Problems 3901 to 4000

Table 2.81: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	Maple	Mma	Sympy

3901	$[\begin{matrix} x_{1}^{'} = - x_{1} - 5 x_{2} + x_{3} \\ x_{2}^{'} = 4 x_{1} - 9 x_{2} - x_{3} \\ x_{3}^{'} = 3 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3902	$[\begin{matrix} x_{1}^{'} = - 4 x_{1} \\ x_{2}^{'} = 2 x_{1} + 5 x_{2} - 9 x_{3} \\ x_{3}^{'} = 5 x_{2} - x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3903	$[\begin{matrix} x_{1}^{'} = 2 x_{1} - 2 x_{2} + x_{3} \\ x_{2}^{'} = x_{1} - 4 x_{2} + x_{3} \\ x_{3}^{'} = 2 x_{1} + 2 x_{2} - 3 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3904	$[\begin{matrix} x_{1}^{'} = 2 x_{1} - 4 x_{2} + 3 x_{3} \\ x_{2}^{'} = - 9 x_{1} - 3 x_{2} - 9 x_{3} \\ x_{3}^{'} = 4 x_{1} + 4 x_{2} + 3 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3905	$[\begin{matrix} x_{1}^{'} = - 17 x_{1} - 42 x_{3} \\ x_{2}^{'} = - 7 x_{1} + 4 x_{2} - 14 x_{3} \\ x_{3}^{'} = 7 x_{1} + 18 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3906	$[\begin{matrix} x_{1}^{'} = - 16 x_{1} + 30 x_{2} - 18 x_{3} \\ x_{2}^{'} = - 8 x_{1} + 8 x_{2} + 16 x_{3} \\ x_{3}^{'} = 8 x_{1} - 15 x_{2} + 9 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3907	$[\begin{matrix} x_{1}^{'} = - 7 x_{1} - 6 x_{2} - 7 x_{3} \\ x_{2}^{'} = - 3 x_{1} - 3 x_{2} - 3 x_{3} \\ x_{3}^{'} = 7 x_{1} + 6 x_{2} + 7 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3908	$[\begin{matrix} x_{1}^{'} = 3 x_{1} - x_{2} - 2 x_{3} \\ x_{2}^{'} = x_{1} + 6 x_{2} + x_{3} \\ x_{3}^{'} = x_{1} + 6 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3909	$[\begin{matrix} x_{1}^{'} = - x_{1} - 4 x_{2} - 2 x_{3} \\ x_{2}^{'} = - 4 x_{1} - 5 x_{2} - 6 x_{3} \\ x_{3}^{'} = 4 x_{1} + 8 x_{2} + 7 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3910	$[\begin{matrix} x_{1}^{'} = 7 x_{1} - 2 x_{2} + 2 x_{3} \\ x_{2}^{'} = 4 x_{2} - x_{3} \\ x_{3}^{'} = - x_{1} + x_{2} + 4 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3911	$[\begin{matrix} x_{1}^{'} = - 3 x_{1} - x_{2} - 2 x_{3} \\ x_{2}^{'} = x_{1} + x_{3} \\ x_{3}^{'} = x_{1} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3912	$[\begin{matrix} x_{1}^{'} = - 2 x_{1} - x_{3} \\ x_{2}^{'} = - x_{2} \\ x_{3}^{'} = x_{1} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3913	$[\begin{matrix} x_{1}^{'} = 2 x_{1} + 13 x_{2} \\ x_{2}^{'} = - x_{1} - 2 x_{2} \\ x_{3}^{'} = 2 x_{3} + 4 x_{4} \\ x_{4}^{'} = 2 x_{4} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3914	$[\begin{matrix} x_{1}^{'} = 7 x_{1} - x_{4} \\ x_{2}^{'} = 6 x_{2} \\ x_{3}^{'} = - x_{3} \\ x_{4}^{'} = 2 x_{1} + 5 x_{4} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3915	$[\begin{matrix} x_{1}^{'} = - 6 x_{1} + x_{2} + 1 \\ x_{2}^{'} = 6 x_{1} - 5 x_{2} + e^{- t} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3916	$[\begin{matrix} x_{1}^{'} = 9 x_{1} - 2 x_{2} + 9 t \\ x_{2}^{'} = 5 x_{1} - 2 x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3917	$[\begin{matrix} x_{1}^{'} = 10 x_{1} - 4 x_{2} \\ x_{2}^{'} = 4 x_{1} + 2 x_{2} + \frac{e^{6 t}}{t} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3918	$[\begin{matrix} x_{1}^{'} = 2 x_{1} - 4 x_{2} + 3 x_{3} + e^{6 t} \\ x_{2}^{'} = - 9 x_{1} - 3 x_{2} - 9 x_{3} + 1 \\ x_{3}^{'} = 4 x_{1} + 4 x_{2} + 3 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3919	$[\begin{matrix} x_{1}^{'} = 2 x_{1} - 2 x_{2} + x_{3} + t \\ x_{2}^{'} = x_{1} - 4 x_{2} + x_{3} \\ x_{3}^{'} = 2 x_{1} + 2 x_{2} - 3 x_{3} + 1 \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3920	$[\begin{matrix} x_{1}^{'} = - 3 x_{1} + 4 x_{2} \\ x_{2}^{'} = 8 x_{1} + x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3921	$[\begin{matrix} x_{1}^{'} = - 6 x_{2} \\ x_{2}^{'} = x_{1} - 5 x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3922	$[\begin{matrix} x_{1}^{'} = 5 x_{1} + 9 x_{2} \\ x_{2}^{'} = - 2 x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3923	$[\begin{matrix} x_{1}^{'} = - 4 x_{1} \\ x_{2}^{'} = - 4 x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3924	$[\begin{matrix} x_{1}^{'} = 7 x_{1} - 2 x_{2} \\ x_{2}^{'} = x_{1} + 4 x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3925	$[\begin{matrix} x_{1}^{'} = - 3 x_{1} - 5 x_{2} \\ x_{2}^{'} = x_{1} - 7 x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3926	$[\begin{matrix} x_{1}^{'} = - 2 x_{1} - x_{2} \\ x_{2}^{'} = x_{1} - 4 x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3927	$[\begin{matrix} x_{1}^{'} = 10 x_{1} - 8 x_{2} \\ x_{2}^{'} = 2 x_{1} + 2 x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

3928	$- 2 y + y^{'} = 6 e^{5 t}$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

3929	$y + y^{'} = 8 e^{3 t}$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

3930	$3 y + y^{'} = 2 e^{- t}$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

3931	$y^{'} + 2 y = 4 t$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

3932	$- y + y^{'} = 6 \cos (t)$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

3933	$- y + y^{'} = 5 \sin (2 t)$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

3934	$y + y^{'} = 5 e^{t} \sin (t)$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

3935	$y^{''} + y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

3936	$y^{''} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

3937	$y^{''} - 3 y^{'} + 2 y = 4$ i.c.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

3938	$y^{''} - y^{'} - 12 y = 36$ i.c.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

3939	$y^{''} + y^{'} - 2 y = 10 e^{- t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

3940	$y^{''} - 3 y^{'} + 2 y = 4 e^{3 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

3941	$y^{''} - 2 y^{'} = 30 e^{- 3 t}$ i.c.	[[_2nd_order, _missing_y]]	✓	✓	✓	✓

3942	$y^{''} - y = 12 e^{2 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

3943	$y^{''} + 4 y = 10 e^{- t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

3944	$y^{''} - y^{'} - 6 y = 12 - 6 e^{t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

3945	$y^{''} - y = 6 \cos (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3946	$y^{''} - 9 y = 13 \sin (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3947	$y^{''} - y = 8 \sin (t) - 6 \cos (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3948	$y^{''} - y^{'} - 2 y = 10 \cos (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3949	$y^{''} + 5 y^{'} + 4 y = 20 \sin (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3950	$y^{''} + 5 y^{'} + 4 y = 20 \sin (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3951	$y^{''} - 3 y^{'} + 2 y = 3 \cos (t) + \sin (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3952	$y^{''} + 4 y = 9 \sin (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3953	$y^{''} + y = 6 \cos (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3954	$y^{''} + 9 y = 7 \sin (4 t) + 14 \cos (4 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3955	$y^{''} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

3956	$y^{'} + 2 y = 2 Heaviside (t - 1)$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

3957	$- 2 y + y^{'} = Heaviside (t - 2) e^{t - 2}$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

3958	$- y + y^{'} = 4 Heaviside (t - \frac{π}{4}) \sin (t + \frac{π}{4})$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

3959	$y^{'} + 2 y = Heaviside (t - π) \sin (2 t)$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

3960	$3 y + y^{'} = {\begin{array}{cc} 1 & 0 \leq t < 1 \\ 0 & 1 \leq t \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✗

3961	$y^{'} - 3 y = {\begin{array}{cc} \sin (t) & 0 \leq t < \frac{π}{2} \\ 1 & \frac{π}{2} \leq t \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✗

3962	$y^{'} - 3 y = - 10 e^{- t + a} \sin (- 2 t + 2 a) Heaviside (t - a)$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

3963	$y^{''} - y = Heaviside (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3964	$y^{''} - y^{'} - 2 y = 1 - 3 Heaviside (t - 2)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3965	$y^{''} - 4 y = Heaviside (t - 1) - Heaviside (t - 2)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3966	$y^{''} + y = t - Heaviside (t - 1) (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3967	$y^{''} + 3 y^{'} + 2 y = - 10 Heaviside (t - \frac{π}{4}) \cos (t + \frac{π}{4})$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3968	$y^{''} + y^{'} - 6 y = 30 Heaviside (t - 1) e^{1 - t}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3969	$y^{''} + 4 y^{'} + 5 y = 5 Heaviside (- 3 + t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3970	$y^{''} - 2 y^{'} + 5 y = 2 \sin (t) + Heaviside (t - \frac{π}{2}) (1 + \cos (t))$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✗

3971	$- y + y^{'} = {\begin{array}{cc} 2 & 0 \leq t < 1 \\ - 1 & 1 \leq t \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✗

3972	$- y + y^{'} = {\begin{array}{cc} 2 & 0 \leq t < 1 \\ - 1 & 1 \leq t \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✗

3973	$y + y^{'} = δ (t - 5)$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

3974	$- 2 y + y^{'} = δ (t - 2)$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

3975	$y^{'} + 4 y = 3 δ (t - 1)$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

3976	$y^{'} - 5 y = 2 e^{- t} + δ (- 3 + t)$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✗

3977	$y^{''} - 3 y^{'} + 2 y = δ (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3978	$y^{''} - 4 y = δ (- 3 + t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3979	$y^{''} + 2 y^{'} + 5 y = δ (t - \frac{π}{2})$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3980	$y^{''} - 4 y^{'} + 13 y = δ (t - \frac{π}{4})$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3981	$y^{''} + 4 y^{'} + 3 y = δ (t - 2)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3982	$y^{''} + 6 y^{'} + 13 y = δ (t - \frac{π}{4})$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3983	$y^{''} + 9 y = 15 \sin (2 t) + δ (t - \frac{π}{6})$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3984	$y^{''} + 16 y = 4 \cos (3 t) + δ (t - \frac{π}{3})$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3985	$y^{''} + 2 y^{'} + 5 y = 4 \sin (t) + δ (t - \frac{π}{6})$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

3986	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

3987	$y^{''} + 2 y^{'} x + 4 y = 0$	[_erf]	✓	✓	✓	✓

3988	$y^{''} - 2 y^{'} x - 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓

3989	$y^{''} - x^{2} y^{'} - 2 x y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓

3990	$y^{''} + x y = 0$	[[_Emden, _Fowler]]	✓	✓	✓	✓

3991	$y^{''} + y^{'} x + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

3992	$y^{''} - x^{2} y^{'} - 3 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

3993	$y^{''} + 2 x^{2} y^{'} + 2 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

3994	$(x^{2} - 3) y^{''} - 3 y^{'} x - 5 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓

3995	$(x^{2} + 1) y^{''} + 4 y^{'} x + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓

3996	$(- 4 x^{2} + 1) y^{''} - 20 y^{'} x - 16 y = 0$	[_Gegenbauer]	✓	✓	✓	✓

3997	$(x^{2} - 1) y^{''} - 6 y^{'} x + 12 y = 0$	[_Gegenbauer]	✓	✓	✓	✓

3998	$y^{''} + 2 y^{'} + 4 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

3999	$y^{''} + y^{'} x + (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

4000	$y^{''} - y e^{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2.2.40 Problems 3901 to 4000