^{'} = 0$	[_quadrature]	✓	310.709

17872	$y = {y^{'}}^{2} e^{y^{'}}$	[_quadrature]	✓	0.739

17873	$y^{2} (y^{'} - 1) = {(2 - y^{'})}^{2}$	[_quadrature]	✓	1.744

17874	$y (1 + {y^{'}}^{2}) = 2 α$	[_quadrature]	✓	0.592

17875	${y^{'}}^{4} = 4 y {(y^{'} x - 2 y)}^{2}$	[[_homogeneous, ‘class G‘]]	✓	0.745

17876	$y = 2 y^{'} x + \frac{x^{2}}{2} + {y^{'}}^{2}$	[[_homogeneous, ‘class G‘]]	✓	1.932

17877	$y = \frac{k (y y^{'} + x)}{\sqrt{1 + {y^{'}}^{2}}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	16.677

17878	$x = y y^{'} + a {y^{'}}^{2}$	[_dAlembert]	✓	111.310

17879	$y = x {y^{'}}^{2} + {y^{'}}^{3}$	[_dAlembert]	✓	2.836

17880	$y = y^{'} x + y^{'} - {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.521

17881	$y = 2 y^{'} x + y^{2} {y^{'}}^{3}$	[[_1st_order, _with_linear_symmetries]]	✓	110.508

17882	${y^{'}}^{2} (x^{2} - 1) - 2 x y^{'} y + y^{2} - 1 = 0$	[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	✓	0.712

17883	${y^{'}}^{2} + 2 y^{'} x + 2 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.552

17884	$y^{'} = \sqrt{y - x}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.314

17885	$y^{'} = \sqrt{y - x} + 1$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	1.282

17886	$y^{'} = \sqrt{y}$	[_quadrature]	✓	0.951

17887	$y^{'} = y \ln (y)$	[_quadrature]	✓	0.761

17888	$y^{'} = y \ln {(y)}^{2}$	[_quadrature]	✓	0.719

17889	$y^{'} = - x + \sqrt{x^{2} + 2 y}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	2.053

17890	$y^{'} = - x - \sqrt{x^{2} + 2 y}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	2.091

17891	$4 x - 2 y y^{'} + x {y^{'}}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.653

17892	$x {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	34.752

17893	$y^{2} (y^{'} - 1) = {(2 - y^{'})}^{2}$	[_quadrature]	✓	1.850

17894	${y^{'}}^{4} = 4 y {(y^{'} x - 2 y)}^{2}$	[[_homogeneous, ‘class G‘]]	✓	0.767

17895	$x^{2} {y^{'}}^{2} - 2 x y^{'} y + 2 x y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.902

17896	$y = {y^{'}}^{2} - y^{'} x + \frac{x^{3}}{2}$	[‘y=_G(x,y’)‘]	✗	4.833

17897	$y = 2 y^{'} x + \frac{x^{2}}{2} + {y^{'}}^{2}$	[[_homogeneous, ‘class G‘]]	✓	1.964

17898	${y^{'}}^{2} - y y^{'} + e^{x} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	6.516

17899	${y^{'''}}^{2} + x^{2} = 1$	[[_3rd_order, _quadrature]]	✓	0.709

17900	$y^{''} = \frac{1}{\sqrt{y}}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	4.522

2.2.179 Problems 17801 to 17900