Problems 6501 to 6600

Table 2.133: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

6501	$y^{''} + 6 y^{'} + 10 y = 50 x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.605

6502	$x^{''} + 2 x^{'} + 2 x = 85 \sin (3 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.936

6503	$y^{''} = 3 \sin (x) - 4 y$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.911

6504	$\frac{x^{''}}{2} = - 48 x$ i.c.	[[_2nd_order, _missing_x]]	✓	1.951

6505	$x^{''} + 5 x^{'} + 6 x = \cos (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.723

6506	$y^{''} - y^{'} - 2 y = 4 x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.515

6507	$y^{''} - y^{'} - 2 y = e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.479

6508	$y^{''} - y^{'} - 2 y = \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.565

6509	$y^{''} - 6 y^{'} + 25 y = 2 \sin (\frac{t}{2}) - \cos (\frac{t}{2})$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.669

6510	$y^{''} - 6 y^{'} + 25 y = 64 e^{- t}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.676

6511	$y^{''} - 6 y^{'} + 25 y = 50 t^{3} - 36 t^{2} - 63 t + 18$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.639

6512	$y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = 2 x e^{- x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.168

6513	$y^{''} = 9 x^{2} + 2 x - 1$	[[_2nd_order, _quadrature]]	✓	0.831

6514	$y^{''} - 5 y = 2 e^{5 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.592

6515	$y^{'} - 5 y = (x - 1) \sin (x) + (x + 1) \cos (x)$	[[_linear, ‘class A‘]]	✓	2.106

6516	$y^{'} - 5 y = 3 e^{x} - 2 x + 1$	[[_linear, ‘class A‘]]	✓	1.305

6517	$y^{'} - 5 y = x^{2} e^{x} - x e^{5 x}$	[[_linear, ‘class A‘]]	✓	1.754

6518	$y^{''} - 2 y^{'} + y = x^{2} - 1$	[[_2nd_order, _with_linear_symmetries]]	✓	0.552

6519	$y^{''} - 2 y^{'} + y = 4 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.575

6520	$y^{''} - 2 y^{'} + y = 4 \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.623

6521	$y^{''} - 2 y^{'} + y = 3 e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.611

6522	$y^{''} - 2 y^{'} + y = x e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.571

6523	$y^{'} - y = e^{x}$	[[_linear, ‘class A‘]]	✓	0.923

6524	$y^{'} - y = x e^{2 x} + 1$	[[_linear, ‘class A‘]]	✓	1.367

6525	$y^{'} - y = \sin (x) + \cos (2 x)$	[[_linear, ‘class A‘]]	✓	2.111

6526	$y^{'''} - 3 y^{''} + 3 y^{'} - y = e^{x} + 1$	[[_3rd_order, _with_linear_symmetries]]	✓	0.157

6527	$y^{'''} + y^{'} = \sec (x)$	[[_3rd_order, _missing_y]]	✓	0.622

6528	$y^{'''} - 3 y^{''} + 2 y^{'} = \frac{e^{x}}{1 + e^{- x}}$	[[_3rd_order, _missing_y]]	✓	0.309

6529	$y^{''} - 2 y^{'} + y = \frac{e^{x}}{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.622

6530	$y^{''} - y^{'} - 2 y = e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.418

6531	$x^{''} + 4 x = \sin {(2 t)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.866

6532	$t^{2} N^{''} - 2 t N^{'} + 2 N = t \ln (t)$	[[_2nd_order, _with_linear_symmetries]]	✓	1.844

6533	$y^{'} + \frac{4 y}{x} = x^{4}$	[_linear]	✓	1.245

6534	$y^{''''} = 5 x$	[[_high_order, _quadrature]]	✓	0.123

6535	$y^{''} - 2 y^{'} + y = \frac{e^{x}}{x^{5}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.611

6536	$y^{''} + y = \sec (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.706

6537	$y^{''} - y^{'} - 2 y = e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.460

6538	$y^{''} - 60 y^{'} - 900 y = 5 e^{10 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.560

6539	$y^{''} - 7 y^{'} = - 3$	[[_2nd_order, _missing_x]]	✓	1.091

6540	$y^{''} + \frac{y^{'}}{x} - \frac{y}{x^{2}} = \ln (x)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.986

6541	$x^{2} y^{''} - y^{'} x = x^{3} e^{x}$	[[_2nd_order, _missing_y]]	✓	0.697

6542	$y^{'} - \frac{y}{x} = x^{2}$	[_linear]	✓	1.304

6543	$2 y + y^{'} = 0$ i.c.	[_quadrature]	✓	0.312

6544	$2 y + y^{'} = 2$ i.c.	[_quadrature]	✓	0.268

6545	$2 y + y^{'} = e^{x}$ i.c.	[[_linear, ‘class A‘]]	✓	0.310

6546	$y^{''} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.283

6547	$y^{''} - y = \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.436

6548	$y^{''} - y = e^{x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.338

6549	$y^{''} + 2 y^{'} - 3 y = \sin (2 x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.473

6550	$y^{''} + y = \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.452

6551	$y^{''} + y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.420

6552	$y^{''} + 2 y^{'} + 5 y = 3 e^{- 2 x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.464

6553	$y^{''} + 5 y^{'} - 3 y = Heaviside (x - 4)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.864

6554	$y^{'''} - y = 5$ i.c.	[[_3rd_order, _missing_x]]	✓	0.517

6555	$y^{''''} - y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.488

6556	$y^{'''} - 3 y^{''} + 3 y^{'} - y = x^{2} e^{x}$ i.c.	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.422

6557	$x^{''} + 4 x^{'} + 4 x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.313

6558	$q^{''} + 9 q^{'} + 14 q = \frac{\sin (t)}{2}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.505

6559	$(x + 1) y^{''} + \frac{y^{'}}{x} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.633

6560	$x^{3} y^{''} + y = 0$	[[_Emden, _Fowler]]	✗	0.147

6561	$y^{''} + x y = 0$	[[_Emden, _Fowler]]	✓	0.296

6562	$y^{''} - 2 y^{'} x - 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.404

6563	$y^{''} + x^{2} y^{'} + 2 x y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.417

6564	$y^{''} - x^{2} y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.406

6565	$y^{''} + 2 x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.286

6566	$(x^{2} - 1) y^{''} + y^{'} x - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.422

6567	$y^{''} - x y = 0$	[[_Emden, _Fowler]]	✓	0.295

6568	$y^{''} - 2 y^{'} x + x^{2} y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.465

6569	$y^{'} x = 2 y$	[_separable]	✓	1.497

6570	$y y^{'} + x = 0$	[_separable]	✓	3.302

6571	$y = y^{'} x + {y^{'}}^{4}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	1.810

6572	$2 x^{3} y^{'} = y (3 x^{2} + y^{2})$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	144.745

6573	$y^{''} - 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.390

6574	$(x - 1) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.773

6575	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	1.526

6576	$y^{''} - y = 4 - x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.496

6577	$y^{''} - 3 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.330

6578	$y^{''} - 3 y^{'} + 2 y = 2 e^{x} (1 - x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.534

6579	$4 y + y^{'} x = 0$	[_separable]	✓	1.583

6580	$1 + 2 y + (- x^{2} + 4) y^{'} = 0$	[_separable]	✓	2.617

6581	$y^{2} - x^{2} y^{'} = 0$	[_separable]	✓	2.087

6582	$1 + y - (x + 1) y^{'} = 0$	[_separable]	✓	1.560

6583	$x y^{2} + y + (x^{2} y - x) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.812

6584	$x \sin (\frac{y}{x}) - y \cos (\frac{y}{x}) + x \cos (\frac{y}{x}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.919

6585	$y^{2} (x^{2} + 2) + (x^{3} + y^{3}) (y - y^{'} x) = 0$	[[_homogeneous, ‘class D‘], _rational]	✓	1.648

6586	$y \sqrt{x^{2} + y^{2}} - x (x + \sqrt{x^{2} + y^{2}}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _dAlembert]	✓	4.934

6587	$x + y + 1 + (2 x + 2 y + 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.786

6588	$1 + 2 y - (4 - x) y^{'} = 0$	[_separable]	✓	1.516

6589	$(x^{2} + 1) y^{'} + x y = 0$	[_separable]	✓	1.243

6590	$x + 2 y + (2 x + 3 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.203

6591	$2 y^{'} x - 2 y = \sqrt{x^{2} + 4 y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.759

6592	$3 y - 7 x + 7 + (7 y - 3 x + 3) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.081

6593	$x y^{'} y = (1 + y) (1 - x)$	[_separable]	✓	1.447

6594	$y^{2} - x^{2} + x y^{'} y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	3.486

6595	$y (1 + 2 x y) + x (1 - x y) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.882

6596	$1 + (- x^{2} + 1) \cot (y) y^{'} = 0$	[_separable]	✓	2.171

6597	$x^{3} + y^{3} + 3 x y^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	✓	12.954

6598	$3 x + 2 y + 1 - (3 x + 2 y - 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.082

6599	$y^{'} x + 2 y = 0$ i.c.	[_separable]	✓	1.878

6600	$x y^{'} y + x^{2} + y^{2} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	4.492

2.2.66 Problems 6501 to 6600