Problems 9001 to 9100

Table 2.183: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

9001	$c y^{'} = y$	[_quadrature]	✓	0.896

9002	$c y^{'} = b y$	[_quadrature]	✓	0.931

9003	$c y^{'} = a x + b y^{2}$	[[_Riccati, _special]]	✓	1.631

9004	$c y^{'} = \frac{a x + b y^{2}}{r}$	[[_Riccati, _special]]	✓	1.620

9005	$c y^{'} = \frac{a x + b y^{2}}{r x}$	[_rational, _Riccati]	✗	6.798

9006	$c y^{'} = \frac{a x + b y^{2}}{r x^{2}}$	[_rational, _Riccati]	✗	8.932

9007	$c y^{'} = \frac{a x + b y^{2}}{y}$	[_rational, _Bernoulli]	✓	2.314

9008	$a \sin (x) y x y^{'} = 0$	[_quadrature]	✓	0.472

9009	$f (x) \sin (x) y x y^{'} π = 0$	[_quadrature]	✓	0.480

9010	$y^{'} = \sin (x) + y$	[[_linear, ‘class A‘]]	✓	1.473

9011	$y^{'} = \sin (x) + y^{2}$	[_Riccati]	✓	3.090

9012	$y^{'} = \cos (x) + \frac{y}{x}$	[_linear]	✓	1.272

9013	$y^{'} = \cos (x) + \frac{y^{2}}{x}$	[_Riccati]	✗	4.612

9014	$y^{'} = x + y + b y^{2}$	[_Riccati]	✓	1.489

9015	$y^{'} x = 0$	[_quadrature]	✓	0.352

9016	$5 y^{'} = 0$	[_quadrature]	✓	0.336

9017	$e y^{'} = 0$	[_quadrature]	✓	0.369

9018	$π y^{'} = 0$	[_quadrature]	✓	0.331

9019	$y^{'} \sin (x) = 0$	[_quadrature]	✓	0.370

9020	$f (x) y^{'} = 0$	[_quadrature]	✓	0.442

9021	$y^{'} x = 1$	[_quadrature]	✓	0.342

9022	$y^{'} x = \sin (x)$	[_quadrature]	✓	0.481

9023	$(x - 1) y^{'} = 0$	[_quadrature]	✓	0.335

9024	$y y^{'} = 0$	[_quadrature]	✓	0.393

9025	$x y^{'} y = 0$	[_quadrature]	✓	0.428

9026	$x y \sin (x) y^{'} = 0$	[_quadrature]	✓	0.459

9027	$π y \sin (x) y^{'} = 0$	[_quadrature]	✓	0.473

9028	$x \sin (x) y^{'} = 0$	[_quadrature]	✓	0.394

9029	$x \sin (x) {y^{'}}^{2} = 0$	[_quadrature]	✓	0.261

9030	$y {y^{'}}^{2} = 0$	[_quadrature]	✓	0.259

9031	${y^{'}}^{n} = 0$	[_quadrature]	✓	0.426

9032	$x {y^{'}}^{n} = 0$	[_quadrature]	✓	0.505

9033	${y^{'}}^{2} = x$	[_quadrature]	✓	0.364

9034	${y^{'}}^{2} = x + y$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	0.782

9035	${y^{'}}^{2} = \frac{y}{x}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.400

9036	${y^{'}}^{2} = \frac{y^{2}}{x}$	[_separable]	✓	1.333

9037	${y^{'}}^{2} = \frac{y^{3}}{x}$	[[_homogeneous, ‘class G‘]]	✓	1.063

9038	${y^{'}}^{3} = \frac{y^{2}}{x}$	[[_homogeneous, ‘class G‘], _rational]	✓	2.184

9039	${y^{'}}^{2} = \frac{1}{x y}$	[[_homogeneous, ‘class G‘]]	✓	0.957

9040	${y^{'}}^{2} = \frac{1}{x y^{3}}$	[[_homogeneous, ‘class G‘]]	✓	0.912

9041	${y^{'}}^{2} = \frac{1}{x^{2} y^{3}}$	[_separable]	✓	0.940

9042	${y^{'}}^{4} = \frac{1}{x y^{3}}$	[[_homogeneous, ‘class G‘], _rational]	✓	1.340

9043	${y^{'}}^{2} = \frac{1}{y^{4} x^{3}}$	[_separable]	✓	1.162

9044	$y^{'} = \sqrt{1 + 6 x + y}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	3.220

9045	$y^{'} = {(1 + 6 x + y)}^{1 / 3}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.024

9046	$y^{'} = {(1 + 6 x + y)}^{1 / 4}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.746

9047	$y^{'} = {(a + b x + y)}^{4}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	295.368

9048	$y^{'} = {(π + x + 7 y)}^{7 / 2}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	9.587

9049	$y^{'} = {(a + b x + c y)}^{6}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	6.140

9050	$y^{'} = e^{x + y}$	[_separable]	✓	2.030

9051	$y^{'} = 10 + e^{x + y}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.210

9052	$y^{'} = 10 e^{x + y} + x^{2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	1.561

9053	$y^{'} = x e^{x + y} + \sin (x)$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	2.341

9054	$y^{'} = 5 e^{x^{2} + 20 y} + \sin (x)$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	2.292

9055	$[\begin{matrix} x^{'} + y^{'} - x = t + y \\ x^{'} + y^{'} = 2 x + 3 y + e^{t} \end{matrix}]$	system_of_ODEs	✓	0.214

9056	$[\begin{matrix} 2 x^{'} + y^{'} - x = t + y \\ x^{'} + y^{'} = 2 x + 3 y + e^{t} \end{matrix}]$	system_of_ODEs	✓	2.396

9057	$[\begin{matrix} x^{'} + y^{'} - x = y + t + \sin (t) + \cos (t) \\ x^{'} + y^{'} = 2 x + 3 y + e^{t} \end{matrix}]$	system_of_ODEs	✓	0.448

9058	$y^{'} t + y = t$ i.c.	[_linear]	✓	0.296

9059	$y^{'} - t y = 0$ i.c.	[_separable]	✓	0.317

9060	$y^{'} t + y = 0$ i.c.	[_separable]	✓	0.315

9061	$y^{'} t + y = 0$ i.c.	[_separable]	✓	0.287

9062	$y^{'} t + y = 0$ i.c.	[_separable]	✓	0.494

9063	$y^{'} t + y = 0$	[_separable]	✓	0.354

9064	$y^{'} t + y = 0$ i.c.	[_separable]	✓	0.482

9065	$y^{'} t + y = \sin (t)$ i.c.	[_linear]	✓	0.774

9066	$y^{'} t + y = t$ i.c.	[_linear]	✓	0.599

9067	$y^{'} t + y = t$ i.c.	[_linear]	✓	0.602

9068	$t^{2} y + y^{'} = 0$ i.c.	[_separable]	✓	0.405

9069	$(a t + 1) y^{'} + y = t$ i.c.	[_linear]	✓	0.537

9070	$y^{'} + (a t + b t) y = 0$ i.c.	[_separable]	✓	0.337

9071	$y^{'} + (a t + b t) y = 0$ i.c.	[_separable]	✓	0.333

9072	$y^{''} = 0$	[[_2nd_order, _quadrature]]	✓	0.689

9073	${y^{''}}^{2} = 0$	[[_2nd_order, _quadrature]]	✓	0.642

9074	${y^{''}}^{n} = 0$	[[_2nd_order, _quadrature]]	✗	0.589

9075	$a y^{''} = 0$	[[_2nd_order, _quadrature]]	✓	0.741

9076	$a {y^{''}}^{2} = 0$	[[_2nd_order, _quadrature]]	✓	0.646

9077	$a {y^{''}}^{n} = 0$	[[_2nd_order, _quadrature]]	✓	0.461

9078	$y^{''} = 1$	[[_2nd_order, _quadrature]]	✓	0.767

9079	${y^{''}}^{2} = 1$	[[_2nd_order, _quadrature]]	✓	1.092

9080	$y^{''} = x$	[[_2nd_order, _quadrature]]	✓	0.847

9081	${y^{''}}^{2} = x$	[[_2nd_order, _quadrature]]	✓	0.566

9082	${y^{''}}^{3} = 0$	[[_2nd_order, _quadrature]]	✓	0.673

9083	$y^{''} + y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	0.997

9084	${y^{''}}^{2} + y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	1.672

9085	$y^{''} + {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]	✓	0.524

9086	$y^{''} + y^{'} = 1$	[[_2nd_order, _missing_x]]	✓	1.065

9087	${y^{''}}^{2} + y^{'} = 1$	[[_2nd_order, _missing_x]]	✓	1.763

9088	$y^{''} + {y^{'}}^{2} = 1$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	✓	1.784

9089	$y^{''} + y^{'} = x$	[[_2nd_order, _missing_y]]	✓	0.968

9090	${y^{''}}^{2} + y^{'} = x$	[[_2nd_order, _missing_y]]	✓	1.150

9091	$y^{''} + {y^{'}}^{2} = x$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]]	✓	0.932

9092	$y^{''} + y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.522

9093	${y^{''}}^{2} + y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✗	0.098

9094	$y^{''} + {y^{'}}^{2} + y = 0$	[[_2nd_order, _missing_x]]	✓	2.033

9095	$y^{''} + y^{'} + y = 1$	[[_2nd_order, _missing_x]]	✓	0.637

9096	$y^{''} + y^{'} + y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.683

9097	$y^{''} + y^{'} + y = x + 1$	[[_2nd_order, _with_linear_symmetries]]	✓	0.661

9098	$y^{''} + y^{'} + y = x^{2} + x + 1$	[[_2nd_order, _with_linear_symmetries]]	✓	0.680

9099	$y^{''} + y^{'} + y = x^{3} + x^{2} + x + 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.696

9100	$y^{''} + y^{'} + y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.714

2.2.91 Problems 9001 to 9100