Problems 6901 to 7000

Table 2.141: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

6901	$2 y^{'} x - y = 2 x \cos (x)$	[_linear]	✓	1.596

6902	$x y + x^{2} y^{'} = 10 \sin (x)$	[_linear]	✓	1.413

6903	$y^{'} + 2 x y = 1$	[_linear]	✓	0.946

6904	$y^{'} x - 2 y = 0$	[_separable]	✓	1.526

6905	$y^{'} = - \frac{x}{y}$	[_separable]	✓	3.139

6906	$2 y + y^{'} = 0$	[_quadrature]	✓	0.825

6907	$5 y^{'} = 2 y$	[_quadrature]	✓	0.753

6908	$y^{''} - 5 y^{'} + 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.341

6909	$2 y^{''} + 7 y^{'} - 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.337

6910	$x y^{''} + 2 y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.891

6911	$4 x^{2} y^{''} + y = 0$	[[_Emden, _Fowler]]	✓	0.417

6912	$x^{2} y^{''} - 7 y^{'} x + 15 y = 0$	[[_Emden, _Fowler]]	✓	0.930

6913	$x^{2} y^{'''} - 3 x y^{''} + 3 y^{'} = 0$	[[_3rd_order, _missing_y]]	✓	0.231

6914	$3 y^{'} x + 5 y = 10$	[_separable]	✓	1.768

6915	$y^{'} = y^{2} + 2 y - 3$	[_quadrature]	✓	0.846

6916	$(- 1 + y) y^{'} = 1$	[_quadrature]	✓	0.941

6917	$y^{''} + 4 y^{'} + 6 y = 10$	[[_2nd_order, _missing_x]]	✓	0.622

6918	${y^{'}}^{2} = 4 y$	[_quadrature]	✓	0.447

6919	${y^{'}}^{2} = 9 - y^{2}$	[_quadrature]	✓	0.922

6920	$y y^{'} + \sqrt{16 - y^{2}} = 0$	[_quadrature]	✓	2.614

6921	${y^{'}}^{2} - 2 y^{'} + 4 y = 4 x - 1$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	0.529

6922	$[\begin{matrix} x^{'} = x + 3 y \\ y^{'} = 5 x + 3 y \end{matrix}]$	system_of_ODEs	✓	0.424

6923	$[\begin{matrix} x^{''} = 4 y + e^{t} \\ y^{''} = 4 x - e^{t} \end{matrix}]$	system_of_ODEs	✓	0.051

6924	$y^{'} = \sqrt{1 - y^{2}}$	[_quadrature]	✓	44.960

6925	$y^{''} + 2 y^{'} + 4 y = 5 \sin (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.720

6926	$y^{'} = f (x)$	[_quadrature]	✓	0.268

6927	$y^{''} = f (x)$	[[_2nd_order, _quadrature]]	✓	0.607

6928	$x {y^{'}}^{2} - 4 y^{'} - 12 x^{3} = 0$	[_quadrature]	✓	0.358

6929	$y^{'} = 5 - y$	[_quadrature]	✓	0.610

6930	$y^{'} = 4 + y^{2}$	[_quadrature]	✓	8.174

6931	$y^{''''} - 20 y^{'''} + 158 y^{''} - 580 y^{'} + 841 y = 0$	[[_high_order, _missing_x]]	✓	0.099

6932	$x^{3} y^{'''} + 2 x^{2} y^{''} + 20 y^{'} x - 78 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.146

6933	$y^{'} = y - y^{2}$ i.c.	[_quadrature]	✓	1.332

6934	$y^{'} = y - y^{2}$ i.c.	[_quadrature]	✓	1.321

6935	$y^{'} + 2 x y^{2} = 0$ i.c.	[_separable]	✓	1.949

6936	$y^{'} + 2 x y^{2} = 0$ i.c.	[_separable]	✓	1.969

6937	$y^{'} + 2 x y^{2} = 0$ i.c.	[_separable]	✓	2.036

6938	$y^{'} + 2 x y^{2} = 0$ i.c.	[_separable]	✓	1.984

6939	$x^{''} + x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	24.052

6940	$x^{''} + x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.262

6941	$x^{''} + x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.823

6942	$x^{''} + x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.921

6943	$y^{''} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.770

6944	$y^{''} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.576

6945	$y^{''} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.431

6946	$y^{''} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.430

6947	$y^{'} = 3 y^{2 / 3}$ i.c.	[_quadrature]	✓	1.544

6948	$y^{'} x = 2 y$ i.c.	[_separable]	✓	1.804

6949	$y^{'} = y^{2 / 3}$	[_quadrature]	✓	1.062

6950	$y^{'} = \sqrt{x y}$	[[_homogeneous, ‘class G‘]]	✓	9.018

6951	$y^{'} x = y$	[_separable]	✓	1.271

6952	$y^{'} - y = x$	[[_linear, ‘class A‘]]	✓	0.929

6953	$(4 - y^{2}) y^{'} = x^{2}$	[_separable]	✓	1.252

6954	$(y^{3} + 1) y^{'} = x^{2}$	[_separable]	✓	1.255

6955	$(x^{2} + y^{2}) y^{'} = y^{2}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.188

6956	$(y - x) y^{'} = x + y$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.923

6957	$y^{'} = \sqrt{y^{2} - 9}$ i.c.	[_quadrature]	✓	24.040

6958	$y^{'} = \sqrt{y^{2} - 9}$ i.c.	[_quadrature]	✓	3.329

6959	$y^{'} = \sqrt{y^{2} - 9}$ i.c.	[_quadrature]	✓	3.545

6960	$y^{'} = \sqrt{y^{2} - 9}$ i.c.	[_quadrature]	✓	9.648

6961	$y^{'} x = y$ i.c.	[_separable]	✓	1.501

6962	$y^{'} = 1 + y^{2}$ i.c.	[_quadrature]	✓	1.631

6963	$y^{'} = y^{2}$ i.c.	[_quadrature]	✓	1.345

6964	$y^{'} = y^{2}$ i.c.	[_quadrature]	✓	1.589

6965	$y^{'} = y^{2}$ i.c.	[_quadrature]	✓	1.266

6966	$y^{'} = y^{2}$ i.c.	[_quadrature]	✓	1.384

6967	$y^{'} = y^{2}$ i.c.	[_quadrature]	✓	1.321

6968	$y y^{'} = 3 x$ i.c.	[_separable]	✓	3.363

6969	$y y^{'} = 3 x$ i.c.	[_separable]	✓	3.156

6970	$y y^{'} = 3 x$ i.c.	[_separable]	✓	6.608

6971	$y^{''} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✗	1.948

6972	$y^{''} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.259

6973	$y^{''} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.272

6974	$y^{''} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.606

6975	$y^{''} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.220

6976	$y^{''} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✗	1.959

6977	$y^{'} = x - 2 y$ i.c.	[[_linear, ‘class A‘]]	✓	1.207

6978	$y^{'} = x^{2} + y^{2}$ i.c.	[[_Riccati, _special]]	✗	1.985

6979	$2 y^{''} - 3 y^{2} = 0$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	2.341

6980	$2 y + y^{'} = 3 x - 6$	[[_linear, ‘class A‘]]	✓	0.978

6981	$y^{'} = x \sqrt{y}$ i.c.	[_separable]	✓	5.470

6982	$y^{'} x = 2 x$	[_quadrature]	✓	0.576

6983	$y^{'} = 2$	[_quadrature]	✓	0.620

6984	$y^{'} = 2 y - 4$	[_quadrature]	✓	0.660

6985	$y^{'} x = y$	[_separable]	✓	1.283

6986	$y^{''} + 9 y = 18$	[[_2nd_order, _missing_x]]	✓	1.600

6987	$x y^{''} - y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.953

6988	$y^{''} = y^{'}$	[[_2nd_order, _missing_x]]	✓	0.749

6989	$y^{'} = y (y - 3)$	[_quadrature]	✓	1.049

6990	$3 y^{'} x - 2 y = 0$	[_separable]	✓	1.575

6991	$(- 2 + 2 y) y^{'} = 2 x - 1$ i.c.	[_separable]	✓	3.188

6992	$y^{'} x + y = 2 x$ i.c.	[_linear]	✓	2.263

6993	$y^{'} = x^{2} + y^{2}$ i.c.	[[_Riccati, _special]]	✓	1.900

6994	${y^{'}}^{2} = 4 x^{2}$	[_quadrature]	✓	0.358

6995	$y^{'} = 6 \sqrt{y} + 5 x^{3}$ i.c.	[_Chini]	✗	1.349

6996	$y^{''} + y = 2 \cos (x) - 2 \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.937

6997	$y^{''} + y = \sec (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.732

6998	$x^{2} y^{''} + y^{'} x + y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.903

6999	$x^{2} y^{''} + y^{'} x + y = \sec (\ln (x))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.544

7000	$y^{'} + y \sin (x) = x$	[_linear]	✓	1.713

2.2.70 Problems 6901 to 7000