Problems 7601 to 7700

Table 2.155: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

7601	$y^{'} + 2 x y = x$	[_separable]	✓	1.107

7602	$y^{'} x + y = 3 x^{3} - 1$	[_linear]	✓	0.969

7603	$y^{'} + y e^{x} = 3 e^{x}$	[_separable]	✓	1.234

7604	$y^{'} - y \tan (x) = e^{\sin (x)}$	[_linear]	✓	1.841

7605	$y^{'} + 2 x y = x e^{- x^{2}}$	[_linear]	✓	2.336

7606	$y^{'} + \cos (x) y = e^{- \sin (x)}$ i.c.	[_linear]	✓	1.974

7607	$x^{2} y^{'} + 2 x y = 1$	[_linear]	✓	1.251

7608	$2 y + y^{'} = b (x)$	[[_linear, ‘class A‘]]	✓	1.071

7609	$y^{'} = 1 + y$ i.c.	[_quadrature]	✓	0.806

7610	$y^{'} = 1 + y^{2}$ i.c.	[_quadrature]	✓	1.611

7611	$y^{'} = 1 + y^{2}$ i.c.	[_quadrature]	✓	1.643

7612	$y^{''} - 4 y = 0$	[[_2nd_order, _missing_x]]	✓	1.445

7613	$3 y^{''} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	1.585

7614	$y^{''} + 16 y = 0$	[[_2nd_order, _missing_x]]	✓	1.464

7615	$y^{''} = 0$	[[_2nd_order, _quadrature]]	✓	0.673

7616	$y^{''} + 2 i y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.499

7617	$y^{''} - 4 y^{'} + 5 y = 0$	[[_2nd_order, _missing_x]]	✓	0.527

7618	$y^{''} + (- 1 + 3 i) y^{'} - 3 i y = 0$	[[_2nd_order, _missing_x]]	✓	0.320

7619	$y^{''} + y^{'} - 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.563

7620	$y^{''} + y^{'} - 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.551

7621	$y^{''} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.107

7622	$y^{''} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.066

7623	$y^{''} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.211

7624	$y^{''} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.227

7625	$y^{''} - 2 y^{'} - 3 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.546

7626	$y^{''} + (1 + 4 i) y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.612

7627	$y^{''} + (- 1 + 3 i) y^{'} - 3 i y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.372

7628	$y^{''} + 10 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.145

7629	$y^{''} + 4 y = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.679

7630	$y^{''} + 9 y = \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.732

7631	$y^{''} + y = \tan (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.724

7632	$y^{''} + 2 i y^{'} + y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.578

7633	$y^{''} - 4 y^{'} + 5 y = 3 e^{- x} + 2 x^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.634

7634	$y^{''} - 7 y^{'} + 6 y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.581

7635	$y^{''} + y = 2 \sin (2 x) \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.205

7636	$y^{''} + y = \sec (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.696

7637	$4 y^{''} - y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.426

7638	$6 y^{''} + 5 y^{'} - 6 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.484

7639	$y^{''} + ω^{2} y = A \cos (ω x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.194

7640	$y^{'''} - 8 y = 0$	[[_3rd_order, _missing_x]]	✓	0.082

7641	$y^{''''} + 16 y = 0$	[[_high_order, _missing_x]]	✓	0.101

7642	$y^{'''} - 5 y^{''} + 6 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.065

7643	$y^{'''} - i y^{''} + 4 y^{'} - 4 i y = 0$	[[_3rd_order, _missing_x]]	✓	0.097

7644	$y^{''''} + 5 y^{''} + 4 y = 0$	[[_high_order, _missing_x]]	✓	0.084

7645	$y^{''''} - 16 y = 0$	[[_high_order, _missing_x]]	✓	0.089

7646	$y^{'''} - 3 y^{'} - 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.080

7647	$y^{'''} - 3 i y^{''} - 3 y^{'} + i y = 0$	[[_3rd_order, _missing_x]]	✓	0.106

7648	$y^{'''} - 4 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.141

7649	$y^{(5)} - y^{''''} - y^{'} + y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.115

7650	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	1.377

7651	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	1.502

7652	$y^{''''} - y = 0$	[[_high_order, _missing_x]]	✓	0.076

7653	$y^{(5)} + 2 y = 0$	[[_high_order, _missing_x]]	✓	0.164

7654	$y^{''''} - 5 y^{''} + 4 y = 0$	[[_high_order, _missing_x]]	✓	0.075

7655	$y^{'''} + y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.173

7656	$y^{'''} - i y^{''} + y^{'} - i y = 0$	[[_3rd_order, _missing_x]]	✓	0.095

7657	$y^{''} - 2 i y^{'} - y = 0$	[[_2nd_order, _missing_x]]	✓	0.336

7658	$y^{''''} - k^{4} y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.200

7659	$y^{'''} - y = x$	[[_3rd_order, _with_linear_symmetries]]	✓	0.138

7660	$y^{'''} - 8 y = e^{i x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.558

7661	$y^{''''} + 16 y = \cos (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.176

7662	$y^{''''} - 4 y^{'''} + 6 y^{''} - 4 y^{'} + y = e^{x}$	[[_high_order, _with_linear_symmetries]]	✓	0.165

7663	$y^{''''} - y = \cos (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.571

7664	$y^{''} - 2 i y^{'} - y = e^{i x} - 2 e^{- i x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.597

7665	$y^{''} + 4 y = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.730

7666	$y^{''} + 4 y = \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.716

7667	$y^{''} - 4 y = 3 e^{2 x} + 4 e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.682

7668	$y^{''} - y^{'} - 2 y = x^{2} + \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.629

7669	$y^{''} + 9 y = x^{2} e^{3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.650

7670	$y^{''} + y = x e^{x} \cos (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.034

7671	$y^{''} + i y^{'} + 2 y = 2 \cosh (2 x) + e^{- 2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.681

7672	$y^{'''} = x^{2} + e^{- x} \sin (x)$	[[_3rd_order, _quadrature]]	✓	0.751

7673	$y^{'''} + 3 y^{''} + 3 y^{'} + y = x^{2} e^{- x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.170

7674	$y^{''} + \frac{y^{'}}{x} - \frac{y}{x^{2}} = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	2.008

7675	$y^{''} + \frac{y^{'}}{x} - \frac{y}{x^{2}} = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.809

7676	${(3 x - 1)}^{2} y^{''} + (9 x - 3) y^{'} - 9 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.334

7677	$x^{2} y^{''} - 7 y^{'} x + 15 y = 0$	[[_Emden, _Fowler]]	✓	0.145

7678	$x^{2} y^{''} - y^{'} x + y = 0$	[[_Emden, _Fowler]]	✓	0.132

7679	$y^{''} - 4 y^{'} x + (4 x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.158

7680	$x y^{''} - (x + 1) y^{'} + y = 0$	[_Laguerre]	✓	0.163

7681	$(- x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[_Gegenbauer]	✓	0.160

7682	$y^{''} - 2 y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.157

7683	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 y^{'} x - 6 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.139

7684	$x^{2} y^{''} - 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.127

7685	$x^{2} y^{''} - y^{'} x + y = 0$	[[_Emden, _Fowler]]	✓	0.127

7686	$x^{2} y^{''} + 4 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.624

7687	$y^{''} - y^{'} x + y = 0$	[_Hermite]	✓	0.336

7688	$y^{''} + 3 x^{2} y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.427

7689	$y^{''} - x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.265

7690	$y^{''} + x^{3} y^{'} + x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.381

7691	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.388

7692	$y^{''} + {(x - 1)}^{2} y^{'} - (x - 1) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.420

7693	$(x^{2} + 1) y^{''} + y = 0$ i.c.	[[_Emden, _Fowler]]	✓	0.500

7694	$y^{''} + y e^{x} = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.533

7695	$y^{'''} - x y = 0$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✗	0.077

7696	$(- x^{2} + 1) y^{''} - 2 y^{'} x + α (α + 1) y = 0$	[_Gegenbauer]	✓	0.662

7697	$(- x^{2} + 1) y^{''} - y^{'} x + α^{2} y = 0$	[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.015

7698	$y^{''} - 2 y^{'} x + 2 α y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.892

7699	$x^{2} y^{''} + 2 y^{'} x - 6 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.694

7700	$2 x^{2} y^{''} + y^{'} x - y = 0$	[[_Emden, _Fowler]]	✓	0.878

2.2.77 Problems 7601 to 7700