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]	✓	1.475

7602	$x y^{'} + y = 3 x^{3} - 1$	[_linear]	✓	1.266

7603	$y^{'} + y e^{x} = 3 e^{x}$	[_separable]	✓	1.652

7604	$y^{'} - \tan (x) y = e^{\sin (x)}$	[_linear]	✓	1.907

7605	$y^{'} + 2 x y = x e^{- x^{2}}$	[_linear]	✓	2.520

7606	$y^{'} + \cos (x) y = e^{- \sin (x)}$ i.c.	[_linear]	✓	2.082

7607	$x^{2} y^{'} + 2 x y = 1$	[_linear]	✓	1.561

7608	$y^{'} + 2 y = b (x)$	[[_linear, ‘class A‘]]	✓	0.997

7609	$y^{'} = y + 1$ i.c.	[_quadrature]	✓	1.682

7610	$y^{'} = 1 + y^{2}$ i.c.	[_quadrature]	✓	2.847

7611	$y^{'} = 1 + y^{2}$ i.c.	[_quadrature]	✓	2.847

7612	$y^{''} - 4 y = 0$	[[_2nd_order, _missing_x]]	✓	1.949

7613	$3 y^{''} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	2.379

7614	$y^{''} + 16 y = 0$	[[_2nd_order, _missing_x]]	✓	2.172

7615	$y^{''} = 0$	[[_2nd_order, _quadrature]]	✓	1.903

7616	$y^{''} + 2 i y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.833

7617	$y^{''} - 4 y^{'} + 5 y = 0$	[[_2nd_order, _missing_x]]	✓	1.992

7618	$y^{''} + (- 1 + 3 i) y^{'} - 3 i y = 0$	[[_2nd_order, _missing_x]]	✓	0.543

7619	$y^{''} + y^{'} - 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.398

7620	$y^{''} + y^{'} - 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.411

7621	$y^{''} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.242

7622	$y^{''} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.286

7623	$y^{''} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.352

7624	$y^{''} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.407

7625	$y^{''} - 2 y^{'} - 3 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.372

7626	$y^{''} + (1 + 4 i) y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.657

7627	$y^{''} + (- 1 + 3 i) y^{'} - 3 i y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.602

7628	$y^{''} + 10 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.802

7629	$y^{''} + 4 y = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.622

7630	$y^{''} + 9 y = \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.532

7631	$y^{''} + y = \tan (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.915

7632	$y^{''} + 2 i y^{'} + y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	1.553

7633	$y^{''} - 4 y^{'} + 5 y = 3 e^{- x} + 2 x^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	22.470

7634	$y^{''} - 7 y^{'} + 6 y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.391

7635	$y^{''} + y = 2 \sin (x) \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.123

7636	$y^{''} + y = \sec (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.691

7637	$4 y^{''} - y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.993

7638	$6 y^{''} + 5 y^{'} - 6 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	1.699

7639	$y^{''} + ω^{2} y = A \cos (ω x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.500

7640	$y^{'''} - 8 y = 0$	[[_3rd_order, _missing_x]]	✓	0.056

7641	$y^{''''} + 16 y = 0$	[[_high_order, _missing_x]]	✓	0.069

7642	$y^{'''} - 5 y^{''} + 6 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.049

7643	$y^{'''} - i y^{''} + 4 y^{'} - 4 i y = 0$	[[_3rd_order, _missing_x]]	✓	0.076

7644	$y^{''''} + 5 y^{''} + 4 y = 0$	[[_high_order, _missing_x]]	✓	0.058

7645	$y^{''''} - 16 y = 0$	[[_high_order, _missing_x]]	✓	0.057

7646	$y^{'''} - 3 y^{'} - 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.051

7647	$y^{'''} - 3 i y^{''} - 3 y^{'} + i y = 0$	[[_3rd_order, _missing_x]]	✓	0.073

7648	$y^{'''} - 4 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.111

7649	$y^{(5)} - y^{''''} - y^{'} + y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.090

7650	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	2.021

7651	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	2.039

7652	$y^{''''} - y = 0$	[[_high_order, _missing_x]]	✓	0.055

7653	$y^{(5)} + 2 y = 0$	[[_high_order, _missing_x]]	✓	0.136

7654	$y^{''''} - 5 y^{''} + 4 y = 0$	[[_high_order, _missing_x]]	✓	0.055

7655	$y^{'''} + y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.139

7656	$y^{'''} - i y^{''} + y^{'} - i y = 0$	[[_3rd_order, _missing_x]]	✓	0.074

7657	$y^{''} - 2 i y^{'} - y = 0$	[[_2nd_order, _missing_x]]	✓	0.409

7658	$y^{''''} - k^{4} y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.155

7659	$y^{'''} - y = x$	[[_3rd_order, _with_linear_symmetries]]	✓	0.092

7660	$y^{'''} - 8 y = e^{i x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.473

7661	$y^{''''} + 16 y = \cos (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.132

7662	$y^{''''} - 4 y^{'''} + 6 y^{''} - 4 y^{'} + y = e^{x}$	[[_high_order, _with_linear_symmetries]]	✓	0.115

7663	$y^{''''} - y = \cos (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.506

7664	$y^{''} - 2 i y^{'} - y = e^{i x} - 2 e^{- i x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.197

7665	$y^{''} + 4 y = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.638

7666	$y^{''} + 4 y = \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.605

7667	$y^{''} - 4 y = 3 e^{2 x} + 4 e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.292

7668	$y^{''} - y^{'} - 2 y = x^{2} + \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.733

7669	$y^{''} + 9 y = x^{2} e^{3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.711

7670	$y^{''} + y = x e^{x} \cos (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.474

7671	$y^{''} + i y^{'} + 2 y = 2 \cosh (2 x) + e^{- 2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.115

7672	$y^{'''} = x^{2} + e^{- x} \sin (x)$	[[_3rd_order, _quadrature]]	✓	0.676

7673	$y^{'''} + 3 y^{''} + 3 y^{'} + y = x^{2} e^{- x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.125

7674	$y^{''} + \frac{y^{'}}{x} - \frac{y}{x^{2}} = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	2.094

7675	$y^{''} + \frac{y^{'}}{x} - \frac{y}{x^{2}} = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.684

7676	${(3 x - 1)}^{2} y^{''} + (9 x - 3) y^{'} - 9 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.319

7677	$x^{2} y^{''} - 7 x y^{'} + 15 y = 0$	[[_Emden, _Fowler]]	✓	0.082

7678	$x^{2} y^{''} - x y^{'} + y = 0$	[[_Emden, _Fowler]]	✓	0.078

7679	$y^{''} - 4 x y^{'} + (4 x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.088

7680	$x y^{''} - (x + 1) y^{'} + y = 0$	[_Laguerre]	✓	0.096

7681	$(- x^{2} + 1) y^{''} - 2 x y^{'} + 2 y = 0$	[_Gegenbauer]	✓	0.101

7682	$y^{''} - 2 x y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.094

7683	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 x y^{'} - 6 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.107

7684	$x^{2} y^{''} - 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.075

7685	$x^{2} y^{''} - x y^{'} + y = 0$	[[_Emden, _Fowler]]	✓	0.079

7686	$x^{2} y^{''} + 4 x y^{'} + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.418

7687	$y^{''} - x y^{'} + y = 0$	[_Hermite]	✓	0.367

7688	$y^{''} + 3 x^{2} y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.402

7689	$y^{''} - x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.264

7690	$y^{''} + x^{3} y^{'} + x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.392

7691	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.416

7692	$y^{''} + {(- 1 + x)}^{2} y^{'} - (- 1 + x) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.346

7693	$(x^{2} + 1) y^{''} + y = 0$ i.c.	[[_Emden, _Fowler]]	✓	0.352

7694	$y^{''} + y e^{x} = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.432

7695	$y^{'''} - x y = 0$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✗	0.039

7696	$(- x^{2} + 1) y^{''} - 2 x y^{'} + α (1 + α) y = 0$	[_Gegenbauer]	✓	0.560

7697	$(- x^{2} + 1) y^{''} - x y^{'} + α^{2} y = 0$	[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.557

7698	$y^{''} - 2 x y^{'} + 2 α y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.592

7699	$x^{2} y^{''} + 2 x y^{'} - 6 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.714

7700	$2 x^{2} y^{''} + x y^{'} - y = 0$	[[_Emden, _Fowler]]	✓	0.921

2.2.77 Problems 7601 to 7700