2.3.11 Problems 1001 to 1100

Table 2.553: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1001	6602	\begin{align*} \sin \left (x \right )+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.078
1002	14591	\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.078
1003	14594	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.078
1004	15421	\begin{align*} -a^{3} y+3 a^{2} y^{\prime }-3 a y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.078
1005	15696	\begin{align*} 2 y+y^{\prime }&=4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.078
1006	16536	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+2 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.078
1007	19453	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.078
1008	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*}	✓	✓	✓	✓	0.078
1009	268	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.079
1010	311	\begin{align*} y^{\prime \prime }&=\left (-2+2 i \sqrt {3}\right ) y \\ \end{align*}	✓	✓	✓	✓	0.079
1011	2134	\begin{align*} 2 y^{\prime \prime \prime }-11 y^{\prime \prime }+12 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= 13 \\ \end{align*}	✓	✓	✓	✓	0.079
1012	3067	\begin{align*} 2 y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1013	3096	\begin{align*} 4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1014	7060	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1015	10961	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.079
1016	14595	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+15 y^{\prime \prime }+20 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1017	16715	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1018	19444	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1019	19448	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1020	22674	\begin{align*} y^{\left (5\right )}-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
1021	3105	\begin{align*} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+10 y^{\prime }-15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
1022	3700	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
1023	3704	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
1024	6638	\begin{align*} 10 y+3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
1025	7242	\begin{align*} x^{\prime }&=\frac {3 y^{{2}/{3}}-x}{3 y} \\ \end{align*}	✓	✓	✓	✓	0.080
1026	7968	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
1027	15678	\begin{align*} y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
1028	20377	\begin{align*} y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
1029	23232	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.080
1030	1196	\begin{align*} 2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.081
1031	7073	\begin{align*} 3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.081
1032	7983	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+9 y^{\prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.081
1033	15691	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ y^{\prime \prime \prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.081
1034	18186	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.081
1035	19273	\begin{align*} 2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.081
1036	21199	\begin{align*} x^{\prime \prime \prime }-x^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.081
1037	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*}	✓	✓	✓	✓	0.082
1038	930	\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.082
1039	956	\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*}	✓	✓	✓	✓	0.082
1040	2711	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
1041	2815	\begin{align*} x^{\prime }&=x^{2}+y^{2}-1 \\ y^{\prime }&=2 x y \\ \end{align*}	✗	✓	✓	✗	0.082
1042	3108	\begin{align*} 4 y^{\prime \prime \prime }+12 y^{\prime \prime }-3 y^{\prime }+14 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
1043	6780	\begin{align*} -b^{4} x^{\frac {2}{a}} y+16 \left (-2 a +1\right ) \left (1-a \right ) a^{2} x^{2} y^{\prime \prime }-32 \left (-2 a +1\right ) a^{2} x^{3} y^{\prime \prime \prime }+16 a^{4} x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.082
1044	7232	\begin{align*} 2 y^{\prime } x +y&=2 x^{{5}/{2}} \\ \end{align*}	✓	✓	✓	✓	0.082
1045	7618	\begin{align*} y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+15 y^{\prime \prime }+4 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
1046	8923	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.082
1047	10960	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.082
1048	12797	\begin{align*} 2 y^{\prime \prime }+4 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
1049	18166	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=3 \\ \end{align*}	✓	✓	✓	✓	0.082
1050	18622	\begin{align*} 5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
1051	21179	\begin{align*} x^{\prime \prime \prime }-3 x^{\prime \prime }+4 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
1052	22494	\begin{align*} x y^{\prime \prime \prime }+y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.082
1053	270	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.083
1054	1680	\begin{align*} 6 y^{2} x^{2}+4 y y^{\prime } x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.083
1055	2139	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-8 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -2 \\ y^{\prime \prime }\left (0\right ) &= 6 \\ y^{\prime \prime \prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.083
1056	3106	\begin{align*} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+11 y^{\prime }-40 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.083
1057	4008	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x \left (x -3\right )}-\frac {y}{x^{3} \left (x +3\right )}&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.083
1058	4142	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.083
1059	6665	\begin{align*} 2 y \left (2 f \left (x \right ) g \left (x \right )+g^{\prime }\left (x \right )\right )+\left (4 g \left (x \right )+f^{\prime }\left (x \right )+2 {f^{\prime }\left (x \right )}^{2}\right ) y^{\prime }+3 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.083
1060	7984	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.083
1061	9296	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.083
1062	9304	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.083
1063	11073	\begin{align*} y^{\prime \prime }-4 y^{\prime } t +\left (4 t^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.083
1064	14774	\begin{align*} x^{\prime }+y^{\prime }-x-2 y&=2 \,{\mathrm e}^{t} \\ x^{\prime }+y^{\prime }-3 x-4 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✗	0.083
1065	15701	\begin{align*} y^{\prime }&={\mathrm e}^{x} \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.083
1066	16720	\begin{align*} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.083
1067	20071	\begin{align*} y^{\prime \prime \prime }-13 y^{\prime }+12 y&=x \\ \end{align*}	✓	✓	✓	✓	0.083
1068	22240	\begin{align*} y^{\prime }+2 y&=2 \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.083
1069	265	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.084
1070	3081	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-7 y^{\prime \prime }-8 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.084
1071	9298	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.084
1072	10796	\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.084
1073	11263	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.084
1074	14347	\begin{align*} x^{\prime \prime \prime }-x^{\prime }-8 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.084
1075	15694	\begin{align*} y^{\prime }-y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.084
1076	19451	\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.084
1077	21177	\begin{align*} x^{\prime \prime \prime }+5 x^{\prime \prime }-6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.084
1078	21415	\begin{align*} y^{2}+y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.084
1079	24445	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.084
1080	2144	\begin{align*} y^{\left (6\right )}-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.085
1081	3075	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-7 y^{\prime \prime }-y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.085
1082	3094	\begin{align*} 4 y^{\left (5\right )}-3 y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.085
1083	6756	\begin{align*} -y^{\prime }+y^{\prime \prime }-3 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.085
1084	9301	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.085
1085	10816	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.085
1086	18165	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.085
1087	19447	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.085
1088	23291	\begin{align*} \left (x^{3}-1\right ) y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y x&=0 \\ y \left (-1\right ) &= 0 \\ y^{\prime }\left (-1\right ) &= 2 \\ y^{\prime \prime }\left (-1\right ) &= 2 \\ \end{align*}	✗	✗	✗	✗	0.085
1089	24441	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.085
1090	931	\begin{align*} \left (x +1\right ) y^{\prime \prime }-\left (2+x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.086
1091	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*}	✓	✓	✓	✓	0.086
1092	2137	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+7 y^{\prime \prime }+6 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= -8 \\ y^{\prime \prime }\left (0\right ) &= -14 \\ y^{\prime \prime \prime }\left (0\right ) &= -62 \\ \end{align*}	✓	✓	✓	✓	0.086
1093	3070	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.086
1094	3085	\begin{align*} -4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.086
1095	3092	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.086
1096	7190	\begin{align*} x^{3} y^{\prime \prime }+y&=x^{{3}/{2}} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.086
1097	9299	\begin{align*} y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.086
1098	10913	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.086
1099	11178	\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.086
1100	12818	\begin{align*} y^{\prime \prime \prime \prime } \sin \left (x \right )^{4}+2 y^{\prime \prime \prime } \sin \left (x \right )^{3} \cos \left (x \right )+y^{\prime \prime } \sin \left (x \right )^{2} \left (\sin \left (x \right )^{2}-3\right )+y^{\prime } \sin \left (x \right ) \cos \left (x \right ) \left (2 \sin \left (x \right )^{2}+3\right )+\left (a^{4} \sin \left (x \right )^{4}-3\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.086