2.3.8 Problems 701 to 800

Table 2.589: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
701	12809	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-\rho ^{2}-\sigma ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-\rho ^{2}-\sigma ^{2}+1\right ) x \right ) y^{\prime }+\left (\rho ^{2} \sigma ^{2}+8 x^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.069
702	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*}	✓	✓	✓	✓	0.069
703	15755	\begin{align*} y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\ y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \\ \end{align*}	✗	✓	✓	✓	0.069
704	18426	\begin{align*} {\mathrm e}^{t} x^{\prime }&=\frac {1}{y} \\ {\mathrm e}^{t} y^{\prime }&=\frac {1}{x} \\ \end{align*}	✗	✓	✓	✗	0.069
705	19533	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
706	19830	\begin{align*} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
707	24414	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-15 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
708	24423	\begin{align*} 4 y^{\prime \prime \prime }-13 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
709	25920	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
710	26493	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
711	304	\begin{align*} 3 y^{\prime \prime \prime }-2 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.070
712	1473	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.070
713	2125	\begin{align*} 6 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+7 y^{\prime \prime }+5 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.070
714	14346	\begin{align*} x^{\prime \prime \prime }+x^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.070
715	16528	\begin{align*} y^{\prime \prime \prime \prime }-34 y^{\prime \prime }+225 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.070
716	18142	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.070
717	19538	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.070
718	23312	\begin{align*} 2 y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.070
719	24416	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.070
720	24417	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.070
721	25925	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.070
722	26490	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+10 y^{\prime \prime }+12 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.070
723	941	\begin{align*} y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.071
724	2712	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.071
725	3795	\begin{align*} y^{\prime \prime \prime }+11 y^{\prime \prime }+36 y^{\prime }+26 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.071
726	7980	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+12 y^{\prime \prime }-8 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.071
727	12810	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-2 \mu ^{2}-2 \nu ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-2 \mu ^{2}-2 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (8 x^{2}+\left (\mu ^{2}-\nu ^{2}\right )^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.071
728	16530	\begin{align*} y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.071
729	18143	\begin{align*} y^{\left (5\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.071
730	24415	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-8 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.071
731	24418	\begin{align*} 4 y^{\prime \prime \prime }-13 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.071
732	24442	\begin{align*} 9 y^{\prime \prime \prime }+6 y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.071
733	24517	\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+7 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.071
734	25145	\begin{align*} y^{\left (5\right )}+t y^{\prime \prime }-3 y&=0 \\ \end{align*}	✗	✗	✗	✗	0.071
735	26498	\begin{align*} y^{\left (10\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.071
736	27609	\begin{align*} y^{\prime \prime \prime }&=3 y y^{\prime } \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= {\frac {9}{2}} \\ \end{align*}	✗	✗	✗	✗	0.071
737	287	\begin{align*} 6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
738	942	\begin{align*} 6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
739	945	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
740	4146	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
741	8916	\begin{align*} y^{\prime \prime \prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
742	16400	\begin{align*} y^{\prime \prime \prime \prime }&=-2 y^{\prime \prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.072
743	16487	\begin{align*} y^{\prime \prime \prime \prime }-10 y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
744	16534	\begin{align*} y^{\prime \prime \prime }-8 y^{\prime \prime }+37 y^{\prime }-50 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
745	16535	\begin{align*} y^{\prime \prime \prime }-9 y^{\prime \prime }+31 y^{\prime }-39 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
746	16548	\begin{align*} 16 y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
747	16549	\begin{align*} 4 y^{\prime \prime \prime \prime }+15 y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
748	18418	\begin{align*} x^{\prime \prime }+y^{\prime }+x&=0 \\ x^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✓	0.072
749	18980	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
750	19539	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
751	21176	\begin{align*} x^{\prime \prime \prime }-x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
752	21783	\begin{align*} x^{\prime }&=-x^{3}-y \\ y^{\prime }&=x \\ \end{align*}	✗	✗	✗	✗	0.072
753	24419	\begin{align*} 4 y^{\prime \prime \prime }-49 y^{\prime }-60 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
754	24420	\begin{align*} x^{\prime \prime \prime }-2 x^{\prime \prime }-3 x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.072
755	24446	\begin{align*} 4 y^{\prime \prime \prime }-27 y^{\prime }+27 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.072
756	1476	\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
757	3104	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
758	3700	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
759	4145	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
760	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*}	✗	✓	✓	✗	0.073
761	15738	\begin{align*} y_{1}^{\prime }&={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\ y_{2}^{\prime }&=\frac {y_{1}}{\left (x -2\right )^{2}} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	0.073
762	16544	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
763	16715	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
764	18706	\begin{align*} x^{\prime }&=2 y \,x^{2}-3 x^{2}-4 y \\ y^{\prime }&=-2 x \,y^{2}+6 x y \\ \end{align*}	✗	✓	✓	✗	0.073
765	24422	\begin{align*} 10 y^{\prime \prime \prime }+y^{\prime \prime }-7 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
766	24441	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
767	24445	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
768	24447	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
769	24489	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
770	24493	\begin{align*} 4 y^{\prime \prime \prime }+8 y^{\prime \prime }-11 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
771	24518	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.073
772	7045	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
773	12769	\begin{align*} 2 \left (x -\operatorname {a1} \right ) \left (x -\operatorname {a2} \right ) \left (x -\operatorname {a3} \right ) y^{\prime \prime \prime }+\left (9 x^{2}-6 \left (\operatorname {a1} +\operatorname {a2} +\operatorname {a3} \right ) x +3 \operatorname {a1} \operatorname {a2} +3 \operatorname {a1} \operatorname {a3} +3 \operatorname {a2} \operatorname {a3} \right ) y^{\prime \prime }-2 \left (\left (n^{2}+n -3\right ) x +b \right ) y^{\prime }-n \left (n +1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.074
774	14344	\begin{align*} x^{\prime \prime \prime }+x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
775	15670	\begin{align*} -4 y+6 y^{\prime }-4 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
776	16545	\begin{align*} y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
777	16550	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+16 y^{\prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
778	18708	\begin{align*} x^{\prime }&=x-x y \\ y^{\prime }&=y+2 x y \\ \end{align*}	✗	✓	✓	✗	0.074
779	24448	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+12 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
780	24490	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.074
781	2127	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
782	3103	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-6 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
783	15751	\begin{align*} y_{1}^{\prime }&=2 y_{1} x -x^{2} y_{2}+4 x \\ y_{2}^{\prime }&={\mathrm e}^{x} y_{1}+3 \,{\mathrm e}^{-x} y_{2}-\cos \left (3 x \right ) \\ \end{align*}	✗	✗	✗	✗	0.075
784	19832	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
785	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
786	21175	\begin{align*} 2 x^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
787	22669	\begin{align*} y^{\prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
788	24496	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
789	26809	\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.075
790	417	\begin{align*} x^{3} y^{\prime }&=2 y \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.076
791	3109	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }-6 y^{\prime \prime }+8 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
792	4144	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
793	12820	\begin{align*} f \left (y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y\right )+2 \operatorname {df} \left (y^{\prime \prime \prime }-a^{2} y^{\prime }\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
794	19221	\begin{align*} y^{\prime \prime }+z^{\prime }-2 z&={\mathrm e}^{2 x} \\ z^{\prime }+2 y^{\prime }-3 y&=0 \\ \end{align*}	✗	✓	✓	✓	0.076
795	19537	\begin{align*} a^{4} y+2 a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
796	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
797	22659	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
798	24424	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
799	24500	\begin{align*} 18 y^{\prime \prime \prime }-33 y^{\prime \prime }+20 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076
800	24504	\begin{align*} 8 y^{\prime \prime \prime }-4 y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.076