2.3.9 Problems 801 to 900

Table 2.591: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
801	10798	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
802	10894	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.092
803	10960	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.092
804	11078	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
805	11102	\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
806	11230	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+4 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
807	11301	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
808	12722	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime } x +2 \left (4 x^{2}+2 a -1\right ) y^{\prime }-8 a x y&=0 \\ \end{align*}	✗	✓	✓	✗	0.092
809	12734	\begin{align*} 2 x y^{\prime \prime \prime }-4 \left (x +\nu -1\right ) y^{\prime \prime }+\left (2 x +6 \nu -5\right ) y^{\prime }+\left (1-2 \nu \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.092
810	12768	\begin{align*} \left (x +3\right ) x^{2} y^{\prime \prime \prime }-3 x \left (2+x \right ) y^{\prime \prime }+6 \left (x +1\right ) y^{\prime }-6 y&=0 \\ \end{align*}	✗	✓	✓	✗	0.092
811	12776	\begin{align*} \left (x -a \right )^{3} \left (-b +x \right )^{3} y^{\prime \prime \prime }-c y&=0 \\ \end{align*}	✗	✓	✓	✗	0.092
812	13045	\begin{align*} x^{2} y^{\prime \prime \prime }+y^{\prime \prime } x +\left (2 y x -1\right ) y^{\prime }+y^{2}-f \left (x \right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.092
813	16972	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
814	17540	\begin{align*} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
815	18145	\begin{align*} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
816	18707	\begin{align*} x^{\prime }&=3 x-x^{2} \\ y^{\prime }&=2 x y-3 y+2 \\ \end{align*}	✗	✓	✓	✓	0.092
817	18713	\begin{align*} x^{\prime }&=\left (2+x\right ) \left (-x+y\right ) \\ y^{\prime }&=y-x^{2}-y^{2} \\ \end{align*}	✗	✗	✗	✗	0.092
818	18715	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=x-\frac {x^{3}}{5}-\frac {y}{5} \\ \end{align*}	✗	✗	✗	✗	0.092
819	18982	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }-4 y^{\prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
820	19224	\begin{align*} t x^{\prime }-x-3 y&=t \\ y^{\prime } t -x+y&=0 \\ \end{align*}	✗	✓	✓	✓	0.092
821	19831	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
822	20155	\begin{align*} y^{\prime \prime \prime \prime }-a^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
823	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*}	✓	✓	✓	✓	0.092
824	22123	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
825	24418	\begin{align*} 4 y^{\prime \prime \prime }-13 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
826	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*}	✓	✓	✓	✓	0.092
827	25151	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-25 y^{\prime }+50 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
828	25520	\begin{align*} y^{\prime \prime \prime \prime }&=16 y \\ \end{align*}	✓	✓	✓	✓	0.092
829	25926	\begin{align*} y^{\left (6\right )}+18 y^{\prime \prime \prime \prime }+81 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
830	26105	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
831	26497	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
832	27622	\begin{align*} y^{\left (6\right )}+64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
833	472	\begin{align*} x^{3} \left (1-x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.093
834	951	\begin{align*} y^{\prime \prime \prime }+27 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.093
835	2577	\begin{align*} \left (2 t +1\right ) y^{\prime \prime }-4 \left (1+t \right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.093
836	10653	\begin{align*} y^{\prime \prime }-4 y^{\prime } t +\left (4 t^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.093
837	11231	\begin{align*} y^{\prime \prime } x +\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.093
838	12717	\begin{align*} y f^{\prime }\left (x \right )+2 f \left (x \right ) y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.093
839	12751	\begin{align*} x^{2} y^{\prime \prime \prime }-\left (x +\nu \right ) x y^{\prime \prime }+\nu \left (2 x +1\right ) y^{\prime }-\nu \left (x +1\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	0.093
840	13113	\begin{align*} a t x^{\prime }&=b c \left (y-z\right ) \\ b t y^{\prime }&=c a \left (z-x\right ) \\ c t z^{\prime }&=a b \left (x-y\right ) \\ \end{align*}	✗	✓	✓	✓	0.093
841	14588	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.093
842	20676	\begin{align*} t x^{\prime }+y&=0 \\ y^{\prime } t +x&=0 \\ \end{align*}	✗	✓	✓	✓	0.093
843	21570	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.093
844	22314	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.093
845	22633	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.093
846	24516	\begin{align*} y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+11 y^{\prime \prime }+5 y^{\prime }-14 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.093
847	25929	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.093
848	2132	\begin{align*} 3 y^{\prime \prime \prime }-y^{\prime \prime }-7 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= {\frac {14}{5}} \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	0.094
849	10492	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.094
850	10845	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.094
851	10850	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.094
852	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*}	✓	✓	✓	✗	0.094
853	12758	\begin{align*} x^{3} y^{\prime \prime \prime }+\left (4 x^{3}+\left (-4 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (4 \nu ^{2}-1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.094
854	13115	\begin{align*} x^{\prime }&=-x \left (x+y\right ) \\ y^{\prime }&=y \left (x+y\right ) \\ \end{align*}	✗	✓	✓	✗	0.094
855	14579	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.094
856	20041	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.094
857	21879	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+3 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.094
858	936	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+16 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
859	3103	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-6 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
860	4454	\begin{align*} y^{\left (6\right )}-64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
861	6754	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
862	10245	\begin{align*} y^{\prime }&=\frac {1}{x} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.095
863	10489	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
864	10821	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
865	10842	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
866	10877	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
867	10901	\begin{align*} y^{\prime \prime } x +\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.095
868	10916	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
869	10961	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.095
870	12726	\begin{align*} y^{\prime \prime \prime }+f \left (x \right ) \left (x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y\right )&=0 \\ \end{align*}	✗	✓	✓	✗	0.095
871	12750	\begin{align*} x^{2} y^{\prime \prime \prime }-\left (x^{2}-2 x \right ) y^{\prime \prime }-\left (x^{2}+\nu ^{2}-\frac {1}{4}\right ) y^{\prime }+\left (x^{2}-2 x +\nu ^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.095
872	12762	\begin{align*} -2 \left (x^{2}+4\right ) y+x \left (x^{2}+8\right ) y^{\prime }-4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.095
873	12796	\begin{align*} x^{2} y^{\prime \prime \prime \prime }+2 x y^{\prime \prime \prime }+a y-b \,x^{2}&=0 \\ \end{align*}	✗	✓	✗	✗	0.095
874	12799	\begin{align*} x^{2} y^{\prime \prime \prime \prime }+6 x y^{\prime \prime \prime }+6 y^{\prime \prime }-\lambda ^{2} y&=0 \\ \end{align*}	✗	✓	✓	✗	0.095
875	12801	\begin{align*} x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime }-\lambda ^{2} y&=0 \\ \end{align*}	✗	✓	✓	✗	0.095
876	13046	\begin{align*} x^{2} y^{\prime \prime \prime }+x \left (-1+y\right ) y^{\prime \prime }+x {y^{\prime }}^{2}+\left (1-y\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✗	✗	0.095
877	13049	\begin{align*} 40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.095
878	13116	\begin{align*} x^{\prime }&=\left (a y+b \right ) x \\ y^{\prime }&=\left (c x+d \right ) y \\ \end{align*}	✗	✓	✓	✗	0.095
879	13120	\begin{align*} x^{\prime }&=-x \,y^{2}+x+y \\ y^{\prime }&=y \,x^{2}-x-y \\ \end{align*}	✗	✗	✗	✗	0.095
880	14586	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
881	18711	\begin{align*} x^{\prime }&=-\left (x-y\right ) \left (1-x-y\right ) \\ y^{\prime }&=x \left (2+y\right ) \\ \end{align*}	✗	✗	✗	✗	0.095
882	20333	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
883	21193	\begin{align*} x^{\left (5\right )}+x^{\prime \prime \prime \prime }-x^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
884	22125	\begin{align*} -y-2 y^{\prime }+2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
885	22494	\begin{align*} x y^{\prime \prime \prime }+y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.095
886	24449	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
887	24463	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+2 y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= -5 \\ y^{\prime \prime \prime }\left (0\right ) &= 9 \\ \end{align*}	✓	✓	✓	✓	0.095
888	937	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.096
889	939	\begin{align*} -4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.096
890	2129	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 14 \\ y^{\prime \prime }\left (0\right ) &= -40 \\ \end{align*}	✓	✓	✓	✓	0.096
891	2680	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{t} t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.096
892	7983	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+9 y^{\prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.096
893	10783	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.096
894	10904	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.096
895	11232	\begin{align*} x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.096
896	11246	\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.096
897	12752	\begin{align*} x^{2} y^{\prime \prime \prime }-2 \left (x^{2}-x \right ) y^{\prime \prime }+\left (x^{2}-2 x +\frac {1}{4}-\nu ^{2}\right ) y^{\prime }+\left (\nu ^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.096
898	13112	\begin{align*} t x^{\prime }&=2 x-t \\ t^{3} y^{\prime }&=-x+t^{2} y+t \\ t^{4} z^{\prime }&=-x-t^{2} y+t^{3} z+t \\ \end{align*}	✗	✓	✓	✗	0.096
899	14356	\begin{align*} x^{\prime \prime }-x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.096
900	18165	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.096