Problems 15401 to 15500

Table 2.311: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

15401	$y^{''} + y = 6 \cos (2 x) - 3 \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.888

15402	$y^{''} - 4 y^{'} + 5 y = x^{3} e^{- x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.257

15403	$y^{''} - 4 y^{'} + 5 y = x^{3} e^{2 x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.060

15404	$y^{''} - 5 y^{'} + 6 y = x^{2} e^{- 7 x} + 2 e^{- 7 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.599

15405	$y^{''} - 5 y^{'} + 6 y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.467

15406	$y^{''} - 5 y^{'} + 6 y = 4 e^{- 8 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.540

15407	$y^{''} - 5 y^{'} + 6 y = 4 e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.525

15408	$y^{''} - 5 y^{'} + 6 y = x^{2} e^{3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.600

15409	$y^{''} - 5 y^{'} + 6 y = x^{2} \cos (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.150

15410	$y^{''} - 5 y^{'} + 6 y = x^{2} e^{3 x} \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.103

15411	$y^{''} - 4 y^{'} + 20 y = e^{4 x} \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.736

15412	$y^{''} - 4 y^{'} + 20 y = e^{2 x} \sin (4 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.756

15413	$y^{''} - 4 y^{'} + 20 y = x^{3} \sin (4 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.888

15414	$y^{''} - 10 y^{'} + 25 y = 3 x^{2} e^{5 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.621

15415	$y^{''} - 10 y^{'} + 25 y = 3 x^{4}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.639

15416	$y^{''''} - 4 y^{'''} = 12 e^{- 2 x}$	[[_high_order, _missing_y]]	✓	0.168

15417	$y^{''''} - 4 y^{'''} = 10 \sin (2 x)$	[[_high_order, _missing_y]]	✓	0.201

15418	$y^{''''} - 4 y^{'''} = 32 e^{4 x}$	[[_high_order, _missing_y]]	✓	0.162

15419	$y^{''''} - 4 y^{'''} = 32 x$	[[_high_order, _missing_y]]	✓	0.151

15420	$y^{'''} - y^{''} + y^{'} - y = x^{2}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.144

15421	$y^{'''} - y^{''} + y^{'} - y = 30 \cos (2 x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.201

15422	$y^{'''} - y^{''} + y^{'} - y = 6 e^{x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.166

15423	$y^{(5)} + 18 y^{'''} + 81 y^{'} = x^{2} e^{3 x}$	[[_high_order, _missing_y]]	✓	0.203

15424	$y^{(5)} + 18 y^{'''} + 81 y^{'} = x^{2} \sin (3 x)$	[[_high_order, _missing_y]]	✓	0.950

15425	$y^{(5)} + 18 y^{'''} + 81 y^{'} = x^{2} e^{3 x} \sin (3 x)$	[[_high_order, _missing_y]]	✓	0.528

15426	$y^{'''} - y^{''} + y^{'} - y = 30 x \cos (2 x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.263

15427	$y^{'''} - y^{''} + y^{'} - y = 3 x \cos (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.820

15428	$y^{'''} - y^{''} + y^{'} - y = 3 x e^{x} \cos (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.259

15429	$y^{'''} - y^{''} + y^{'} - y = 5 x^{5} e^{2 x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.199

15430	$y^{''} - 6 y^{'} + 9 y = 27 e^{6 x} + 25 \sin (6 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.012

15431	$y^{''} + 9 y = 25 x \cos (2 x) + 3 \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.414

15432	$y^{''} - 4 y^{'} + 5 y = 5 \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.764

15433	$y^{''} - 4 y^{'} + 5 y = 20 \sinh (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.862

15434	$x^{2} y^{''} - 5 y^{'} x + 8 y = \frac{5}{x^{3}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.529

15435	$2 x^{2} y^{''} - y^{'} x + y = \frac{50}{x^{3}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.864

15436	$2 x^{2} y^{''} + 5 y^{'} x + y = 85 \cos (2 \ln (x))$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	3.612

15437	$x^{2} y^{''} - 2 y = 15 \cos (3 \ln (x)) - 10 \sin (3 \ln (x))$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.690

15438	$3 x^{2} y^{''} - 7 y^{'} x + 3 y = 4 x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.901

15439	$2 x^{2} y^{''} + 5 y^{'} x + y = \frac{10}{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	2.129

15440	$x^{2} y^{''} - 5 y^{'} x + 9 y = 6 x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.636

15441	$x^{2} y^{''} + 5 y^{'} x + 4 y = 64 x^{2} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.539

15442	$x^{2} y^{''} - 2 y^{'} x + 2 y = 3 \sqrt{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.827

15443	$y^{''} + y = \cot (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.847

15444	$y^{''} + 4 y = \csc (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.101

15445	$y^{''} - 7 y^{'} + 10 y = 6 e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.560

15446	$y^{''} - 4 y^{'} + 4 y = (24 x^{2} + 2) e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.640

15447	$y^{''} + 4 y^{'} + 4 y = \frac{e^{- 2 x}}{x^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.674

15448	$x^{2} y^{''} + y^{'} x - y = \sqrt{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	2.155

15449	$x^{2} y^{''} + y^{'} x - 9 y = 12 x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.816

15450	$x^{2} y^{''} - 3 y^{'} x + 4 y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.535

15451	$x^{2} y^{''} + 5 y^{'} x + 4 y = \ln (x)$	[[_2nd_order, _with_linear_symmetries]]	✓	1.491

15452	$x^{2} y^{''} - 2 y = \frac{1}{x - 2}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	0.937

15453	$x y^{''} - y^{'} - 4 x^{3} y = x^{3} e^{x^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.647

15454	$x y^{''} + (2 x + 2) y^{'} + 2 y = 8 e^{2 x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.298

15455	$(x + 1) y^{''} + y^{'} x - y = {(x + 1)}^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.975

15456	$x^{2} y^{''} - 2 y^{'} x - 4 y = \frac{10}{x}$ i.c.	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	2.160

15457	$y^{''} - y^{'} - 6 y = 12 e^{2 x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.761

15458	$y^{'''} - 4 y^{'} = 30 e^{3 x}$	[[_3rd_order, _missing_y]]	✓	0.158

15459	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 y^{'} x - 6 y = x^{3}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.275

15460	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 y^{'} x - 6 y = e^{- x^{2}}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.419

15461	$y^{'''} - y^{''} + y^{'} - y = \tan (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	1.005

15462	$y^{''''} - 81 y = \sinh (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.630

15463	$x^{4} y^{''''} + 6 x^{3} y^{'''} - 3 x^{2} y^{''} - 9 y^{'} x + 9 y = 12 x \sin (x^{2})$	[[_high_order, _exact, _linear, _nonhomogeneous]]	✓	0.496

15464	$y^{''} + 36 y = 0$	[[_2nd_order, _missing_x]]	✓	1.442

15465	$y^{''} - 12 y^{'} + 36 y = 0$	[[_2nd_order, _missing_x]]	✓	0.399

15466	$x^{2} y^{''} + y^{'} x - 9 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.889

15467	$y^{''} - 36 y = 0$	[[_2nd_order, _missing_x]]	✓	1.537

15468	$y^{''} - 9 y^{'} + 14 y = 0$	[[_2nd_order, _missing_x]]	✓	0.375

15469	$x^{2} y^{''} - 7 y^{'} x + 16 y = 0$	[[_Emden, _Fowler]]	✓	0.862

15470	$2 x y^{''} + y^{'} = \sqrt{x}$	[[_2nd_order, _missing_y]]	✓	0.999

15471	$y^{''''} - 8 y^{''} + 16 y = 0$	[[_high_order, _missing_x]]	✓	0.085

15472	$y^{''} + 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.479

15473	$y^{''} + 3 y = 0$	[[_2nd_order, _missing_x]]	✓	1.573

15474	$x^{2} y^{''} + 7 y^{'} x + 9 y = 0$	[[_Emden, _Fowler]]	✓	0.910

15475	$x^{2} y^{''} + \frac{5 y}{2} = 0$	[[_Emden, _Fowler]]	✓	0.511

15476	$y^{(5)} - 6 y^{''''} + 13 y^{'''} = 0$	[[_high_order, _missing_x]]	✓	0.093

15477	$x^{2} y^{''} - 6 y = 0$	[[_Emden, _Fowler]]	✓	0.339

15478	$y^{''} - 6 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓	0.559

15479	$y^{''} = {y^{'}}^{2}$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]	✓	0.543

15480	$x^{2} y^{''} + y^{'} x + 9 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.973

15481	$y^{''} - 8 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓	0.569

15482	$x^{2} y^{''} + 2 y^{'} x - 30 y = 0$	[[_Emden, _Fowler]]	✓	0.782

15483	$y^{''} + y^{'} - 30 y = 0$	[[_2nd_order, _missing_x]]	✓	0.353

15484	$16 y^{''} - 8 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.416

15485	$4 x^{2} y^{''} + 8 y^{'} x + y = 0$	[[_Emden, _Fowler]]	✓	0.899

15486	$y^{'''} - 6 y^{''} + 12 y^{'} = 8$	[[_3rd_order, _missing_x]]	✓	0.149

15487	$2 x^{2} y^{''} - 3 y^{'} x + 2 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.918

15488	$9 x^{2} y^{''} + 3 y^{'} x + y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.955

15489	$y^{''''} - 16 y = 0$	[[_high_order, _missing_x]]	✓	0.089

15490	$2 y^{''} - 7 y^{'} + 3 = 0$	[[_2nd_order, _missing_x]]	✓	1.237

15491	$y^{''} + 20 y^{'} + 100 y = 0$	[[_2nd_order, _missing_x]]	✓	0.410

15492	$x y^{''} = 3 y^{'}$	[[_2nd_order, _missing_y]]	✓	1.130

15493	$y^{''} - 5 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	1.026

15494	$y^{''} - 9 y^{'} + 14 y = 98 x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.479

15495	$y^{''} - 12 y^{'} + 36 y = 25 \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.840

15496	$y^{''} - 9 y^{'} + 14 y = 576 x^{2} e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.549

15497	$y^{''} - 12 y^{'} + 36 y = 81 e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.600

15498	$x^{2} y^{''} + y^{'} x - 9 y = 3 \sqrt{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.808

15499	$y^{''} - 12 y^{'} + 36 y = 3 x e^{6 x} - 2 e^{6 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.672

15500	$y^{''} + 36 y = 6 \sec (6 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.375

2.2.155 Problems 15401 to 15500