Problems 3701 to 3800

Table 2.77: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

3701	$y^{'''} + 3 y^{''} - 4 y^{'} - 12 y = 0$	[[_3rd_order, _missing_x]]	✓	0.078

3702	$y^{'''} + 3 y^{''} - 18 y^{'} - 40 y = 0$	[[_3rd_order, _missing_x]]	✓	0.078

3703	$y^{'''} - y^{''} - 2 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.070

3704	$y^{'''} + y^{''} - 10 y^{'} + 8 y = 0$	[[_3rd_order, _missing_x]]	✓	0.074

3705	$y^{''''} - 2 y^{'''} - y^{''} + 2 y^{'} = 0$	[[_high_order, _missing_x]]	✓	0.075

3706	$y^{''''} - 13 y^{''} + 36 y = 0$	[[_high_order, _missing_x]]	✓	0.080

3707	$x^{2} y^{''} + 3 y^{'} x - 8 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.682

3708	$2 x^{2} y^{''} + 5 y^{'} x + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.177

3709	$x^{3} y^{'''} + x^{2} y^{''} - 2 y^{'} x + 2 y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	0.135

3710	$x^{3} y^{'''} + 3 x^{2} y^{''} - 6 y^{'} x = 0$	[[_3rd_order, _missing_y]]	✓	0.150

3711	$y^{''} + y^{'} - 6 y = 18 e^{5 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.511

3712	$y^{''} + y^{'} - 2 y = 4 x^{2} + 5$	[[_2nd_order, _with_linear_symmetries]]	✓	0.456

3713	$y^{'''} + 2 y^{''} - y^{'} - 2 y = 4 e^{2 x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.159

3714	$y^{'''} + y^{''} - 10 y^{'} + 8 y = 24 e^{- 3 x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.140

3715	$y^{'''} + 5 y^{''} + 6 y^{'} = 6 e^{- x}$	[[_3rd_order, _missing_y]]	✓	0.166

3716	$y^{''} + y = 6 e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.654

3717	$y^{''} + 4 y^{'} + 4 y = 5 x e^{- 2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.632

3718	$y^{''} + 4 y = 8 \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.779

3719	$y^{''} - y^{'} - 2 y = 5 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.603

3720	$y^{''} + 2 y^{'} + 5 y = 3 \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.677

3721	$y^{'''} + 2 y^{''} - 5 y^{'} - 6 y = 4 x^{2}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.141

3722	$y^{'''} - y^{''} + y^{'} - y = 9 e^{- x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.151

3723	$y^{'''} + 3 y^{''} + 3 y^{'} + y = 2 e^{- x} + 3 e^{2 x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.189

3724	$y^{''} + 9 y = 5 \cos (2 x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.952

3725	$y^{''} - y = 9 x e^{2 x}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.754

3726	$y^{''} + y^{'} - 2 y = - 10 \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.791

3727	$y^{''} + y^{'} - 2 y = 4 \cos (x) - 2 \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.835

3728	$y^{''} + ω^{2} y = \frac{F_{0} \cos (ω t)}{m}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.227

3729	$y^{''} - 4 y^{'} + 6 y = 7 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.704

3730	$y^{'''} + y^{''} + y^{'} + y = 4 x e^{x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.154

3731	$y^{''''} + 104 y^{'''} + 2740 y^{''} = 5 e^{- 2 x} \cos (3 x)$	[[_high_order, _missing_y]]	✓	0.235

3732	$y^{''} + 2 y^{'} - 3 y = \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.617

3733	$y^{''} + 6 y = \sin {(x)}^{2} \cos {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.943

3734	$y^{''} - 16 y = 20 \cos (4 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.745

3735	$y^{''} + 2 y^{'} + y = 50 \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.739

3736	$y^{''} - y = 10 e^{2 x} \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.855

3737	$y^{''} + 4 y^{'} + 4 y = 169 \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.817

3738	$y^{''} - y^{'} - 2 y = 40 \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.661

3739	$y^{''} + y = 3 e^{x} \cos (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.871

3740	$y^{''} + 2 y^{'} + 2 y = 2 e^{- x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.681

3741	$y^{''} - 4 y = 100 x e^{x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.907

3742	$y^{''} + 2 y^{'} + 5 y = 4 e^{- x} \cos (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.702

3743	$y^{''} - 2 y^{'} + 10 y = 24 e^{x} \cos (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.740

3744	$y^{''} + 16 y = 34 e^{x} + 16 \cos (4 x) - 8 \sin (4 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.282

3745	$y^{''} - 6 y^{'} + 9 y = 4 e^{3 x} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.718

3746	$y^{''} + 4 y^{'} + 4 y = \frac{e^{- 2 x}}{x^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.654

3747	$y^{''} + 9 y = 18 \sec {(3 x)}^{3}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.165

3748	$y^{''} + 6 y^{'} + 9 y = \frac{2 e^{- 3 x}}{x^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.709

3749	$y^{''} - 4 y = \frac{8}{e^{2 x} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.869

3750	$y^{''} - 4 y^{'} + 5 y = e^{2 x} \tan (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.806

3751	$y^{''} + 9 y = \frac{36}{4 - \cos {(3 x)}^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.273

3752	$y^{''} - 10 y^{'} + 25 y = \frac{2 e^{5 x}}{x^{2} + 4}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.680

3753	$y^{''} - 6 y^{'} + 13 y = 4 e^{3 x} \sec {(2 x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.848

3754	$y^{''} + y = \sec (x) + 4 e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.967

3755	$y^{''} + y = \csc (x) + 2 x^{2} + 5 x + 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.923

3756	$y^{''} - y = 2 \tanh (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.811

3757	$y^{''} - 2 m y^{'} + m^{2} y = \frac{e^{m x}}{x^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.696

3758	$y^{''} - 2 y^{'} + y = \frac{4 e^{x} \ln (x)}{x^{3}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.709

3759	$y^{''} + 2 y^{'} + y = \frac{e^{- x}}{\sqrt{- x^{2} + 4}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.737

3760	$y^{''} + 2 y^{'} + 17 y = \frac{64 e^{- x}}{3 + \sin {(4 x)}^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.064

3761	$y^{''} + 4 y^{'} + 4 y = \frac{4 e^{- 2 x}}{x^{2} + 1} + 2 x^{2} - 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.827

3762	$y^{''} + 4 y^{'} + 4 y = 15 e^{- 2 x} \ln (x) + 25 \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.981

3763	$y^{'''} - 3 y^{''} + 3 y^{'} - y = \frac{2 e^{x}}{x^{2}}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.319

3764	$y^{'''} - 6 y^{''} + 12 y^{'} - 8 y = 36 e^{2 x} \ln (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.324

3765	$y^{'''} + 3 y^{''} + 3 y^{'} + y = \frac{2 e^{- x}}{x^{2} + 1}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.436

3766	$y^{'''} - 6 y^{''} + 9 y^{'} = 12 e^{3 x}$	[[_3rd_order, _missing_y]]	✓	0.169

3767	$y^{''} - 9 y = F (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.624

3768	$y^{''} + 5 y^{'} + 4 y = F (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.660

3769	$y^{''} + y^{'} - 2 y = F (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.614

3770	$y^{''} + 4 y^{'} - 12 y = F (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.704

3771	$y^{''} - 4 y^{'} + 4 y = 5 x e^{2 x}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.914

3772	$y^{''} + y = \sec (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.173

3773	$x^{2} y^{''} + 4 y^{'} x + 2 y = 4 \ln (x)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	2.025

3774	$x^{2} y^{''} + 4 y^{'} x + 2 y = \cos (x)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	2.276

3775	$x^{2} y^{''} + y^{'} x + 9 y = 9 \ln (x)$	[[_2nd_order, _with_linear_symmetries]]	✓	1.766

3776	$x^{2} y^{''} - y^{'} x + 5 y = 8 x \ln {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.636

3777	$x^{2} y^{''} - 4 y^{'} x + 6 y = x^{4} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	7.211

3778	$x^{2} y^{''} + 6 y^{'} x + 6 y = 4 e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.875

3779	$x^{2} y^{''} - 3 y^{'} x + 4 y = \frac{x^{2}}{\ln (x)}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.489

3780	$x^{2} y^{''} - (2 m - 1) x y^{'} + m^{2} y = x^{m} \ln {(x)}^{k}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.763

3781	$x^{2} y^{''} - y^{'} x + 5 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	1.967

3782	$t^{2} y^{''} + y^{'} t + 25 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.454

3783	$x^{2} y^{''} - 3 y^{'} x + 4 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.141

3784	$x y^{''} + (- 2 x + 1) y^{'} + (x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.160

3785	$x^{2} y^{''} - 2 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.149

3786	$(- x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[_Gegenbauer]	✓	0.155

3787	$y^{''} - \frac{y^{'}}{x} + 4 x^{2} y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.140

3788	$4 x^{2} y^{''} + 4 y^{'} x + (4 x^{2} - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.146

3789	$y^{''} + y = \csc (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.372

3790	$x y^{''} - (2 x + 1) y^{'} + 2 y = 8 x^{2} e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.361

3791	$x^{2} y^{''} - 3 y^{'} x + 4 y = 8 x^{4}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.233

3792	$y^{''} - 6 y^{'} + 9 y = 15 e^{3 x} \sqrt{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.373

3793	$y^{''} - 4 y^{'} + 4 y = 4 e^{2 x} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.372

3794	$4 x^{2} y^{''} + y = \sqrt{x} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.294

3795	$y^{'''} + 3 y^{''} - 4 y = 0$	[[_3rd_order, _missing_x]]	✓	0.080

3796	$y^{'''} + 11 y^{''} + 36 y^{'} + 26 y = 0$	[[_3rd_order, _missing_x]]	✓	0.089

3797	$y^{''} + 6 y^{'} + 9 y = 4 e^{- 3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.597

3798	$y^{''} + 6 y^{'} + 9 y = 4 e^{- 2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.580

3799	$y^{'''} - 6 y^{''} + 25 y^{'} = x^{2}$	[[_3rd_order, _missing_y]]	✓	0.130

3800	$y^{'''} - 6 y^{''} + 25 y^{'} = \sin (4 x)$	[[_3rd_order, _missing_y]]	✓	0.207

2.2.38 Problems 3701 to 3800