Problems 8901 to 9000

Table 2.181: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

8901	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = \cos (x) + \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.863

8902	$x^{2} y^{''} + (\cos (x) - 1) y^{'} + y e^{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.061

8903	$(x - 2) y^{''} + \frac{y^{'}}{x} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.791

8904	$(x - 2) y^{''} + \frac{y^{'}}{x} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.828

8905	$(x + 1) (3 x - 1) y^{''} + \cos (x) y^{'} - 3 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	2.468

8906	$x y^{''} + 2 y^{'} + x y = 0$ i.c.	[_Lienard]	✗	0.618

8907	$2 x^{2} y^{''} + 3 y^{'} x - x y = x^{2} + 2 x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.889

8908	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.735

8909	$2 x^{2} y^{''} + 2 y^{'} x - x y = 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.644

8910	$y^{''} + (x - 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.354

8911	$x^{2} y^{''} + (3 x^{2} + 2 x) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.807

8912	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = x^{2} + \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.954

8913	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.900

8914	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = x^{3} + \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.993

8915	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = x^{3} \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.967

8916	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = x^{3} \cos (x) + \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.027

8917	$2 x^{2} y^{''} - y^{'} x + (- x^{2} + 1) y = \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.670

8918	$2 x^{2} (x^{2} + x + 1) y^{''} + x (11 x^{2} + 11 x + 9) y^{'} + (7 x^{2} + 10 x + 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.927

8919	$(3 + x) x^{2} y^{''} + 5 x (x + 1) y^{'} - (1 - 4 x) y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.782

8920	$x^{2} (- x^{2} + 2) y^{''} - x (4 x^{2} + 3) y^{'} + (- 2 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.728

8921	${y^{'}}^{2} + y^{2} = \sec {(x)}^{4}$	[‘y=_G(x,y’)‘]	✗	34.055

8922	${(y - 2 y^{'} x)}^{2} = {y^{'}}^{3}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	81.651

8923	$x^{2} y^{''} + y = 0$	[[_Emden, _Fowler]]	✓	0.486

8924	$x y^{''} + y^{'} - y = 0$	[[_Emden, _Fowler]]	✓	0.598

8925	$4 x y^{''} + 2 y^{'} + y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.689

8926	$x y^{''} + y^{'} - y = 0$	[[_Emden, _Fowler]]	✓	0.600

8927	$x y^{''} + (x + 1) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.578

8928	$x (x - 1) y^{''} + 3 y^{'} x + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.419

8929	$x^{2} (x^{2} - 2 x + 1) y^{''} - (3 + x) x y^{'} + (x + 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.772

8930	$2 x^{2} (x + 2) y^{''} + 5 x^{2} y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.803

8931	$2 x^{2} y^{''} + y^{'} x + (x - 5) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.922

8932	$2 x^{2} y^{''} + 2 y^{'} x - x y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.865

8933	$2 x^{2} y^{''} + 2 y^{'} x - x y = x \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.776

8934	$2 x^{2} y^{''} + 2 y^{'} x - x y = \sin (x) \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.857

8935	$2 x^{2} y^{''} + 2 y^{'} x - x y = x^{3} + x \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.857

8936	$\cos (x) y^{''} + 2 y^{'} x - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.914

8937	$x^{2} y^{''} + 4 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.655

8938	$x^{2} y^{''} + y^{'} x - x y = 0$	[[_Emden, _Fowler]]	✓	0.591

8939	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.744

8940	$(x^{2} - x) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.402

8941	$x^{2} y^{''} + (x^{2} + 6 x) y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.692

8942	$x^{2} y^{''} - y^{'} x + (x^{2} - 8) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.437

8943	$x^{2} y^{''} - 9 y^{'} x + 25 y = 0$	[[_Emden, _Fowler]]	✓	0.571

8944	$x^{2} y^{''} - y^{'} x - (x^{2} + \frac{5}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.726

8945	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.707

8946	$x y^{''} + (2 - x) y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.677

8947	$2 x^{2} y^{''} + 3 y^{'} x - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.582

8948	$2 x^{2} y^{''} + 5 y^{'} x + 4 y = 0$	[[_Emden, _Fowler]]	✓	0.513

8949	$x^{2} y^{''} + 3 y^{'} x + 4 y x^{4} = 0$	[[_Emden, _Fowler]]	✓	0.627

8950	$x^{2} y^{''} - x y = 0$	[[_Emden, _Fowler]]	✓	1.163

8951	$(- x^{2} + 1) y^{''} + y^{'} + y = x e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.621

8952	$y^{'} = y (1 - y^{2})$	[_quadrature]	✓	2.926

8953	$\frac{x y^{''}}{1 - x} + y = \frac{1}{1 - x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.671

8954	$\frac{x y^{''}}{1 - x} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.020

8955	$\frac{x y^{''}}{1 - x} + y = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	1.112

8956	$\frac{x y^{''}}{- x^{2} + 1} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.568

8957	$y^{''} = (x^{2} + 3) y$	[[_2nd_order, _with_linear_symmetries]]	✓	0.486

8958	$y^{''} + (x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.400

8959	$[\begin{matrix} x^{'} = x + 2 y + 2 t + 1 \\ y^{'} = 5 x + y + 3 t - 1 \end{matrix}]$	system_of_ODEs	✓	1.396

8960	$y^{''} + 20 y^{'} + 500 y = 100000 \cos (100 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.710

8961	$y^{''} \sin {(2 x)}^{2} + y^{'} \sin (4 x) - 4 y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.740

8962	$y^{''} = A y^{2 / 3}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	48.967

8963	$y^{''} + 2 y^{'} x + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.504

8964	$y^{''} + 2 \cot (x) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.697

8965	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.681

8966	$4 x^{2} y^{''} + (- 8 x^{2} + 4 x) y^{'} + (4 x^{2} - 4 x - 1) y = 4 \sqrt{x} e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.765

8967	$x y^{''} - (2 x + 2) y^{'} + (x + 2) y = 6 x^{3} e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.548

8968	$y^{'} + y = \frac{1}{x}$	[[_linear, ‘class A‘]]	✗	0.319

8969	$y^{'} + y = \frac{1}{x^{2}}$	[[_linear, ‘class A‘]]	✗	0.282

8970	$y^{'} x + y = 0$	[_separable]	✓	0.255

8971	$y^{'} = \frac{1}{x}$	[_quadrature]	✗	0.189

8972	$y^{''} = \frac{1}{x}$	[[_2nd_order, _quadrature]]	✗	0.120

8973	$y^{''} + y^{'} = \frac{1}{x}$	[[_2nd_order, _missing_y]]	✗	0.133

8974	$y^{''} + y = \frac{1}{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.121

8975	$y^{''} + y^{'} + y = \frac{1}{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.139

8976	$h^{2} + \frac{2 a h}{\sqrt{1 + {h^{'}}^{2}}} = b^{2}$	[_quadrature]	✓	2.777

8977	$y^{''} + 2 y^{'} - 24 y = 16 - (x + 2) e^{4 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.642

8978	$y^{''} + 3 y^{'} - 4 y = 6 e^{2 t - 2}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.441

8979	$y^{''} + y = e^{a \cos (x)}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.130

8980	$y^{'} = \frac{y}{2 y \ln (y) + y - x}$	[[_1st_order, _with_linear_symmetries]]	✓	1.695

8981	$x y^{''} - (2 x + 1) y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.481

8982	$x^{2} y^{'} + e^{- y} = 0$	[_separable]	✓	1.260

8983	$y^{''} + e^{y} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.914

8984	$y^{'} = \frac{x y + 3 x - 2 y + 6}{x y - 3 x - 2 y + 6}$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✗	1.713

8985	$y^{'} = 0$	[_quadrature]	✓	0.331

8986	$y^{'} = a$	[_quadrature]	✓	0.611

8987	$y^{'} = x$	[_quadrature]	✓	0.323

8988	$y^{'} = 1$	[_quadrature]	✓	0.666

8989	$y^{'} = a x$	[_quadrature]	✓	0.286

8990	$y^{'} = y a x$	[_separable]	✓	1.084

8991	$y^{'} = a x + y$	[[_linear, ‘class A‘]]	✓	0.902

8992	$y^{'} = a x + b y$	[[_linear, ‘class A‘]]	✓	1.071

8993	$y^{'} = y$	[_quadrature]	✓	0.724

8994	$y^{'} = b y$	[_quadrature]	✓	0.746

8995	$y^{'} = a x + b y^{2}$	[[_Riccati, _special]]	✓	1.550

8996	$c y^{'} = 0$	[_quadrature]	✓	0.318

8997	$c y^{'} = a$	[_quadrature]	✓	0.562

8998	$c y^{'} = a x$	[_quadrature]	✓	0.311

8999	$c y^{'} = a x + y$	[[_linear, ‘class A‘]]	✓	1.017

9000	$c y^{'} = a x + b y$	[[_linear, ‘class A‘]]	✓	1.069

2.2.90 Problems 8901 to 9000