Problems 14901 to 15000

Table 2.301: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

14901	$y^{''} + y^{'} + 5 y = Heaviside (t - 2) \sin (4 t - 8)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.914

14902	$y^{''} + y^{'} + 8 y = (1 - Heaviside (t - 4)) \cos (t - 4)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	8.874

14903	$y^{''} + y^{'} + 3 y = (1 - Heaviside (t - 2)) e^{- \frac{t}{10} + \frac{1}{5}} \sin (t - 2)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	7.952

14904	$y^{''} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.472

14905	$y^{''} + 4 y = \sin (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.412

14906	$y^{''} + 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.340

14907	$y^{''} + 16 y = t$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.512

14908	$y^{'} = 3 - \sin (x)$	[_quadrature]	✓	0.434

14909	$y^{'} = 3 - \sin (y)$	[_quadrature]	✓	71.791

14910	$y^{'} + 4 y = e^{2 x}$	[[_linear, ‘class A‘]]	✓	1.244

14911	$y^{'} x = \arcsin (x^{2})$	[_quadrature]	✓	1.698

14912	$y y^{'} = 2 x$	[_separable]	✓	3.331

14913	$y^{''} = \frac{x + 1}{x - 1}$	[[_2nd_order, _quadrature]]	✓	1.134

14914	$x^{2} y^{''} = 1$	[[_2nd_order, _quadrature]]	✓	0.499

14915	$y^{2} y^{''} = 8 x^{2}$	[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]	✗	0.271

14916	$y^{''} + 3 y^{'} + 8 y = e^{- x^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.373

14917	$x^{2} y^{''} + 3 y^{'} x = 0$	[[_2nd_order, _missing_y]]	✓	0.574

14918	$y^{'} = 4 x^{3}$	[_quadrature]	✓	0.325

14919	$y^{'} = 20 e^{- 4 x}$	[_quadrature]	✓	0.377

14920	$y^{'} x + \sqrt{x} = 2$	[_quadrature]	✓	0.449

14921	$\sqrt{x + 4} y^{'} = 1$	[_quadrature]	✓	0.523

14922	$y^{'} = x \cos (x^{2})$	[_quadrature]	✓	0.457

14923	$y^{'} = x \cos (x)$	[_quadrature]	✓	0.428

14924	$x = (x^{2} - 9) y^{'}$	[_quadrature]	✓	0.489

14925	$1 = (x^{2} - 9) y^{'}$	[_quadrature]	✓	0.608

14926	$1 = x^{2} - 9 y^{'}$	[_quadrature]	✓	0.320

14927	$y^{''} = \sin (2 x)$	[[_2nd_order, _quadrature]]	✓	1.183

14928	$y^{''} - 3 = x$	[[_2nd_order, _quadrature]]	✓	0.939

14929	$y^{''''} = 1$	[[_high_order, _quadrature]]	✓	0.139

14930	$y^{'} = 40 x e^{2 x}$ i.c.	[_quadrature]	✓	0.654

14931	${(6 + x)}^{1 / 3} y^{'} = 1$ i.c.	[_quadrature]	✓	0.753

14932	$y^{'} = \frac{x - 1}{x + 1}$ i.c.	[_quadrature]	✓	0.668

14933	$y^{'} x + 2 = \sqrt{x}$ i.c.	[_quadrature]	✓	0.720

14934	$\cos (x) y^{'} - \sin (x) = 0$ i.c.	[_quadrature]	✓	1.007

14935	$(x^{2} + 1) y^{'} = 1$ i.c.	[_quadrature]	✓	0.623

14936	$x y^{''} + 2 = \sqrt{x}$ i.c.	[[_2nd_order, _quadrature]]	✓	1.269

14937	$y^{'} = \sin (\frac{x}{2})$	[_quadrature]	✓	0.455

14938	$y^{'} = \sin (\frac{x}{2})$ i.c.	[_quadrature]	✓	0.651

14939	$y^{'} = \sin (\frac{x}{2})$ i.c.	[_quadrature]	✓	0.638

14940	$y^{'} = 3 \sqrt{3 + x}$	[_quadrature]	✓	0.395

14941	$y^{'} = 3 \sqrt{3 + x}$ i.c.	[_quadrature]	✓	0.609

14942	$y^{'} = 3 \sqrt{3 + x}$ i.c.	[_quadrature]	✓	0.689

14943	$y^{'} = 3 \sqrt{3 + x}$ i.c.	[_quadrature]	✓	0.641

14944	$y^{'} = x e^{- x^{2}}$ i.c.	[_quadrature]	✓	0.634

14945	$y^{'} = \frac{x}{\sqrt{x^{2} + 5}}$ i.c.	[_quadrature]	✓	0.791

14946	$y^{'} = \frac{1}{x^{2} + 1}$ i.c.	[_quadrature]	✓	0.608

14947	$y^{'} = e^{- 9 x^{2}}$ i.c.	[_quadrature]	✓	0.643

14948	$y^{'} x = \sin (x)$ i.c.	[_quadrature]	✓	0.668

14949	$y^{'} x = \sin (x^{2})$ i.c.	[_quadrature]	✓	0.840

14950	$y^{'} = {\begin{array}{cc} 0 & x < 0 \\ 1 & 0 \leq x \end{array}$ i.c.	[_quadrature]	✓	0.409

14951	$y^{'} = {\begin{array}{cc} 0 & x < 1 \\ 1 & 1 \leq x \end{array}$ i.c.	[_quadrature]	✓	0.392

14952	$y^{'} = {\begin{array}{cc} 0 & x < 1 \\ 1 & 1 \leq x < 2 \\ 0 & 2 \leq x \end{array}$ i.c.	[_quadrature]	✓	0.428

14953	$y^{'} + 3 x y = 6 x$	[_separable]	✓	1.259

14954	$\sin (x + y) - y y^{'} = 0$	[‘y=_G(x,y’)‘]	✗	12.151

14955	$y^{'} - y^{3} = 8$	[_quadrature]	✓	218.538

14956	$x^{2} y^{'} + x y^{2} = x$	[_separable]	✓	1.419

14957	$y^{'} - y^{2} = x$	[[_Riccati, _special]]	✓	1.337

14958	$y^{3} - 25 y + y^{'} = 0$	[_quadrature]	✓	1.809

14959	$(x - 2) y^{'} = 3 + y$	[_separable]	✓	1.569

14960	$(- 2 + y) y^{'} = x - 3$	[_separable]	✓	2.882

14961	$y^{'} + 2 y - y^{2} = - 2$	[_quadrature]	✓	0.614

14962	$y^{'} + (8 - x) y - y^{2} = - 8 x$	[_Riccati]	✓	1.758

14963	$y^{'} = 2 \sqrt{y}$ i.c.	[_quadrature]	✓	1.226

14964	$y^{'} = 3 y^{2} - \sin (x) y^{2}$	[_separable]	✓	1.785

14965	$y^{'} = 3 x - y \sin (x)$	[_linear]	✓	1.727

14966	$y^{'} x = {(x - y)}^{2}$	[_rational, _Riccati]	✓	1.971

14967	$y^{'} = \sqrt{x^{2} + 1}$	[_quadrature]	✓	0.389

14968	$y^{'} + 4 y = 8$	[_quadrature]	✓	1.011

14969	$y^{'} + x y = 4 x$	[_separable]	✓	1.152

14970	$y^{'} + 4 y = x^{2}$	[[_linear, ‘class A‘]]	✓	1.001

14971	$y^{'} = x y - 3 x - 2 y + 6$	[_separable]	✓	1.254

14972	$y^{'} = \sin (x + y)$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.235

14973	$y y^{'} = e^{x - 3 y^{2}}$	[_separable]	✓	1.760

14974	$y^{'} = \frac{x}{y}$	[_separable]	✓	3.551

14975	$y^{'} = y^{2} + 9$	[_quadrature]	✓	11.303

14976	$x y^{'} y = y^{2} + 9$	[_separable]	✓	2.894

14977	$y^{'} = \frac{1 + y^{2}}{x^{2} + 1}$	[_separable]	✓	1.699

14978	$y^{'} \cos (y) = \sin (x)$	[_separable]	✓	2.087

14979	$y^{'} = e^{2 x - 3 y}$	[_separable]	✓	2.106

14980	$y^{'} = \frac{x}{y}$ i.c.	[_separable]	✓	3.488

14981	$y^{'} = 2 x - 1 + 2 x y - y$ i.c.	[_separable]	✓	1.501

14982	$y y^{'} = x y^{2} + x$ i.c.	[_separable]	✓	2.302

14983	$y y^{'} = 3 \sqrt{x y^{2} + 9 x}$ i.c.	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	3.286

14984	$y^{'} = x y - 4 x$	[_separable]	✓	1.173

14985	$y^{'} - 4 y = 2$	[_quadrature]	✓	0.695

14986	$y y^{'} = x y^{2} - 9 x$	[_separable]	✓	2.256

14987	$y^{'} = \sin (y)$	[_quadrature]	✓	41.411

14988	$y^{'} = e^{x + y^{2}}$	[_separable]	✓	1.233

14989	$y^{'} = 200 y - 2 y^{2}$	[_quadrature]	✓	1.143

14990	$y^{'} = x y - 4 x$	[_separable]	✓	1.162

14991	$y^{'} = x y - 3 x - 2 y + 6$	[_separable]	✓	1.271

14992	$y^{'} = 3 y^{2} - \sin (x) y^{2}$	[_separable]	✓	1.871

14993	$y^{'} = \tan (y)$	[_quadrature]	✓	1.286

14994	$y^{'} = \frac{y}{x}$	[_separable]	✓	1.281

14995	$y^{'} = \frac{6 x^{2} + 4}{3 y^{2} - 4 y}$	[_separable]	✓	1.460

14996	$(x^{2} + 1) y^{'} = 1 + y^{2}$	[_separable]	✓	1.797

14997	$(- 1 + y^{2}) y^{'} = 4 x y^{2}$	[_separable]	✓	13.867

14998	$y^{'} = e^{- y}$	[_quadrature]	✓	0.696

14999	$y^{'} = e^{- y} + 1$	[_quadrature]	✓	1.199

15000	$y^{'} = 3 x y^{3}$	[_separable]	✓	3.249

2.2.150 Problems 14901 to 15000