Problems 15701 to 15800

Table 2.317: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

15701	$[\begin{matrix} x^{'} = - y \\ y^{'} = 4 x + 24 t \end{matrix}]$ i.c.	system_of_ODEs	✓	0.677

15702	$[\begin{matrix} x^{'} = 4 x - 13 y \\ y^{'} = x + 19 \cos (4 t) - 13 \sin (4 t) \end{matrix}]$ i.c.	system_of_ODEs	✓	2.006

15703	$[\begin{matrix} x^{'} = 4 x + 3 y + 5 Heaviside (t - 2) \\ y^{'} = x + 6 y + 17 Heaviside (t - 2) \end{matrix}]$ i.c.	system_of_ODEs	✓	1.250

15704	$[\begin{matrix} x^{'} = 5 x + 4 y \\ y^{'} = 8 x + y \end{matrix}]$	system_of_ODEs	✓	0.329

15705	$[\begin{matrix} x^{'} = 2 x - 5 y \\ y^{'} = 3 x - 7 y \end{matrix}]$	system_of_ODEs	✓	0.555

15706	$[\begin{matrix} x^{'} = 2 x - 5 y + 4 \\ y^{'} = 3 x - 7 y + 5 \end{matrix}]$	system_of_ODEs	✓	1.994

15707	$[\begin{matrix} x^{'} = 3 x + y \\ y^{'} = 6 x + 2 y \end{matrix}]$	system_of_ODEs	✓	0.346

15708	$[\begin{matrix} x^{'} = x y - 6 y \\ y^{'} = x - y - 5 \end{matrix}]$	system_of_ODEs	✓	0.059

15709	$[\begin{matrix} x^{'} = - x + 2 y \\ y^{'} = 2 x - y \end{matrix}]$	system_of_ODEs	✓	0.343

15710	$y^{''} + y^{'} - 2 y = x^{3}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.538

15711	$y y^{'} + y^{4} = \sin (x)$	[‘y=_G(x,y’)‘]	✗	2.631

15712	$y^{'''} - 2 y^{''} + 5 y^{'} + y = e^{x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.225

15713	${y^{'}}^{2} + y = 0$	[_quadrature]	✓	0.463

15714	$t^{2} y^{''} + y^{'} t + 2 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.009

15715	$x {y^{''}}^{2} + 2 y = 2 x$	[[_2nd_order, _with_linear_symmetries]]	✗	0.124

15716	$x^{''} + 2 \sin (x) = \sin (2 t)$	[NONE]	✗	1.098

15717	$2 x - 1 - y^{'} = 0$	[_quadrature]	✓	0.354

15718	$2 x - y - y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.559

15719	$2 y + y^{'} = 0$	[_quadrature]	✓	0.824

15720	$y^{'} + x y = 0$	[_separable]	✓	1.166

15721	$y^{'} + y = \sin (x)$	[[_linear, ‘class A‘]]	✓	1.494

15722	$y^{''} - y^{'} - 12 y = 0$	[[_2nd_order, _missing_x]]	✓	0.367

15723	$y^{''} + 9 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	1.130

15724	$x^{''} + 2 x^{'} - 10 x = 0$	[[_2nd_order, _missing_x]]	✓	0.515

15725	$x^{''} + x = t \cos (t) - \cos (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.841

15726	$y^{''} - 12 y^{'} + 40 y = 0$	[[_2nd_order, _missing_x]]	✓	0.433

15727	$y^{'''} - 4 y^{''} = 0$	[[_3rd_order, _missing_x]]	✓	0.084

15728	$y^{'''} - 2 y^{''} = 0$	[[_3rd_order, _missing_x]]	✓	0.080

15729	$x^{2} y^{''} - 12 y^{'} x + 42 y = 0$	[[_Emden, _Fowler]]	✓	1.071

15730	$t^{2} y^{''} + 3 y^{'} t + 5 y = 0$	[[_Emden, _Fowler]]	✓	1.048

15731	$y^{'} = - \frac{x}{y}$	[_separable]	✓	3.379

15732	$3 y (t^{2} + y) + t (t^{2} + 6 y) y^{'} = 0$	[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	3.622

15733	$y^{'} = - \frac{2 y}{x} - 3$	[_linear]	✓	2.250

15734	$\cos (t) y + (2 y + \sin (t)) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.148

15735	$\frac{y}{x} + \cos (y) + (\ln (x) - x \sin (y)) y^{'} = 0$	[_exact]	✓	5.352

15736	$y^{'} = (x^{2} - 1) {(x^{3} - 3 x)}^{3}$	[_quadrature]	✓	0.445

15737	$y^{'} = x \sin (x^{2})$	[_quadrature]	✓	0.417

15738	$y^{'} = \frac{x}{\sqrt{x^{2} - 16}}$	[_quadrature]	✓	0.343

15739	$y^{'} = \frac{1}{x \ln (x)}$	[_quadrature]	✓	0.344

15740	$y^{'} = x \ln (x)$	[_quadrature]	✓	0.350

15741	$y^{'} = x e^{- x}$	[_quadrature]	✓	0.397

15742	$y^{'} = \frac{- 10 - 2 x}{(x + 2) (x - 4)}$	[_quadrature]	✓	0.398

15743	$y^{'} = \frac{- x^{2} + x}{(x + 1) (x^{2} + 1)}$	[_quadrature]	✓	0.557

15744	$y^{'} = \frac{\sqrt{x^{2} - 16}}{x}$	[_quadrature]	✓	0.387

15745	$y^{'} = {(- x^{2} + 4)}^{3 / 2}$	[_quadrature]	✓	0.439

15746	$y^{'} = \frac{1}{x^{2} - 16}$	[_quadrature]	✓	0.482

15747	$y^{'} = \cos (x) \cot (x)$	[_quadrature]	✓	0.554

15748	$y^{'} = \sin {(x)}^{3} \tan (x)$	[_quadrature]	✓	0.639

15749	$2 y + y^{'} = 0$ i.c.	[_quadrature]	✓	2.235

15750	$y + y^{'} = \sin (t)$ i.c.	[[_linear, ‘class A‘]]	✓	1.647

15751	$y^{''} - y^{'} - 12 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.599

15752	$y^{''} + 9 y^{'} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.530

15753	$y^{'''} - 2 y^{''} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.124

15754	$y^{'''} - 4 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.123

15755	$t^{2} y^{''} - 12 y^{'} t + 42 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	1.698

15756	$x^{2} y^{''} + 3 y^{'} x + 5 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	1.709

15757	$y^{'} = 4 x^{3} - x + 2$ i.c.	[_quadrature]	✓	0.550

15758	$y^{'} = \sin (2 t) - \cos (2 t)$ i.c.	[_quadrature]	✓	0.713

15759	$y^{'} = \frac{\cos (\frac{1}{x})}{x^{2}}$ i.c.	[_quadrature]	✓	0.837

15760	$y^{'} = \frac{\ln (x)}{x}$ i.c.	[_quadrature]	✓	0.631

15761	$y^{'} = \frac{(x - 4) y^{3}}{x^{3} (- 2 + y)}$	[_separable]	✓	3.683

15762	$y^{'} = \frac{y^{2} + 2 x y}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.285

15763	$y^{'} x + y = \cos (x)$	[_linear]	✓	1.360

15764	$16 y^{''} + 24 y^{'} + 153 y = 0$	[[_2nd_order, _missing_x]]	✓	0.589

15765	$[\begin{matrix} x^{'} = 4 y \\ y^{'} = - x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.712

15766	$4 x (x^{2} + y^{2}) - 5 y + 4 y (x^{2} + y^{2} - 5 x) y^{'} = 0$	[_rational]	✗	32.559

15767	$y^{'} = \sin {(x)}^{4}$ i.c.	[_quadrature]	✓	0.897

15768	$y^{''''} + \frac{25 y^{''}}{2} - 5 y^{'} + \frac{629 y}{16} = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.125

15769	$[\begin{matrix} x^{'} = 4 y \\ y^{'} = - 4 x \end{matrix}]$ i.c.	system_of_ODEs	✓	0.459

15770	$[\begin{matrix} x^{'} = - 5 x + 4 y \\ y^{'} = 2 x + 2 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.480

15771	$y^{'} + \cos (x) y = 0$	[_separable]	✓	1.540

15772	$y^{'} - y = \sin (x)$	[[_linear, ‘class A‘]]	✓	1.422

15773	$y^{''} + 4 y^{'} - 5 y = 0$	[[_2nd_order, _missing_x]]	✓	0.349

15774	$y^{''} - 6 y^{'} + 45 y = 0$	[[_2nd_order, _missing_x]]	✓	0.524

15775	$x^{2} y^{''} - y^{'} x - 16 y = 0$	[[_Emden, _Fowler]]	✓	0.932

15776	$x^{2} y^{''} + 3 y^{'} x + 2 y = 0$	[[_Emden, _Fowler]]	✓	0.999

15777	$y^{''} + 2 y^{'} + 2 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.654

15778	$y^{''} - 7 y^{'} + 12 y = 2$	[[_2nd_order, _missing_x]]	✓	0.379

15779	$2 x - 3 y + (2 y - 3 x) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.162

15780	$y \cos (x y) + \sin (x) + x \cos (x y) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	37.048

15781	$y^{'} = x e^{- x^{2}}$	[_quadrature]	✓	0.360

15782	$y^{'} = x^{2} \sin (x)$	[_quadrature]	✓	0.489

15783	$y^{'} = \frac{2 x^{2} - x + 1}{(x - 1) (x^{2} + 1)}$	[_quadrature]	✓	0.409

15784	$y^{'} = \frac{x^{2}}{\sqrt{x^{2} - 1}}$	[_quadrature]	✓	0.477

15785	$2 y + y^{'} = x^{2}$ i.c.	[[_linear, ‘class A‘]]	✓	1.364

15786	$y^{''} + 4 y = t$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.840

15787	$x^{2} y^{''} + 5 y^{'} x + 4 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	1.211

15788	$y^{'} = \cos {(x)}^{2} \sin (x)$ i.c.	[_quadrature]	✓	0.684

15789	$y^{'} = \frac{4 x - 9}{3 {(x - 3)}^{2 / 3}}$ i.c.	[_quadrature]	✓	0.691

15790	$y^{'} + t^{2} = y^{2}$ i.c.	[_Riccati]	✓	1.810

15791	$y^{'} + t^{2} = \frac{1}{y^{2}}$	[_rational]	✗	0.914

15792	$y^{'} = y + \frac{1}{1 - t}$	[_linear]	✓	1.312

15793	$y^{'} = y^{1 / 5}$ i.c.	[_quadrature]	✓	1.436

15794	$\frac{y^{'}}{t} = \sqrt{y}$ i.c.	[_separable]	✓	5.467

15795	$y^{'} = 4 t^{2} - t y^{2}$ i.c.	[_Riccati]	✓	2.796

15796	$y^{'} = y \sqrt{t}$ i.c.	[_separable]	✓	1.553

15797	$y^{'} = 6 y^{2 / 3}$ i.c.	[_quadrature]	✓	1.519

15798	$y^{'} t = y$	[_separable]	✓	1.388

15799	$y^{'} = \tan (t) y$ i.c.	[_separable]	✓	1.738

15800	$y^{'} = \frac{1}{t^{2} + 1}$ i.c.	[_quadrature]	✓	0.527

2.2.158 Problems 15701 to 15800