2.3.7 Problems 601 to 700

Table 2.587: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
601	26479	\begin{align*} y^{2} y^{\prime \prime \prime }-3 y y^{\prime } y^{\prime \prime }+2 {y^{\prime }}^{3}+\frac {y \left (y y^{\prime \prime }-{y^{\prime }}^{2}\right )}{x}&=\frac {y^{3}}{x^{2}} \\ \end{align*}	✗	✓	✗	✗	0.062
602	26798	\begin{align*} 2 y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime }+6 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
603	27621	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
604	302	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
605	306	\begin{align*} 9 y^{\prime \prime \prime }+11 y^{\prime \prime }+4 y^{\prime }-14 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
606	1477	\begin{align*} y^{\left (6\right )}-y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
607	2142	\begin{align*} y^{\prime \prime \prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
608	3101	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
609	3102	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-8 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
610	7968	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
611	7984	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
612	9047	\begin{align*} y_{1}^{\prime }&=3 y_{1}+x y_{3} \\ y_{2}^{\prime }&=y_{2}+x^{3} y_{3} \\ y_{3}^{\prime }&=2 y_{1} x -y_{2}+{\mathrm e}^{x} y_{3} \\ \end{align*}	✗	✗	✗	✗	0.063
613	10381	\begin{align*} {y^{\prime \prime }}^{2}+y^{\prime }+y&=0 \\ \end{align*}	✗	✗	✗	✗	0.063
614	12791	\begin{align*} a^{4} x^{4} y+4 a^{3} x^{3} y^{\prime }+6 a^{2} x^{2} y^{\prime \prime }+4 a x y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.063
615	16465	\begin{align*} y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
616	20044	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
617	20577	\begin{align*} a^{2} y^{\prime \prime \prime \prime }&=y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.063
618	26779	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+7 y^{\prime \prime }+6 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
619	286	\begin{align*} y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.064
620	1480	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.064
621	3082	\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*}	✓	✓	✓	✓	0.064
622	3106	\begin{align*} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+11 y^{\prime }-40 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.064
623	4535	\begin{align*} x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=0 \\ x^{\prime }+x-y^{\prime }&=0 \\ \end{align*}	✗	✓	✓	✓	0.064
624	7609	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-6 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.064
625	12775	\begin{align*} x^{2} \left (x^{4}+2 x^{2}+2 x +1\right ) y^{\prime \prime \prime }-\left (2 x^{6}+3 x^{4}-6 x^{2}-6 x -1\right ) y^{\prime \prime }+\left (x^{6}-6 x^{3}-15 x^{2}-12 x -2\right ) y^{\prime }+\left (x^{4}+4 x^{3}+8 x^{2}+6 x +1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.064
626	12805	\begin{align*} x^{4} y^{\prime \prime \prime \prime }-2 n \left (n +1\right ) x^{2} y^{\prime \prime }+4 n \left (n +1\right ) x y^{\prime }+\left (a \,x^{4}+n \left (n +1\right ) \left (n +3\right ) \left (-2+n \right )\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.064
627	12808	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}+3\right ) x^{2} y^{\prime \prime }+\left (12 n^{2}-3\right ) x y^{\prime }-\left (4 x^{4}+12 n^{2}-3\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.064
628	12834	\begin{align*} \left (x -a \right )^{5} \left (x -b \right )^{5} y^{\left (5\right )}-c y&=0 \\ \end{align*}	✗	✗	✗	✗	0.064
629	19827	\begin{align*} 2 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.064
630	19828	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.064
631	20341	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.064
632	21782	\begin{align*} x^{\prime }&=-x^{2}-y \\ y^{\prime }&=x \\ \end{align*}	✗	✓	✓	✗	0.064
633	26803	\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.064
634	2113	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+7 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
635	2118	\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+9 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
636	3703	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
637	3794	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
638	7068	\begin{align*} y^{\prime }+2 y^{\prime \prime \prime }+y^{\left (5\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
639	7610	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }-y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
640	7666	\begin{align*} x^{\prime \prime \prime }-x^{\prime \prime }+x^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
641	8927	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
642	16526	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
643	16533	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
644	17551	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
645	18124	\begin{align*} y^{\prime \prime \prime }&=3 y y^{\prime } \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= {\frac {3}{2}} \\ \end{align*}	✗	✓	✗	✗	0.065
646	18427	\begin{align*} x^{\prime }&=\cos \left (x\right )^{2} \cos \left (y\right )^{2}+\sin \left (x\right )^{2} \cos \left (y\right )^{2} \\ y^{\prime }&=-\frac {\sin \left (2 x\right ) \sin \left (2 y\right )}{2} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	0.065
647	18967	\begin{align*} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y&=\cos \left (t \right ) \\ \end{align*}	✗	✗	✗	✗	0.065
648	21957	\begin{align*} y^{\prime \prime \prime \prime }+x y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-x y^{\prime }+\sin \left (y\right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.065
649	26804	\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
650	27633	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
651	1059	\begin{align*} x^{3} y^{\prime }&=2 y \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.066
652	2115	\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
653	3891	\begin{align*} x_{1}^{\prime }&=t \cot \left (t^{2}\right ) x_{1}+\frac {t \cos \left (t^{2}\right ) x_{3}}{2} \\ x_{2}^{\prime }&=\frac {x_{2}}{t}-x_{3}+2-t \sin \left (t \right ) \\ x_{3}^{\prime }&=\csc \left (t^{2}\right ) x_{1}+x_{2}-x_{3}+1-\cos \left (t \right ) t \\ \end{align*}	✗	✗	✗	✗	0.066
654	4150	\begin{align*} y^{\prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
655	7613	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
656	7668	\begin{align*} x^{\prime \prime \prime \prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
657	8920	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
658	16527	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
659	16532	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
660	18977	\begin{align*} \left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y&=0 \\ \end{align*}	✗	✗	✗	✗	0.066
661	19535	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
662	19581	\begin{align*} x^{2} y^{\prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.066
663	20337	\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
664	25520	\begin{align*} y^{\prime \prime \prime \prime }&=16 y \\ \end{align*}	✓	✓	✓	✓	0.066
665	25993	\begin{align*} y^{\prime \prime }-y+5 y^{\prime }&=t \\ 2 y^{\prime }-x^{\prime \prime }+4 x&=2 \\ \end{align*}	✗	✓	✓	✓	0.066
666	26811	\begin{align*} y^{\left (5\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
667	27592	\begin{align*} y^{2} \left (y^{\prime } y^{\prime \prime \prime }-2 {y^{\prime \prime }}^{2}\right )&={y^{\prime }}^{4} \\ \end{align*}	✗	✓	✗	✗	0.066
668	282	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
669	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*}	✓	✓	✓	✓	0.067
670	3086	\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
671	3107	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-12 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
672	9297	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
673	14863	\begin{align*} x^{\prime }&=4 x-4 y-x \left (x^{2}+y^{2}\right ) \\ y^{\prime }&=4 x+4 y-y \left (x^{2}+y^{2}\right ) \\ \end{align*}	✗	✗	✗	✗	0.067
674	20043	\begin{align*} y^{\prime \prime \prime \prime }-m^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
675	20064	\begin{align*} y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
676	20779	\begin{align*} y^{\prime \prime \prime \prime }-a^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
677	23332	\begin{align*} y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
678	25650	\begin{align*} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\ \end{align*}	✗	✗	✓	✗	0.067
679	2124	\begin{align*} 16 y^{\prime \prime \prime \prime }-72 y^{\prime \prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.068
680	2709	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.068
681	2710	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.068
682	7353	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+13 y^{\prime \prime }-18 y^{\prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.068
683	15733	\begin{align*} y_{1}^{\prime }&=\frac {2 y_{1}}{x}-\frac {y_{2}}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}} \\ y_{2}^{\prime }&=2 y_{1}+1-6 x \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (1\right ) &= -2 \\ y_{2} \left (1\right ) &= -5 \\ \end{align*}	✗	✓	✓	✗	0.068
684	18134	\begin{align*} y^{\prime \prime \prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.068
685	19541	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.068
686	20698	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.068
687	21895	\begin{align*} x^{\prime \prime }-x+y&={\mathrm e}^{t} \\ x^{\prime }+x-y^{\prime }-y&=3 \,{\mathrm e}^{t} \\ \end{align*}	✗	✓	✓	✓	0.068
688	26487	\begin{align*} y^{\left (6\right )}+2 y^{\left (5\right )}+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.068
689	27631	\begin{align*} y^{\left (5\right )}+8 y^{\prime \prime \prime }+16 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.068
690	305	\begin{align*} 6 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+25 y^{\prime \prime }+20 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
691	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*}	✓	✓	✓	✓	0.069
692	2126	\begin{align*} 4 y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+3 y^{\prime \prime }-13 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
693	3083	\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-13 y^{\prime \prime \prime }-13 y^{\prime \prime }+36 y^{\prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
694	3704	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
695	3705	\begin{align*} y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
696	4141	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
697	4446	\begin{align*} y^{\prime \prime \prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
698	4447	\begin{align*} y^{\prime \prime \prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
699	7985	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
700	12787	\begin{align*} y^{\prime \prime \prime \prime }+\left (1+\lambda \right ) a^{2} y^{\prime \prime }+\lambda \,a^{4} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069