Problems 901 to 1000

Table 2.21: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	Maple	Mma	Sympy

901	$y^{''} - 4 y = x e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

902	$x^{2} y^{''} + y^{'} x - y = 72 x^{5}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	✓	✓	✓

903	$x^{2} y^{''} - 4 y^{'} x + 6 y = x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

904	$x^{2} y^{''} - 3 y^{'} x + 4 y = x^{4}$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

905	$4 x^{2} y^{''} - 4 y^{'} x + 3 y = 8 x^{4 / 3}$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

906	$x^{2} y^{''} + y^{'} x + y = \ln (x)$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

907	$(x^{2} - 1) y^{''} - 2 y^{'} x + 2 y = x^{2} - 1$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

908	$x^{''} + 9 x = 10 \cos (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

909	$x^{''} + 4 x = 5 \sin (3 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

910	$x^{''} + 100 x = 225 \cos (5 t) + 300 \sin (5 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

911	$x^{''} + 25 x = 90 \cos (4 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

912	$m x^{''} + k x = F_{0} \cos (ω t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

913	$x^{''} + 4 x^{'} + 4 x = 10 \cos (3 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

914	$x^{''} + 3 x^{'} + 5 x = - 4 \cos (5 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

915	$2 x^{''} + 2 x^{'} + x = 3 \sin (10 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

916	$x^{''} + 3 x^{'} + 3 x = 8 \cos (10 t) + 6 \sin (10 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

917	$x^{''} + 4 x^{'} + 5 x = 10 \cos (3 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

918	$x^{''} + 6 x^{'} + 13 x = 10 \sin (5 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

919	$x^{''} + 6 x^{'} + 13 x = 10 \sin (5 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

920	$x^{''} + 2 x^{'} + 26 x = 600 \cos (10 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

921	$x^{''} + 8 x^{'} + 25 x = 200 \cos (t) + 520 \sin (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

922	$[\begin{matrix} x^{'} = - 3 y \\ y^{'} = 3 x \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

923	$[\begin{matrix} x^{'} = 3 x - 2 y \\ y^{'} = 2 x + y \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

924	$[\begin{matrix} x^{'} = 2 x + 4 y + 3 e^{t} \\ y^{'} = 5 x - y - t^{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

925	$[\begin{matrix} x^{'} = y + z \\ y^{'} = x + z \\ z^{'} = x + y \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

926	$[\begin{matrix} x_{1}^{'} = x_{2} \\ x_{2}^{'} = 2 x_{3} \\ x_{3}^{'} = 3 x_{4} \\ x_{4}^{'} = 4 x_{1} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

927	$[\begin{matrix} x_{1}^{'} = x_{2} + x_{3} + 1 \\ x_{2}^{'} = x_{3} + x_{4} + t \\ x_{3}^{'} = x_{1} + x_{4} + t^{2} \\ x_{4}^{'} = x_{1} + x_{2} + t^{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

928	$x^{2} y^{''} + y^{'} x - 9 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓	✓	✓

929	$4 y^{''} - 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

930	$x^{2} y^{''} - x (x + 2) y^{'} + (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

931	$(x + 1) y^{''} - (x + 2) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

932	$(- x^{2} + 1) y^{''} + 2 y^{'} x - 2 y = 0$	[_Gegenbauer]	✓	✓	✓	✗

933	$(- x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[_Gegenbauer]	✓	✓	✓	✗

934	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

935	$5 y^{''''} + 3 y^{'''} = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

936	$y^{''''} - 8 y^{'''} + 16 y^{''} = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

937	$y^{''''} - 3 y^{'''} + 3 y^{''} - y^{'} = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

938	$9 y^{'''} + 12 y^{''} + 4 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

939	$y^{''''} + 3 y^{''} - 4 y = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

940	$y^{''''} - 16 y^{''} + 16 y = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

941	$y^{''''} + 18 y^{''} + 81 y = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

942	$6 y^{''''} + 11 y^{''} + 4 y = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

943	$y^{''''} = 16 y$	[[_high_order, _missing_x]]	✓	✓	✓	✓

944	$y^{'''} + y^{''} - y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

945	$y^{''''} + 2 y^{'''} + 3 y^{''} + 2 y^{'} + y = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

946	$2 y^{'''} - 3 y^{''} - 2 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

947	$3 y^{'''} + 2 y^{''} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

948	$y^{'''} + 10 y^{''} + 25 y^{'} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

949	$y^{'''} + 3 y^{''} - 4 y = 0$	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

950	$2 y^{'''} - y^{''} - 5 y^{'} - 2 y = 0$	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

951	$y^{'''} + 27 y = 0$	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

952	$y^{''''} - y^{'''} + y^{''} - 3 y^{'} - 6 y = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

953	$y^{'''} + 3 y^{''} + 4 y^{'} - 8 y = 0$	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

954	$y^{''''} + y^{'''} - 3 y^{''} - 5 y^{'} - 2 y = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

955	$y^{'''} - 5 y^{''} + 100 y^{'} - 500 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

956	$y^{'''} = y$ i.c.	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

957	$y^{''''} = y^{'''} + y^{''} + y^{'} + 2 y$ i.c.	[[_high_order, _missing_x]]	✓	✓	✓	✓

958	$x^{3} y^{'''} + 6 x^{2} y^{''} + 4 y^{'} x = 0$	[[_3rd_order, _missing_y]]	✓	✓	✓	✓

959	$x^{3} y^{'''} - x^{2} y^{''} + y^{'} x = 0$	[[_3rd_order, _missing_y]]	✓	✓	✓	✓

960	$x^{3} y^{'''} + 3 x^{2} y^{''} + y^{'} x = 0$	[[_3rd_order, _missing_y]]	✓	✓	✓	✓

961	$x^{3} y^{'''} - 3 x^{2} y^{''} + y^{'} x = 0$	[[_3rd_order, _missing_y]]	✓	✓	✓	✓

962	$x^{3} y^{'''} + 6 x^{2} y^{''} + 7 y^{'} x + y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓

963	$[\begin{matrix} x_{1}^{'} = 6 x_{1} \\ x_{2}^{'} = - 3 x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

964	$[\begin{matrix} x_{1}^{'} = - 3 x_{1} + 2 x_{2} \\ x_{2}^{'} = - 3 x_{1} + 4 x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

965	$[\begin{matrix} x_{1}^{'} = x_{1} + 2 x_{2} \\ x_{2}^{'} = 2 x_{1} + x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

966	$[\begin{matrix} x_{1}^{'} = 2 x_{1} + 3 x_{2} \\ x_{2}^{'} = 2 x_{1} + x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

967	$[\begin{matrix} x_{1}^{'} = 3 x_{1} + 4 x_{2} \\ x_{2}^{'} = 3 x_{1} + 2 x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	✓	✓	✓

968	$[\begin{matrix} x_{1}^{'} = 4 x_{1} + x_{2} \\ x_{2}^{'} = 6 x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

969	$[\begin{matrix} x_{1}^{'} = 6 x_{1} - 7 x_{2} \\ x_{2}^{'} = x_{1} - 2 x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

970	$[\begin{matrix} x_{1}^{'} = 9 x_{1} + 5 x_{2} \\ x_{2}^{'} = - 6 x_{1} - 2 x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	✓	✓	✓

971	$[\begin{matrix} x_{1}^{'} = - 3 x_{1} + 4 x_{2} \\ x_{2}^{'} = 6 x_{1} - 5 x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

972	$[\begin{matrix} x_{1}^{'} = x_{1} - 5 x_{2} \\ x_{2}^{'} = x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

973	$[\begin{matrix} x_{1}^{'} = 2 x_{1} - 5 x_{2} \\ x_{2}^{'} = 4 x_{1} - 2 x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	✓	✓	✓

974	$[\begin{matrix} x_{1}^{'} = - 3 x_{1} - 2 x_{2} \\ x_{2}^{'} = 9 x_{1} + 3 x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

975	$[\begin{matrix} x_{1}^{'} = x_{1} - 2 x_{2} \\ x_{2}^{'} = 2 x_{1} + x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	✓	✓	✓

976	$[\begin{matrix} x_{1}^{'} = x_{1} - 5 x_{2} \\ x_{2}^{'} = x_{1} + 3 x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

977	$[\begin{matrix} x_{1}^{'} = 5 x_{1} - 9 x_{2} \\ x_{2}^{'} = 2 x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

978	$[\begin{matrix} x_{1}^{'} = 3 x_{1} - 4 x_{2} \\ x_{2}^{'} = 4 x_{1} + 3 x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

979	$[\begin{matrix} x_{1}^{'} = 7 x_{1} - 5 x_{2} \\ x_{2}^{'} = 4 x_{1} + 3 x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

980	$[\begin{matrix} x_{1}^{'} = - 50 x_{1} + 20 x_{2} \\ x_{2}^{'} = 100 x_{1} - 60 x_{2} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

981	$[\begin{matrix} x_{1}^{'} = 4 x_{1} + x_{2} + 4 x_{3} \\ x_{2}^{'} = x_{1} + 7 x_{2} + x_{3} \\ x_{3}^{'} = 4 x_{1} + x_{2} + 4 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

982	$[\begin{matrix} x_{1}^{'} = x_{1} + 2 x_{2} + 2 x_{3} \\ x_{2}^{'} = 2 x_{1} + 7 x_{2} + x_{3} \\ x_{3}^{'} = 2 x_{1} + x_{2} + 7 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

983	$[\begin{matrix} x_{1}^{'} = 4 x_{1} + x_{2} + x_{3} \\ x_{2}^{'} = x_{1} + 4 x_{2} + x_{3} \\ x_{3}^{'} = x_{1} + x_{2} + 4 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

984	$[\begin{matrix} x_{1}^{'} = 5 x_{1} + x_{2} + 3 x_{3} \\ x_{2}^{'} = x_{1} + 7 x_{2} + x_{3} \\ x_{3}^{'} = 3 x_{1} + x_{2} + 5 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

985	$[\begin{matrix} x_{1}^{'} = 5 x_{1} - 6 x_{3} \\ x_{2}^{'} = 2 x_{1} - x_{2} - 2 x_{3} \\ x_{3}^{'} = 4 x_{1} - 2 x_{2} - 4 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

986	$[\begin{matrix} x_{1}^{'} = 3 x_{1} + 2 x_{2} + 2 x_{3} \\ x_{2}^{'} = - 5 x_{1} - 4 x_{2} - 2 x_{3} \\ x_{3}^{'} = 5 x_{1} + 5 x_{2} + 3 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

987	$[\begin{matrix} x_{1}^{'} = 3 x_{1} + x_{2} + x_{3} \\ x_{2}^{'} = - 5 x_{1} - 3 x_{2} - x_{3} \\ x_{3}^{'} = 5 x_{1} + 5 x_{2} + 3 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

988	$[\begin{matrix} x_{1}^{'} = 2 x_{1} + x_{2} - x_{3} \\ x_{2}^{'} = - 4 x_{1} - 3 x_{2} - x_{3} \\ x_{3}^{'} = 4 x_{1} + 4 x_{2} + 2 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

989	$[\begin{matrix} x_{1}^{'} = 5 x_{1} + 5 x_{2} + 2 x_{3} \\ x_{2}^{'} = - 6 x_{1} - 6 x_{2} - 5 x_{3} \\ x_{3}^{'} = 6 x_{1} + 6 x_{2} + 5 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

990	$[\begin{matrix} x_{1}^{'} = 3 x_{1} + x_{3} \\ x_{2}^{'} = 9 x_{1} - x_{2} + 2 x_{3} \\ x_{3}^{'} = - 9 x_{1} + 4 x_{2} - x_{3} \end{matrix}]$ i.c.	system_of_ODEs	✓	✓	✓	✓

991	$[\begin{matrix} x_{1}^{'} = x_{1} \\ x_{2}^{'} = 2 x_{1} + 2 x_{2} \\ x_{3}^{'} = 3 x_{2} + 3 x_{3} \\ x_{4}^{'} = 4 x_{3} + 4 x_{4} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

992	$[\begin{matrix} x_{1}^{'} = - 2 x_{1} + 9 x_{4} \\ x_{2}^{'} = 4 x_{1} + 2 x_{2} - 10 x_{4} \\ x_{3}^{'} = - x_{3} + 8 x_{4} \\ x_{4}^{'} = x_{4} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

993	$[\begin{matrix} x_{1}^{'} = 2 x_{1} \\ x_{2}^{'} = - 21 x_{1} - 5 x_{2} - 27 x_{3} - 9 x_{4} \\ x_{3}^{'} = 5 x_{3} \\ x_{4}^{'} = - 21 x_{3} - 2 x_{4} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

994	$[\begin{matrix} x_{1}^{'} = 4 x_{1} + x_{2} + x_{3} + 7 x_{4} \\ x_{2}^{'} = x_{1} + 4 x_{2} + 10 x_{3} + x_{4} \\ x_{3}^{'} = x_{1} + 10 x_{2} + 4 x_{3} + x_{4} \\ x_{4}^{'} = 7 x_{1} + x_{2} + x_{3} + 4 x_{4} \end{matrix}]$ i.c.	system_of_ODEs	✓	✓	✓	✓

995	$[\begin{matrix} x_{1}^{'} = - 40 x_{1} - 12 x_{2} + 54 x_{3} \\ x_{2}^{'} = 35 x_{1} + 13 x_{2} - 46 x_{3} \\ x_{3}^{'} = - 25 x_{1} - 7 x_{2} + 34 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

996	$[\begin{matrix} x_{1}^{'} = - 20 x_{1} + 11 x_{2} + 13 x_{3} \\ x_{2}^{'} = 12 x_{1} - x_{2} - 7 x_{3} \\ x_{3}^{'} = - 48 x_{1} + 21 x_{2} + 31 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

997	$[\begin{matrix} x_{1}^{'} = 147 x_{1} + 23 x_{2} - 202 x_{3} \\ x_{2}^{'} = - 90 x_{1} - 9 x_{2} + 129 x_{3} \\ x_{3}^{'} = 90 x_{1} + 15 x_{2} - 123 x_{3} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

998	$[\begin{matrix} x_{1}^{'} = 9 x_{1} - 7 x_{2} - 5 x_{3} \\ x_{2}^{'} = - 12 x_{1} + 7 x_{2} + 11 x_{3} + 9 x_{4} \\ x_{3}^{'} = 24 x_{1} - 17 x_{2} - 19 x_{3} - 9 x_{4} \\ x_{4}^{'} = - 18 x_{1} + 13 x_{2} + 17 x_{3} + 9 x_{4} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

999	$[\begin{matrix} x_{1}^{'} = 13 x_{1} - 42 x_{2} + 106 x_{3} + 139 x_{4} \\ x_{2}^{'} = 2 x_{1} - 16 x_{2} + 52 x_{3} + 70 x_{4} \\ x_{3}^{'} = x_{1} + 6 x_{2} - 20 x_{3} - 31 x_{4} \\ x_{4}^{'} = - x_{1} - 6 x_{2} + 22 x_{3} + 33 x_{4} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

1000	$[\begin{matrix} x_{1}^{'} = 23 x_{1} - 18 x_{2} - 16 x_{3} \\ x_{2}^{'} = - 8 x_{1} + 6 x_{2} + 7 x_{3} + 9 x_{4} \\ x_{3}^{'} = 34 x_{1} - 27 x_{2} - 26 x_{3} - 9 x_{4} \\ x_{4}^{'} = - 26 x_{1} + 21 x_{2} + 25 x_{3} + 12 x_{4} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

2.2.10 Problems 901 to 1000