Problems 15501 to 15600

Table 2.313: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

15501	$x^{2} y^{''} + 2 y^{'} x - 6 y = 18 \ln (x)$	[[_2nd_order, _with_linear_symmetries]]	✓	1.135

15502	$y^{''} + 6 y^{'} + 9 y = 10 e^{- 3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.593

15503	$2 x^{2} y^{''} - y^{'} x - 2 y = 10 x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.216

15504	$y^{''} + 6 y^{'} + 9 y = 2 \cos (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.804

15505	$x y^{''} - y^{'} = - 3 x {y^{'}}^{3}$	[[_2nd_order, _missing_y]]	✓	1.078

15506	$x^{2} y^{''} + 3 y^{'} x + 2 y = 6$	[[_2nd_order, _with_linear_symmetries]]	✓	1.513

15507	$x^{2} y^{''} + y^{'} x - y = \frac{1}{x^{2} + 1}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	2.232

15508	$4 y^{''} - 12 y^{'} + 9 y = x e^{\frac{3 x}{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.666

15509	$3 y^{''} + 8 y^{'} - 3 y = 123 x \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.846

15510	$y^{'''} + 8 y = e^{- 2 x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.179

15511	$y^{(6)} - 64 y = e^{- 2 x}$	[[_high_order, _with_linear_symmetries]]	✓	0.219

15512	$x^{2} y^{''} + 3 y^{'} x + y = \frac{1}{{(x + 1)}^{2}}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.700

15513	$x^{2} y^{''} + 3 y^{'} x + y = \frac{1}{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.741

15514	$y^{'} + 4 y = 0$ i.c.	[_quadrature]	✓	0.269

15515	$- 2 y + y^{'} = t^{3}$ i.c.	[[_linear, ‘class A‘]]	✓	0.337

15516	$3 y + y^{'} = Heaviside (t - 4)$ i.c.	[[_linear, ‘class A‘]]	✓	0.540

15517	$y^{''} - 4 y = t^{3}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.345

15518	$y^{''} + 4 y = 20 e^{4 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.498

15519	$y^{''} + 4 y = \sin (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.476

15520	$y^{''} + 4 y = 3 Heaviside (t - 2)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.932

15521	$y^{''} + 5 y^{'} + 6 y = e^{4 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.339

15522	$y^{''} - 5 y^{'} + 6 y = t^{2} e^{4 t}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.343

15523	$y^{''} - 5 y^{'} + 6 y = 7$ i.c.	[[_2nd_order, _missing_x]]	✓	0.319

15524	$y^{''} - 4 y^{'} + 13 y = e^{2 t} \sin (3 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.559

15525	$y^{''} + 4 y^{'} + 13 y = 4 t + 2 e^{2 t} \sin (3 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.586

15526	$y^{'''} - 27 y = e^{- 3 t}$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓	0.611

15527	$t y^{''} + y^{'} + t y = 0$ i.c.	[_Lienard]	✓	0.291

15528	$y^{''} - 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.310

15529	$y^{''} + 9 y = 27 t^{3}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.383

15530	$y^{''} + 8 y^{'} + 7 y = 165 e^{4 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.333

15531	$y^{''} - 8 y^{'} + 17 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.380

15532	$y^{''} - 6 y^{'} + 9 y = t^{2} e^{3 t}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.336

15533	$y^{''} + 6 y^{'} + 13 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.477

15534	$y^{''} + 8 y^{'} + 17 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.340

15535	$y^{''} = e^{t} \sin (t)$ i.c.	[[_2nd_order, _quadrature]]	✓	0.372

15536	$y^{''} - 4 y^{'} + 40 y = 122 e^{- 3 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.526

15537	$y^{''} - 9 y = 24 e^{- 3 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.360

15538	$y^{''} - 4 y^{'} + 13 y = e^{2 t} \sin (3 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.539

15539	$y^{''} + 4 y = 1$ i.c.	[[_2nd_order, _missing_x]]	✓	0.340

15540	$y^{''} + 4 y = t$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.375

15541	$y^{''} + 4 y = e^{3 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.494

15542	$y^{''} + 4 y = \sin (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.388

15543	$y^{''} + 4 y = \sin (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.488

15544	$y^{''} - 6 y^{'} + 9 y = 1$ i.c.	[[_2nd_order, _missing_x]]	✓	0.303

15545	$y^{''} - 6 y^{'} + 9 y = t$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.386

15546	$y^{''} - 6 y^{'} + 9 y = e^{3 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.280

15547	$y^{''} - 6 y^{'} + 9 y = e^{- 3 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.429

15548	$y^{''} - 6 y^{'} + 9 y = e^{t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.326

15549	$y^{'} = Heaviside (- 3 + t)$ i.c.	[_quadrature]	✓	0.337

15550	$y^{'} = Heaviside (- 3 + t)$ i.c.	[_quadrature]	✓	0.342

15551	$y^{''} = Heaviside (t - 2)$ i.c.	[[_2nd_order, _quadrature]]	✓	0.327

15552	$y^{''} = Heaviside (t - 2)$ i.c.	[[_2nd_order, _quadrature]]	✓	0.455

15553	$y^{''} + 9 y = Heaviside (t - 10)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.723

15554	$y^{'} = {\begin{array}{cc} 0 & t < 1 \\ 1 & 1 < t < 3 \\ 0 & 3 < t \end{array}$ i.c.	[_quadrature]	✓	0.552

15555	$y^{''} = {\begin{array}{cc} 0 & t < 1 \\ 1 & 1 < t < 3 \\ 0 & 3 < t \end{array}$ i.c.	[[_2nd_order, _quadrature]]	✓	0.487

15556	$y^{''} + 9 y = {\begin{array}{cc} 0 & t < 1 \\ 1 & 1 < t < 3 \\ 0 & 3 < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.795

15557	$y^{'} = 3 δ (t - 2)$ i.c.	[_quadrature]	✓	0.326

15558	$y^{'} = δ (t - 2) - δ (t - 4)$ i.c.	[_quadrature]	✓	0.449

15559	$y^{''} = δ (- 3 + t)$ i.c.	[[_2nd_order, _quadrature]]	✓	0.318

15560	$y^{''} = δ (t - 1) - δ (t - 4)$ i.c.	[[_2nd_order, _quadrature]]	✓	0.387

15561	$y^{'} + 2 y = 4 δ (t - 1)$ i.c.	[[_linear, ‘class A‘]]	✓	0.544

15562	$y^{''} + y = δ (t) + δ (t - π)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.168

15563	$y^{''} + y = - 2 δ (t - \frac{π}{2})$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.624

15564	$3 y + y^{'} = δ (t - 2)$ i.c.	[[_linear, ‘class A‘]]	✓	0.595

15565	$y^{''} + 3 y^{'} = δ (t)$	[[_2nd_order, _missing_y]]	✓	0.270

15566	$y^{''} + 3 y^{'} = δ (t - 1)$ i.c.	[[_2nd_order, _missing_y]]	✓	0.700

15567	$y^{''} + 16 y = δ (t - 2)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.737

15568	$y^{''} - 16 y = δ (t - 10)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.725

15569	$y^{''} + y = δ (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.223

15570	$y^{''} + 4 y^{'} - 12 y = δ (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.290

15571	$y^{''} + 4 y^{'} - 12 y = δ (- 3 + t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.066

15572	$y^{''} + 6 y^{'} + 9 y = δ (t - 4)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.674

15573	$y^{''} - 12 y^{'} + 45 y = δ (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.327

15574	$y^{'''} + 9 y^{'} = δ (t - 1)$ i.c.	[[_3rd_order, _missing_y]]	✓	1.259

15575	$y^{''''} - 16 y = δ (t)$ i.c.	[[_high_order, _linear, _nonhomogeneous]]	✓	0.478

15576	$y^{'} - 2 y = 0$	[_quadrature]	✓	0.286

15577	$y^{'} - 2 x y = 0$	[_separable]	✓	0.332

15578	$y^{'} + \frac{2 y}{2 x - 1} = 0$	[_separable]	✓	0.323

15579	$(x - 3) y^{'} - 2 y = 0$	[_separable]	✓	0.371

15580	$(x^{2} + 1) y^{'} - 2 x y = 0$	[_separable]	✓	0.292

15581	$y^{'} + \frac{y}{x - 1} = 0$	[_separable]	✓	0.325

15582	$y^{'} + \frac{y}{x - 1} = 0$	[_separable]	✓	0.398

15583	$(1 - x) y^{'} - 2 y = 0$	[_separable]	✓	0.383

15584	$(- x^{3} + 2) y^{'} - 3 x^{2} y = 0$	[_separable]	✓	0.353

15585	$(- x^{3} + 2) y^{'} + 3 x^{2} y = 0$	[_separable]	✓	0.325

15586	$(x + 1) y^{'} - x y = 0$	[_separable]	✓	0.355

15587	$(x + 1) y^{'} + (1 - x) y = 0$	[_separable]	✓	0.362

15588	$(x^{2} + 1) y^{''} - 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.371

15589	$y^{''} + y^{'} x + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.384

15590	$(x^{2} + 4) y^{''} + 2 y^{'} x = 0$	[[_2nd_order, _missing_y]]	✓	0.344

15591	$y^{''} - 3 x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.319

15592	$(- x^{2} + 4) y^{''} - 5 y^{'} x - 3 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.464

15593	$(- x^{2} + 1) y^{''} - y^{'} x + 4 y = 0$	[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.467

15594	$y^{''} - 2 y^{'} x + 6 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.391

15595	$(x^{2} - 6 x) y^{''} + 4 (x - 3) y^{'} + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.675

15596	$y^{''} + (x + 2) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.452

15597	$(x^{2} - 2 x + 2) y^{''} + (1 - x) y^{'} - 3 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.499

15598	$y^{''} - 2 y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.391

15599	$y^{''} - y^{'} x - 2 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.373

15600	$(- x^{2} + 1) y^{''} - y^{'} x + λ y = 0$	[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.528

2.2.156 Problems 15501 to 15600