2.3.10 Problems 901 to 1000

Table 2.563: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
901	19540	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
902	23436	\begin{align*} y^{\prime \prime \prime \prime }-\ln \left (x +1\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.072
903	24427	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-13 y^{\prime \prime }+38 y^{\prime }-24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
904	24483	\begin{align*} 2 y^{\prime \prime \prime \prime }+11 y^{\prime \prime \prime }-4 y^{\prime \prime }-69 y^{\prime }+34 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
905	24507	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
906	24514	\begin{align*} 4 y^{\prime \prime \prime \prime }-24 y^{\prime \prime \prime }+35 y^{\prime \prime }+6 y^{\prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
907	25150	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
908	25974	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }&={\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.072
909	250	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.073
910	1482	\begin{align*} y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+6 y^{\prime \prime }+30 y^{\prime }-36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
911	2817	\begin{align*} x^{\prime }&=\tan \left (x+y\right ) \\ y^{\prime }&=x+x^{3} \\ \end{align*}	✗	✗	✗	✗	0.073
912	3795	\begin{align*} y^{\prime \prime \prime }+11 y^{\prime \prime }+36 y^{\prime }+26 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
913	6639	\begin{align*} 2 a^{2} y-a^{2} y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
914	6651	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
915	7274	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
916	9295	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
917	9303	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
918	10783	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
919	10790	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
920	10803	\begin{align*} x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
921	11078	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
922	11158	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
923	11232	\begin{align*} x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
924	11239	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
925	12826	\begin{align*} y^{\left (5\right )}+a \,x^{\nu } y^{\prime }+a \nu \,x^{\nu -1} y&=0 \\ \end{align*}	✗	✗	✓	✗	0.073
926	16526	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
927	17549	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
928	20698	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
929	22301	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
930	23263	\begin{align*} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
931	24455	\begin{align*} 4 y^{\left (5\right )}-23 y^{\prime \prime \prime }-33 y^{\prime \prime }-17 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
932	24456	\begin{align*} 4 y^{\left (5\right )}-15 y^{\prime \prime \prime }-5 y^{\prime \prime }+15 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
933	24481	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
934	24482	\begin{align*} y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
935	24505	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-4 y^{\prime \prime }-4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
936	25147	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
937	268	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.074
938	4445	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
939	6752	\begin{align*} -y-2 y^{\prime }+2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
940	8144	\begin{align*} x^{3} y^{\prime \prime }+\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.074
941	8919	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
942	10843	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
943	13125	\begin{align*} {x^{\prime }}^{2}+t x^{\prime }+a y^{\prime }-x&=0 \\ x^{\prime } y^{\prime }+y^{\prime } t -y&=0 \\ \end{align*}	✗	✓	✓	✓	0.074
944	15675	\begin{align*} 36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
945	16465	\begin{align*} y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
946	16527	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
947	16533	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
948	18169	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime }&=3 \\ \end{align*}	✓	✓	✓	✓	0.074
949	18187	\begin{align*} 5 y^{\prime \prime \prime }-7 y^{\prime \prime }&=3 \\ \end{align*}	✓	✓	✓	✓	0.074
950	18311	\begin{align*} x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.074
951	18464	\begin{align*} x^{\prime \prime }+x^{\prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.074
952	19762	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
953	21570	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
954	22120	\begin{align*} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
955	22121	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
956	417	\begin{align*} x^{3} y^{\prime }&=2 y \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.075
957	1476	\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
958	1478	\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*}	✓	✓	✓	✓	0.075
959	4148	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
960	6649	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
961	6734	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
962	6740	\begin{align*} -4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
963	10873	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
964	10893	\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*}	✓	✓	✓	✗	0.075
965	12759	\begin{align*} x^{3} y^{\prime \prime \prime }+\left (a \,x^{2 \nu }+1-\nu ^{2}\right ) x y^{\prime }+\left (b \,x^{3 \nu }+a \left (\nu -1\right ) x^{2 \nu }+\nu ^{2}-1\right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	0.075
966	13126	\begin{align*} x&=t x^{\prime }+f \left (x^{\prime }, y^{\prime }\right ) \\ y&=y^{\prime } t +g \left (x^{\prime }, y^{\prime }\right ) \\ \end{align*}	✗	✓	✓	✓	0.075
967	16972	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
968	18164	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.075
969	18983	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
970	19528	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
971	19826	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
972	20108	\begin{align*} 16 \left (x +1\right )^{4} y^{\prime \prime \prime \prime }+96 \left (x +1\right )^{3} y^{\prime \prime \prime }+104 \left (x +1\right )^{2} y^{\prime \prime }+8 \left (x +1\right ) y^{\prime }+y&=x^{2}+4 x +3 \\ \end{align*}	✗	✓	✓	✗	0.075
973	21199	\begin{align*} x^{\prime \prime \prime }-x^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.075
974	24055	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=2 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -{\frac {1}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.075
975	25152	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+25 y^{\prime }+50 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
976	267	\begin{align*} \left (x +1\right ) y^{\prime \prime }-\left (2+x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.076
977	947	\begin{align*} 3 y^{\prime \prime \prime }+2 y^{\prime \prime }&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.076
978	2112	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
979	2117	\begin{align*} 2 y^{\prime \prime \prime }+3 y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
980	2120	\begin{align*} 27 y^{\prime \prime \prime }+27 y^{\prime \prime }+9 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
981	3832	\begin{align*} x_{1}^{\prime }&=\frac {x_{1}}{t}+t x_{2} \\ x_{2}^{\prime }&=-\frac {x_{1}}{t} \\ \end{align*}	✗	✓	✓	✓	0.076
982	4143	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
983	6630	\begin{align*} -15 y-7 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
984	7048	\begin{align*} y^{\prime \prime \prime \prime }-a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
985	10911	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
986	10912	\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*}	✓	✓	✓	✗	0.076
987	10924	\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*}	✓	✓	✓	✗	0.076
988	11159	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
989	11250	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
990	13054	\begin{align*} y^{\prime } y^{\prime \prime \prime \prime }-y^{\prime \prime } y^{\prime \prime \prime }+{y^{\prime }}^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.076
991	18366	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ y \left (0\right ) &= -1 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.076
992	19828	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
993	20043	\begin{align*} y^{\prime \prime \prime \prime }-m^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
994	20756	\begin{align*} 16 \left (x +1\right )^{4} y^{\prime \prime \prime \prime }+96 \left (x +1\right )^{3} y^{\prime \prime \prime }+104 \left (x +1\right )^{2} y^{\prime \prime }+8 \left (x +1\right ) y^{\prime }+y&=x^{2}+4 x +3 \\ \end{align*}	✗	✓	✓	✗	0.076
995	21508	\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
996	21573	\begin{align*} y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+54 y^{\prime \prime }+108 y^{\prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
997	23434	\begin{align*} y^{\prime \prime \prime }-\sin \left (x \right ) y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.076
998	24458	\begin{align*} y^{\left (5\right )}-5 y^{\prime \prime \prime \prime }+7 y^{\prime \prime \prime }+y^{\prime \prime }-8 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
999	24510	\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-9 y^{\prime \prime \prime }-13 y^{\prime \prime }+8 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
1000	25912	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.076