Problems 13901 to 14000

Table 2.281: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

13901	$x^{2} y^{''} - y = \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.995

13902	$y^{''} = y + x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.428

13903	$y^{'''} + x y^{''} - y^{2} = \sin (x)$	[NONE]	✗	0.100

13904	${y^{'}}^{2} + x y {y^{'}}^{2} = \ln (x)$	[‘y=_G(x,y’)‘]	✗	6.277

13905	$\sin (y^{''}) + y y^{''''} = 1$	[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]]	✗	0.094

13906	$\sinh (x) {y^{'}}^{2} + y^{''} = x y$	[NONE]	✗	0.375

13907	$y y^{''} = 1$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	0.936

13908	${y^{'''}}^{2} + \sqrt{y} = \sin (x)$	[NONE]	✗	0.115

13909	$y^{''} + 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.395

13910	$y^{'''} - 5 y^{''} + y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.128

13911	$2 y^{''} - 3 y^{'} - 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.343

13912	$3 y^{''''} - 2 y^{''} + y^{'} = 0$	[[_high_order, _missing_x]]	✓	0.082

13913	$(x - 3) y^{''} + y \ln (x) = x^{2}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.600

13914	$y^{''} + y^{'} \tan (x) + \cot (x) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✗	2.493

13915	$(x^{2} + 1) y^{''} + (x - 1) y^{'} + y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✗	1.431

13916	$x y^{''} + 2 x^{2} y^{'} + y \sin (x) = \sinh (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✗	1.650

13917	$\sin (x) y^{''} + y^{'} x + 7 y = 1$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✗	2.028

13918	$y^{''} - (x - 1) y^{'} + x^{2} y = \tan (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✗	1.098

13919	$(x - 1) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.836

13920	$x^{2} y^{''} - 4 x^{2} y^{'} + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.852

13921	$y^{''} + \frac{k x}{y^{4}} = 0$	[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]	✗	0.273

13922	$y^{''} + 2 y^{'} x + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.687

13923	$x y^{''} + y^{'} \sin (x) + \cos (x) y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.036

13924	$y^{''} + 2 x^{2} y^{'} + 4 x y = 2 x$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.348

13925	$(- x^{2} + 1) y^{''} + (1 - x) y^{'} + y = - 2 x + 1$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.123

13926	$y^{''} + 4 y^{'} x + (4 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.517

13927	$x^{2} y^{''} + x^{2} y^{'} + 2 (1 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.846

13928	$y^{''} + x^{2} y^{'} + 2 x y = 2 x$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.378

13929	$\ln (x^{2} + 1) y^{''} + \frac{4 x y^{'}}{x^{2} + 1} + \frac{(- x^{2} + 1) y}{{(x^{2} + 1)}^{2}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.142

13930	$x y^{''} + x^{2} y^{'} + 2 x y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.883

13931	$y^{''} + y^{'} \sin (x) + \cos (x) y = \cos (x)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.149

13932	$y^{''} + \cot (x) y^{'} - y \csc {(x)}^{2} = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.803

13933	$x \ln (x) y^{''} + 2 y^{'} - \frac{y}{x} = 1$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	0.965

13934	$x y^{''} + (6 x y^{2} + 1) y^{'} + 2 y^{3} + 1 = 0$	[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	✗	2.117

13935	$\frac{x y^{''}}{1 + y} + \frac{y y^{'} - x {y^{'}}^{2} + y^{'}}{{(1 + y)}^{2}} = x \sin (x)$	[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	1.693

13936	$(x \cos (y) + \sin (x)) y^{''} - x {y^{'}}^{2} \sin (y) + 2 (\cos (y) + \cos (x)) y^{'} = y \sin (x)$	[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]	✓	50.893

13937	$y y^{''} \sin (x) + (y^{'} \sin (x) + \cos (x) y) y^{'} = \cos (x)$	[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	✓	1.301

13938	$(1 - y) y^{''} - {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	1.429

13939	$(\cos (y) - y \sin (y)) y^{''} - {y^{'}}^{2} (2 \sin (y) + y \cos (y)) = \sin (x)$	[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	✓	1.322

13940	$y^{''} + \frac{2 x y^{'}}{2 x - 1} - \frac{4 x y}{{(2 x - 1)}^{2}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.699

13941	$(x^{2} + 2 x) y^{''} + (x^{2} + x + 10) y^{'} = (25 - 6 x) y$	[[_2nd_order, _with_linear_symmetries]]	✓	0.712

13942	$y^{''} + \frac{y^{'}}{x + 1} - \frac{(x + 2) y}{x^{2} (x + 1)} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.708

13943	$(x^{2} - x) y^{''} + (2 x^{2} + 4 x - 3) y^{'} + 8 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.636

13944	$\frac{(x^{2} - x) y^{''}}{x} + \frac{(3 x + 1) y^{'}}{x} + \frac{y}{x} = 3 x$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.645

13945	$(2 \sin (x) - \cos (x)) y^{''} + (7 \sin (x) + 4 \cos (x)) y^{'} + 10 \cos (x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	10.349

13946	$y^{''} + \frac{(x - 1) y^{'}}{x} + \frac{y}{x^{3}} = \frac{e^{- \frac{1}{x}}}{x^{3}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	0.802

13947	$y^{''} + (5 + 2 x) y^{'} + (8 + 4 x) y = e^{- 2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.746

13948	$y^{''} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.412

13949	$4 y^{''} - 4 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.441

13950	$y^{''} + 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.288

13951	$y^{''} - 4 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.329

13952	$y^{''} - y^{'} - 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.291

13953	$4 y^{''} - 4 y^{'} + 37 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.470

13954	$y^{''} + 3 y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.331

13955	$y^{''} + 2 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.351

13956	$4 y^{''} - 12 y^{'} + 13 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.353

13957	$y^{''} + 4 y^{'} + 13 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.443

13958	$y^{''} + 6 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.294

13959	$y^{''''} + y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.735

13960	$y^{''} - 2 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.334

13961	$y^{''} - 20 y^{'} + 51 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.298

13962	$2 y^{''} + 3 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.311

13963	$3 y^{''} + 8 y^{'} - 3 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.307

13964	$2 y^{''} + 20 y^{'} + 51 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.434

13965	$4 y^{''} + 40 y^{'} + 101 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.352

13966	$y^{''} + 6 y^{'} + 34 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.468

13967	$y^{'''} + 8 y^{''} + 16 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.330

13968	$y^{'''} + 6 y^{''} + 13 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.471

13969	$y^{'''} - 6 y^{''} + 13 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.472

13970	$y^{'''} + 4 y^{''} + 29 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.497

13971	$y^{'''} + 6 y^{''} + 25 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.459

13972	$y^{'''} - 6 y^{''} + 10 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.498

13973	$y^{''''} + 13 y^{''} + 36 y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.470

13974	$y^{''} + 2 y^{'} + 3 y = 9 t$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.368

13975	$4 y^{''} + 16 y^{'} + 17 y = 17 t - 1$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.369

13976	$4 y^{''} + 5 y^{'} + 4 y = 3 e^{- t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.539

13977	$y^{''} - 4 y^{'} + 4 y = e^{2 t} t^{2}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.314

13978	$y^{''} + 9 y = e^{- 2 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.505

13979	$2 y^{''} - 3 y^{'} + 17 y = 17 t - 1$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.554

13980	$y^{''} + 2 y^{'} + y = e^{- t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.320

13981	$y^{''} - 2 y^{'} + 5 y = t + 2$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.470

13982	$y + 2 y^{'} = e^{- \frac{t}{2}}$ i.c.	[[_linear, ‘class A‘]]	✓	0.306

13983	$y^{''} + 8 y^{'} + 20 y = \sin (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.511

13984	$4 y^{''} - 4 y^{'} + y = t^{2}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.359

13985	$2 y^{''} + y^{'} - y = 4 \sin (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.500

13986	$- y + y^{'} = e^{2 t}$ i.c.	[[_linear, ‘class A‘]]	✓	0.302

13987	$3 y^{''} + 5 y^{'} - 2 y = 7 e^{- 2 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.365

13988	$y + y^{'} = Heaviside (t) - Heaviside (t - 2)$ i.c.	[[_linear, ‘class A‘]]	✓	0.538

13989	$- 2 y + y^{'} = 4 t (Heaviside (t) - Heaviside (t - 2))$ i.c.	[[_linear, ‘class A‘]]	✓	0.956

13990	$y^{''} + 9 y = 24 \sin (t) (Heaviside (t) + Heaviside (t - π))$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.719

13991	$y^{''} + 2 y^{'} + y = Heaviside (t) - Heaviside (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.855

13992	$y^{''} + 2 y^{'} + 2 y = 5 \cos (t) (Heaviside (t) - Heaviside (t - \frac{π}{2}))$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.076

13993	$y^{''} + 5 y^{'} + 6 y = 36 t (Heaviside (t) - Heaviside (t - 1))$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.484

13994	$y^{''} + 4 y^{'} + 13 y = 39 Heaviside (t) - 507 (t - 2) Heaviside (t - 2)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.464

13995	$y^{''} + 4 y = 3 Heaviside (t) - 3 Heaviside (t - 4) + (2 t - 5) Heaviside (t - 4)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.769

13996	$4 y^{''} + 4 y^{'} + 5 y = 25 t (Heaviside (t) - Heaviside (t - \frac{π}{2}))$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.685

13997	$y^{''} + 4 y^{'} + 3 y = Heaviside (t) - Heaviside (t - 1) + Heaviside (t - 2) - Heaviside (- 3 + t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.985

13998	$y^{''} - 2 y^{'} = {\begin{array}{cc} 4 & 0 \leq t < 1 \\ 6 & 1 \leq t \end{array}$ i.c.	[[_2nd_order, _missing_y]]	✓	1.076

13999	$y^{''} - 3 y^{'} + 2 y = {\begin{array}{cc} 0 & 0 \leq t < 1 \\ 1 & 1 \leq t < 2 \\ - 1 & 2 \leq t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.666

14000	$y^{''} + 3 y^{'} + 2 y = {\begin{array}{cc} 1 & 0 \leq t < 2 \\ - 1 & 2 \leq t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.159

2.2.140 Problems 13901 to 14000