Problems 17901 to 18000

Table 2.361: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

17901	$a^{3} y^{'''} y^{''} = \sqrt{1 + c^{2} {y^{''}}^{2}}$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	✓	4.386

17902	$y^{'''} = \sqrt{1 + {y^{''}}^{2}}$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	✓	4.012

17903	$2 (2 a - y) y^{''} = 1 + {y^{'}}^{2}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.675

17904	$y^{''} - x y^{'''} + {y^{'''}}^{3} = 0$	[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]]	✓	0.867

17905	$y y^{''} + {y^{'}}^{2} = y^{2} \ln (y)$	[[_2nd_order, _missing_x]]	✓	1.767

17906	$y y^{''} - {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.516

17907	$x y y^{''} + x {y^{'}}^{2} - y y^{'} = 0$	[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	1.225

17908	$n x^{3} y^{''} = {(y - y^{'} x)}^{2}$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✗	0.300

17909	$y^{2} (x^{2} y^{''} - y^{'} x + y) = x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✗	0.280

17910	$x^{2} y^{2} y^{''} - 3 x y^{2} y^{'} + 4 y^{3} + x^{6} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.270

17911	$y^{'} y^{''} - x^{2} y y^{'} - x y^{2} = 0$	[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]	✗	7.171

17912	$x (x^{2} y^{'} + 2 x y) y^{''} + 4 x {y^{'}}^{2} + 8 x y^{'} y + 4 y^{2} - 1 = 0$	[NONE]	✗	0.317

17913	$x (x y + 1) y^{''} + x^{2} {y^{'}}^{2} + (4 x y + 2) y^{'} + y^{2} + 1 = 0$	[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]	✓	1.298

17914	$y y^{''} - {y^{'}}^{2} - {y^{'}}^{4} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	75.263

17915	$a^{2} y^{''} = 2 x \sqrt{1 + {y^{'}}^{2}}$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	1.123

17916	$x^{2} y y^{''} + x^{2} {y^{'}}^{2} - 5 x y^{'} y = 4 y^{2}$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✗	0.278

17917	$y (1 - \ln (y)) y^{''} + (1 + \ln (y)) {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.893

17918	$5 {y^{'''}}^{2} - 3 y^{''} y^{''''} = 0$	[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]	✓	0.998

17919	$40 {y^{'''}}^{3} - 45 y^{''} y^{'''} y^{''''} + 9 {y^{''}}^{2} y^{(5)} = 0$	[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]	✗	0.117

17920	${y^{''}}^{2} + 2 x y^{''} - y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.914

17921	${y^{''}}^{2} - 2 x y^{''} - y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.922

17922	$2 x^{3} y^{'''} - 6 x^{2} y^{''} + 12 y^{'} x - 12 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.146

17923	$y^{'''} - \frac{3 y^{''}}{x} + \frac{6 y^{'}}{x^{2}} - \frac{6 y}{x^{3}} = 0$	[[_3rd_order, _fully, _exact, _linear]]	✓	0.155

17924	$(- x^{2} + 1) y^{''} - 2 y^{'} x + n (n + 1) y = 0$	[_Gegenbauer]	✗	1.292

17925	$y^{''} + \frac{2 y^{'}}{x} + y = 0$	[_Lienard]	✓	0.583

17926	$\sin {(x)}^{2} y^{''} = 2 y$	[[_2nd_order, _with_linear_symmetries]]	✗	1.085

17927	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 y^{'} x - 6 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.143

17928	$x y^{'''} - y^{''} + y^{'} x - y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.078

17929	$(- x^{2} + 1) y^{'''} - x y^{''} + y^{'} = 0$	[[_3rd_order, _missing_y]]	✓	1.073

17930	$x^{2} y^{''} - 2 y^{'} x + 2 y = 2 x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.521

17931	$y^{''} + \frac{x y^{'}}{1 - x} - \frac{y}{1 - x} = x - 1$	[[_2nd_order, _with_linear_symmetries]]	✓	0.926

17932	$(x^{2} + 2) y^{'''} - 2 x y^{''} + (x^{2} + 2) y^{'} - 2 x y = x^{4} + 12$	[[_3rd_order, _linear, _nonhomogeneous]]	✗	0.082

17933	$y^{'''} + y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.071

17934	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	1.329

17935	$y^{''} + \frac{y}{x^{2} \ln (x)} = e^{x} (\frac{2}{x} + \ln (x))$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.533

17936	$y^{''} + p_{1} y^{'} + p_{2} y = 0$	[[_2nd_order, _missing_x]]	✓	1.384

17937	$(2 x + 1) y^{''} + (4 x - 2) y^{'} - 8 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.533

17938	$\sin {(x)}^{2} y^{''} + \cos (x) \sin (x) y^{'} = y$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.631

17939	$y^{''''} - 2 y^{''} = 0$	[[_high_order, _missing_x]]	✓	0.078

17940	$y^{'''} - 3 y^{''} + 3 y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.081

17941	$y^{''''} + 4 y = 0$	[[_high_order, _missing_x]]	✓	0.092

17942	$y^{''''} - y = 0$	[[_high_order, _missing_x]]	✓	0.082

17943	$2 y^{''} + y^{'} - y = 0$	[[_2nd_order, _missing_x]]	✓	0.352

17944	$y^{''''} + 2 y^{'''} + 3 y^{''} + 2 y^{'} + y = 0$	[[_high_order, _missing_x]]	✓	0.108

17945	$y^{''} - 4 y^{'} + 4 y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.590

17946	$y^{''} - 6 y^{'} + 8 y = e^{x} + e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.511

17947	$y^{'''} + y^{''} + y^{'} + y = x e^{x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.175

17948	$y^{''''} - 4 y^{'''} + 6 y^{''} - 4 y^{'} + y = e^{x} (x + 1)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.186

17949	$y^{''} + 4 y = x \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.880

17950	$y^{''} + y^{'} + y = e^{- \frac{x}{2}} \sin (\frac{\sqrt{3} x}{2})$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.724

17951	$y^{''} - y = \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.813

17952	$y^{''} - 2 y = 4 x^{2} e^{x^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.621

17953	$y^{''} + y = \sin (2 x) \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.254

17954	$y^{''} + 9 y = \ln (2 \sin (\frac{x}{2}))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.009

17955	$y^{''} + \frac{2 y^{'}}{x} - \frac{n (n + 1) y}{x^{2}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.930

17956	$x^{2} y^{''} - 4 y^{'} x + 6 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	1.424

17957	$x^{2} y^{''} - y^{'} x + 2 y = x \ln (x)$	[[_2nd_order, _with_linear_symmetries]]	✓	2.297

17958	$x^{2} y^{''} - 2 y = x^{2} + \frac{1}{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	0.888

17959	$x^{3} y^{'''} - x^{2} y^{''} + 2 y^{'} x - 2 y = x^{3} + 3 x$	[[_3rd_order, _with_linear_symmetries]]	✓	0.342

17960	${(x + 1)}^{2} y^{''} + (x + 1) y^{'} + y = 4 \cos (\ln (x + 1))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.641

17961	$y^{''} - \frac{y^{'}}{x} + (1 - \frac{m^{2}}{x^{2}}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.679

17962	$y^{''} + \frac{2 y^{'}}{x} + y = 0$	[_Lienard]	✓	0.593

17963	$y^{''} + \frac{2 p y^{'}}{x} + y = 0$	[_Lienard]	✓	0.842

17964	$x y^{''} - y^{'} - x^{3} y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.796

17965	$y^{''} - 4 y^{'} x + (4 x^{2} - 1) y = - 3 e^{x^{2}} \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.981

17966	$y^{''} - \frac{y^{'}}{\sqrt{x}} + \frac{(x + \sqrt{x} - 8) y}{4 x^{2}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.532

17967	$[\begin{matrix} x^{'} = y \\ y^{'} = z \\ z^{'} = x \end{matrix}]$	system_of_ODEs	✓	0.820

17968	$[\begin{matrix} y^{'} = y + z \\ z^{'} = y + z + x \end{matrix}]$	system_of_ODEs	✓	0.539

17969	$[\begin{matrix} y^{'} = \frac{y^{2}}{z} \\ z^{'} = \frac{y}{2} \end{matrix}]$	system_of_ODEs	✓	0.060

17970	$[\begin{matrix} y^{'} = 1 - \frac{1}{z} \\ z^{'} = \frac{1}{y - x} \end{matrix}]$	system_of_ODEs	✓	0.065

17971	$[\begin{matrix} y^{'} = - z \\ z^{'} = y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.560

17972	$y^{''} = x + y^{2}$ i.c.	[NONE]	✗	0.331

17973	$y^{''} + 2 y^{'} + y^{2} = 0$ i.c.	[[_2nd_order, _missing_x], [_Emden, _modiﬁed]]	✗	1.836

17974	$[\begin{matrix} y^{'} = \frac{z^{2}}{y} \\ z^{'} = \frac{y^{2}}{z} \end{matrix}]$	system_of_ODEs	✓	0.060

17975	$[\begin{matrix} y^{'} = \frac{y^{2}}{z} \\ z^{'} = \frac{z^{2}}{y} \end{matrix}]$	system_of_ODEs	✓	0.059

17976	$[\begin{matrix} x^{'} = y + z - x \\ y^{'} = x - y + z \\ z^{'} = x + y - z \end{matrix}]$	system_of_ODEs	✓	0.443

17977	$[\begin{matrix} x^{'} + x + y = t^{2} \\ y^{'} + y + z = 2 t \\ z^{'} + z = t \end{matrix}]$	system_of_ODEs	✓	0.570

17978	$[\begin{matrix} x^{'} + 5 x + y = 7 e^{t} - 27 \\ - 2 x + y^{'} + 3 y = - 3 e^{t} + 12 \end{matrix}]$	system_of_ODEs	✓	1.238

17979	$[\begin{matrix} y^{''} + z^{'} - 2 z = e^{2 x} \\ z^{'} + 2 y^{'} - 3 y = 0 \end{matrix}]$	system_of_ODEs	✓	0.053

17980	$[\begin{matrix} x^{'} = y \\ y^{'} = x + e^{t} + e^{- t} \end{matrix}]$	system_of_ODEs	✓	0.771

17981	$[\begin{matrix} y^{'} + \frac{2 z}{x^{2}} = 1 \\ z^{'} + y = x \end{matrix}]$	system_of_ODEs	✓	0.062

17982	$[\begin{matrix} x^{'} t - x - 3 y = t \\ y^{'} t - x + y = 0 \end{matrix}]$	system_of_ODEs	✓	0.066

17983	$[\begin{matrix} x^{'} t + 6 x - y - 3 z = 0 \\ y^{'} t + 23 x - 6 y - 9 z = 0 \\ t z^{'} + x + y - 2 z = 0 \end{matrix}]$	system_of_ODEs	✓	0.079

17984	$[\begin{matrix} x^{'} + 5 x + y = e^{t} \\ y^{'} - x + 3 y = e^{2 t} \end{matrix}]$	system_of_ODEs	✓	0.552

17985	$y^{'} = 2 x$	[_quadrature]	✓	0.290

17986	$y^{'} x = 2 y$	[_separable]	✓	1.589

17987	$y y^{'} = e^{2 x}$	[_separable]	✓	1.795

17988	$y^{'} = k y$	[_quadrature]	✓	0.703

17989	$y^{''} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	1.391

17990	$y^{''} - 4 y = 0$	[[_2nd_order, _missing_x]]	✓	1.504

17991	$y^{'} x + y = y^{'} \sqrt{1 - x^{2} y^{2}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	46.421

17992	$y^{'} x = y + x^{2} + y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	1.505

17993	$y^{'} = \frac{x y}{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	3.336

17994	$2 x y^{'} y = x^{2} + y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	7.160

17995	$y^{'} x + y = x^{4} {y^{'}}^{2}$	[[_homogeneous, ‘class G‘], _rational]	✓	1.753

17996	$y^{'} = \frac{y^{2}}{x y - x^{2}}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	92.691

17997	$(y \cos (y) - \sin (y) + x) y^{'} = y$	[[_1st_order, _with_linear_symmetries]]	✓	1.748

17998	$1 + y^{2} + y^{2} y^{'} = 0$	[_quadrature]	✓	0.607

17999	$y^{'} = e^{3 x} - x$	[_quadrature]	✓	0.362

18000	$y^{'} x = 1$	[_quadrature]	✓	0.334

2.2.180 Problems 17901 to 18000