Problems 17501 to 17600

Table 2.353: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

17501	$x^{2} y^{''} + x y^{'} + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.148

17502	$x y^{''} - (x + n) y^{'} + n y = 0$	[_Laguerre]	✓	0.158

17503	$y^{''} + a (x y^{'} + y) = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.128

17504	$y^{''} + 2 y^{'} - 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.848

17505	$y^{''} + 3 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.842

17506	$y^{''} - 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.959

17507	$9 y^{''} + 6 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.964

17508	$y^{''} - 2 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	2.082

17509	$y^{''} - 2 y^{'} + 6 y = 0$	[[_2nd_order, _missing_x]]	✓	2.075

17510	$4 y^{''} - 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.970

17511	$2 y^{''} - 3 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.861

17512	$6 y^{''} - y^{'} - y = 0$	[[_2nd_order, _missing_x]]	✓	0.876

17513	$9 y^{''} + 12 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.983

17514	$y^{''} + 2 y^{'} - 8 y = 0$	[[_2nd_order, _missing_x]]	✓	0.859

17515	$y^{''} + 2 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	2.020

17516	$y^{''} + 5 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	1.903

17517	$4 y^{''} - 9 y = 0$	[[_2nd_order, _missing_x]]	✓	2.085

17518	$25 y^{''} - 20 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.961

17519	$y^{''} - 4 y^{'} + 16 y = 0$	[[_2nd_order, _missing_x]]	✓	2.318

17520	$y^{''} + 6 y^{'} + 13 y = 0$	[[_2nd_order, _missing_x]]	✓	2.571

17521	$y^{''} + 2 y^{'} + \frac{5 y}{4} = 0$	[[_2nd_order, _missing_x]]	✓	1.577

17522	$y^{''} - 9 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	1.139

17523	$y^{''} - 2 y^{'} - 2 y = 0$	[[_2nd_order, _missing_x]]	✓	1.104

17524	$y^{''} + 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.957

17525	$9 y^{''} - 24 y^{'} + 16 y = 0$	[[_2nd_order, _missing_x]]	✓	0.961

17526	$4 y^{''} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	2.292

17527	$4 y^{''} + 9 y^{'} - 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.872

17528	$y^{''} + y^{'} + \frac{5 y}{4} = 0$	[[_2nd_order, _missing_x]]	✓	2.062

17529	$y^{''} + 4 y^{'} + \frac{25 y}{4} = 0$	[[_2nd_order, _missing_x]]	✓	1.788

17530	$y^{''} + y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.411

17531	$y^{''} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.259

17532	$9 y^{''} - 12 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.390

17533	$y^{''} + 3 y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.168

17534	$y^{''} + 4 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.276

17535	$6 y^{''} - 5 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.201

17536	$y^{''} + 6 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.345

17537	$y^{''} - 2 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.892

17538	$y^{''} + 3 y^{'} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.048

17539	$y^{''} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.161

17540	$y^{''} + 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.390

17541	$y^{''} + 6 y^{'} + 3 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.714

17542	$y^{''} + y^{'} + \frac{5 y}{4} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.477

17543	$2 y^{''} + y^{'} - 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.648

17544	$y^{''} + 8 y^{'} - 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.459

17545	$y^{''} + 2 y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.490

17546	$4 y^{''} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.749

17547	$a x^{2} y^{''} + b x y^{'} + c y = 0$	[[_Emden, _Fowler]]	✓	2.230

17548	$x^{2} y^{''} + x y^{'} + 4 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.336

17549	$x^{2} y^{''} + 4 x y^{'} + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.233

17550	$x^{2} y^{''} + 3 x y^{'} + \frac{5 y}{4} = 0$	[[_Emden, _Fowler]]	✓	1.871

17551	$x^{2} y^{''} - 4 x y^{'} - 6 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.957

17552	$x^{2} y^{''} - 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.697

17553	$x^{2} y^{''} - 5 x y^{'} + 9 y = 0$	[[_Emden, _Fowler]]	✓	0.902

17554	$x^{2} y^{''} + 2 x y^{'} + 4 y = 0$	[[_Emden, _Fowler]]	✓	2.688

17555	$2 x^{2} y^{''} - 4 x y^{'} + 6 y = 0$	[[_Emden, _Fowler]]	✓	2.668

17556	$2 x^{2} y^{''} + x y^{'} - 3 y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.602

17557	$4 x^{2} y^{''} + 8 x y^{'} + 17 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	3.973

17558	$x^{2} y^{''} - 5 x y^{'} + 9 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	1.493

17559	$x^{2} y^{''} + 3 x y^{'} + 5 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	3.994

17560	$y^{''} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.375

17561	$y^{''} + \frac{y^{'}}{4} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.904

17562	$m y^{''} + k y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	10.243

17563	$y^{''} - 2 y^{'} - 3 y = 3 e^{2 t}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.138

17564	$y^{''} + 2 y^{'} + 5 y = 3 \sin (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	15.096

17565	$y^{''} - 2 y^{'} - 3 y = - 3 t e^{- t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.200

17566	$y^{''} + 2 y^{'} = 3 + 4 \sin (2 t)$	[[_2nd_order, _missing_y]]	✓	3.210

17567	$y^{''} + 9 y = t^{2} e^{3 t} + 6$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.610

17568	$y^{''} + 2 y^{'} + y = 2 e^{- t}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.117

17569	$y^{''} - 5 y^{'} + 4 y = 2 e^{t}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.146

17570	$y^{''} - y^{'} - 2 y = 2 e^{- t}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.159

17571	$y^{''} + 2 y^{'} + y = 3 e^{- t}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.188

17572	$4 y^{''} - 4 y^{'} + y = 16 e^{\frac{t}{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.157

17573	$2 y^{''} + 3 y^{'} + y = t^{2} + 3 \sin (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.835

17574	$y^{''} + y = 3 \sin (2 t) + t \cos (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.773

17575	$u^{''} + w_{0}^{2} u = \cos (w t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.639

17576	$y^{''} + y^{'} + 4 y = 2 \sinh (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	29.985

17577	$y^{''} - y^{'} - 2 y = \cosh (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.338

17578	$y^{''} + y^{'} - 2 y = 2 t$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	1.195

17579	$y^{''} + 4 y = t^{2} + 3 e^{t}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	5.536

17580	$y^{''} - 2 y^{'} + y = t e^{t} + 4$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.609

17581	$y^{''} - 2 y^{'} - 3 y = 3 t e^{2 t}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.242

17582	$y^{''} + 4 y = 3 \sin (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.165

17583	$y^{''} + 2 y^{'} + 5 y = 4 e^{- t} \cos (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	8.020

17584	$y^{''} + 3 y^{'} = 2 t^{4} + t^{2} e^{- 3 t} + \sin (3 t)$	[[_2nd_order, _missing_y]]	✓	74.269

17585	$y^{''} + y = t (1 + \sin (t))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.201

17586	$y^{''} - 5 y^{'} + 6 y = e^{t} \cos (2 t) + e^{2 t} (3 t + 4) \sin (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	6.051

17587	$y^{''} + 2 y^{'} + 2 y = 3 e^{- t} + 2 e^{- t} \cos (t) + 4 e^{- t} t^{2} \sin (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	16.003

17588	$y^{''} - 4 y^{'} + 4 y = 2 t^{2} + 4 t e^{2 t} + t \sin (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	31.535

17589	$y^{''} + 4 y = t^{2} \sin (2 t) + (6 t + 7) \cos (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	6.358

17590	$y^{''} + 3 y^{'} + 2 y = e^{t} (t^{2} + 1) \sin (2 t) + 3 e^{- t} \cos (t) + 4 e^{t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	74.162

17591	$y^{''} + 2 y^{'} + 5 y = 3 t e^{- t} \cos (2 t) - 2 t e^{- 2 t} \cos (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	127.983

17592	$y^{''} - 3 y^{'} - 4 y = 2 e^{- t}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.172

17593	$x^{2} y^{''} - 3 x y^{'} + 4 y = \ln (x)$	[[_2nd_order, _with_linear_symmetries]]	✓	1.414

17594	$x^{2} y^{''} + 7 x y^{'} + 5 y = x$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.507

17595	$x^{2} y^{''} - 2 x y^{'} + 2 y = 3 x^{2} + 2 \ln (x)$	[[_2nd_order, _with_linear_symmetries]]	✓	2.102

17596	$x^{2} y^{''} + x y^{'} + 4 y = \sin (\ln (x))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	5.159

17597	$y^{''} + y = {\begin{array}{cc} t & 0 \leq t \leq π \\ π e^{- t + π} & π < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	7.214

17598	$y^{''} + 2 y^{'} + 5 y = {\begin{array}{cc} 1 & 0 \leq t \leq \frac{π}{2} \\ 0 & \frac{π}{2} < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	18.703

17599	$y^{''} + y = {\begin{array}{cc} A t & 0 \leq t \leq π \\ A (2 π - t) & π < t \leq 2 π \\ 0 & 2 π < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.386

17600	$y^{''} + \frac{y^{'}}{4} + 2 y = 2 \cos (w t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	77.405

2.2.176 Problems 17501 to 17600