2.3.11 Problems 1001 to 1100

Table 2.565: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1001	249	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.077
1002	266	\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.077
1003	1059	\begin{align*} x^{3} y^{\prime }&=2 y \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.077
1004	2114	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.077
1005	2116	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+16 y^{\prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.077
1006	6653	\begin{align*} -4 y+6 y^{\prime }-4 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.077
1007	6742	\begin{align*} 27 y-12 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.077
1008	6748	\begin{align*} -2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.077
1009	6761	\begin{align*} -3 y^{\prime }+11 y^{\prime \prime }-12 y^{\prime \prime \prime }+4 y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.077
1010	7989	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&=5 \\ \end{align*}	✓	✓	✓	✓	0.077
1011	10056	\begin{align*} a y y^{\prime \prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	0.077
1012	10917	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.077
1013	11278	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.077
1014	15676	\begin{align*} y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.077
1015	16487	\begin{align*} y^{\prime \prime \prime \prime }-10 y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.077
1016	19182	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.077
1017	19529	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.077
1018	20193	\begin{align*} y^{\prime \prime } x -\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.077
1019	21506	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.077
1020	22114	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+2 y^{\prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.077
1021	22125	\begin{align*} -y-2 y^{\prime }+2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.077
1022	24453	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-6 y^{\prime \prime }-28 y^{\prime }-24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.077
1023	307	\begin{align*} y^{\prime \prime \prime \prime }&=y^{\prime \prime \prime } \\ y \left (0\right ) &= 18 \\ y^{\prime }\left (0\right ) &= 12 \\ y^{\prime \prime }\left (0\right ) &= 13 \\ y^{\prime \prime \prime }\left (0\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	0.078
1024	6668	\begin{align*} -3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.078
1025	6739	\begin{align*} -8 y-2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.078
1026	6757	\begin{align*} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.078
1027	7182	\begin{align*} x^{3} y^{\prime \prime }-\left (2 x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.078
1028	8829	\begin{align*} a^{2} y^{\prime \prime \prime \prime }&=y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.078
1029	8918	\begin{align*} y^{\prime \prime \prime }-i y^{\prime \prime }+4 y^{\prime }-4 i y&=0 \\ \end{align*}	✓	✓	✓	✓	0.078
1030	8922	\begin{align*} y^{\prime \prime \prime }-3 i y^{\prime \prime }-3 y^{\prime }+i y&=0 \\ \end{align*}	✓	✓	✓	✓	0.078
1031	10821	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.078
1032	10906	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.078
1033	10920	\begin{align*} x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.078
1034	16528	\begin{align*} y^{\prime \prime \prime \prime }-34 y^{\prime \prime }+225 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.078
1035	18163	\begin{align*} y^{\prime \prime \prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.078
1036	18170	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }&=4 \\ \end{align*}	✓	✓	✓	✓	0.078
1037	19273	\begin{align*} 2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.078
1038	25143	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.078
1039	25154	\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+18 y^{\prime \prime }-27 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.078
1040	25536	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.078
1041	948	\begin{align*} y^{\prime \prime \prime }+10 y^{\prime \prime }+25 y^{\prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.079
1042	1473	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1043	2113	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+7 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1044	2118	\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+9 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1045	2119	\begin{align*} 4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1046	4443	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1047	6656	\begin{align*} -a^{3} y+3 a^{2} y^{\prime }-3 a y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1048	8931	\begin{align*} y^{\prime \prime \prime }-i y^{\prime \prime }+y^{\prime }-i y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1049	9291	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1050	10801	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+4 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1051	16400	\begin{align*} y^{\prime \prime \prime \prime }&=-2 y^{\prime \prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.079
1052	16530	\begin{align*} y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1053	19827	\begin{align*} 2 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1054	20770	\begin{align*} y^{\prime \prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.079
1055	22123	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1056	265	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
1057	312	\begin{align*} y^{\prime \prime \prime }&=y \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.080
1058	4444	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+9 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
1059	9298	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
1060	10851	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.080
1061	10900	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (3+2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.080
1062	13114	\begin{align*} x_{1}^{\prime }&=a x_{2}+b x_{3} \cos \left (c t \right )+b x_{4} \sin \left (c t \right ) \\ x_{2}^{\prime }&=-a x_{1}+b x_{3} \sin \left (c t \right )-b x_{4} \cos \left (c t \right ) \\ x_{3}^{\prime }&=-b x_{1} \cos \left (c t \right )-b x_{2} \sin \left (c t \right )+a x_{4} \\ x_{4}^{\prime }&=-b x_{1} \sin \left (c t \right )+b x_{2} \cos \left (c t \right )-a x_{3} \\ \end{align*}	✗	✓	✓	✗	0.080
1063	15099	\begin{align*} x^{3} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.080
1064	15673	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
1065	16544	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
1066	16549	\begin{align*} 4 y^{\prime \prime \prime \prime }+15 y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
1067	16715	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
1068	18405	\begin{align*} x_{1}^{\prime }&=\frac {x_{1}^{2}}{x_{2}} \\ x_{2}^{\prime }&=x_{2}-x_{1} \\ \end{align*}	✗	✓	✓	✓	0.080
1069	21878	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+7 y^{\prime \prime }+6 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
1070	22089	\begin{align*} y^{\prime \prime \prime }+\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime }+y&=5 \sin \left (x \right ) \\ \end{align*}	✗	✗	✗	✗	0.080
1071	23265	\begin{align*} y^{\left (5\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
1072	25923	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.080
1073	940	\begin{align*} y^{\prime \prime \prime \prime }-16 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.081
1074	946	\begin{align*} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }-2 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.081
1075	6755	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.081
1076	7836	\begin{align*} x^{3} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.081
1077	9296	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.081
1078	9392	\begin{align*} x^{4} y^{\prime \prime }+\sin \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.081
1079	10854	\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.081
1080	11216	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.081
1081	11271	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.081
1082	15297	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.081
1083	18188	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }&=-6 \\ \end{align*}	✓	✓	✓	✓	0.081
1084	18970	\begin{align*} \left (x -4\right ) y^{\prime \prime \prime \prime }+\left (x +1\right ) y^{\prime \prime }+\tan \left (x \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	0.081
1085	19181	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.081
1086	21879	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+3 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.081
1087	22085	\begin{align*} y^{\prime \prime \prime \prime }+x^{2} y^{\prime \prime \prime }+y^{\prime \prime } x -{\mathrm e}^{x} y^{\prime }+2 y&=x^{2}+x +1 \\ \end{align*}	✗	✗	✗	✗	0.081
1088	22124	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.081
1089	24513	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+2 y^{\prime \prime }-8 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.081
1090	2115	\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
1091	2124	\begin{align*} 16 y^{\prime \prime \prime \prime }-72 y^{\prime \prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
1092	6733	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
1093	6753	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
1094	6786	\begin{align*} a y+y^{\left (6\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
1095	7056	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
1096	7991	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.082
1097	10739	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
1098	10819	\begin{align*} u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u&=0 \\ \end{align*}	✓	✓	✓	✗	0.082
1099	10919	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
1100	12783	\begin{align*} y^{\prime \prime \prime \prime }+4 y-f&=0 \\ \end{align*}	✓	✓	✓	✓	0.082