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	26106	\begin{align*} y^{\prime \prime \prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
602	290	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
603	3092	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
604	10850	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
605	12722	\begin{align*} y^{\prime \prime \prime }-6 x y^{\prime \prime }+2 \left (4 x^{2}+2 a -1\right ) y^{\prime }-8 a x y&=0 \\ \end{align*}	✗	✓	✓	✗	0.101
606	12825	\begin{align*} y^{\left (5\right )}-a x y-b&=0 \\ \end{align*}	✗	✗	✗	✗	0.101
607	15069	\begin{align*} y^{\prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
608	16548	\begin{align*} 16 y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
609	16715	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
610	18466	\begin{align*} x^{\prime \prime }-x^{\prime }&=1 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.101
611	18717	\begin{align*} x^{\prime }&=x \left (1-x-y\right ) \\ y^{\prime }&=y \left (\frac {3}{4}-y-\frac {x}{2}\right ) \\ \end{align*}	✗	✗	✗	✗	0.101
612	19183	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
613	26769	\begin{align*} x^{\prime }&=-2 x+8 \sin \left (y\right )^{2} \\ y^{\prime }&=x-3 y+4 x^{3} \\ \end{align*}	✗	✗	✗	✗	0.101
614	251	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.102
615	296	\begin{align*} y^{\prime \prime \prime }+10 y^{\prime \prime }+25 y^{\prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.102
616	311	\begin{align*} y^{\prime \prime }&=\left (-2+2 i \sqrt {3}\right ) y \\ \end{align*}	✓	✓	✓	✓	0.102
617	4164	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
618	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*}	✓	✓	✓	✓	0.102
619	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*}	✓	✓	✓	✓	0.102
620	10489	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
621	10821	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
622	10843	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
623	10890	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
624	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*}	✓	✓	✓	✗	0.102
625	10916	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
626	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*}	✗	✓	✓	✗	0.102
627	13120	\begin{align*} x^{\prime }&=-x \,y^{2}+x+y \\ y^{\prime }&=y \,x^{2}-x-y \\ \end{align*}	✗	✗	✗	✗	0.102
628	13136	\begin{align*} x^{\prime }&=-x \,y^{2}+x+y \\ y^{\prime }&=y \,x^{2}-x-y \\ z^{\prime }&=y^{2}-x^{2} \\ \end{align*}	✗	✗	✗	✗	0.102
629	14111	\begin{align*} y^{\prime \prime \prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.102
630	18189	\begin{align*} 3 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.102
631	18311	\begin{align*} x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.102
632	18404	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=\frac {y^{2}}{x} \\ \end{align*}	✗	✓	✓	✓	0.102
633	18407	\begin{align*} x^{\prime }&=\frac {y+t}{x+y} \\ y^{\prime }&=\frac {x-t}{x+y} \\ \end{align*}	✗	✓	✗	✗	0.102
634	18424	\begin{align*} x^{\prime }&=\frac {y}{x-y} \\ y^{\prime }&=\frac {x}{x-y} \\ \end{align*}	✗	✓	✓	✓	0.102
635	19529	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
636	21312	\begin{align*} x^{\prime \prime \prime \prime }+8 x^{\prime \prime \prime }+23 x^{\prime \prime }+2 x^{\prime }+12 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
637	22117	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
638	25077	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t} \\ y \left (0\right ) &= -3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.102
639	25250	\begin{align*} t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
640	26107	\begin{align*} y^{\left (5\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
641	26139	\begin{align*} x^{\prime }&=2 x-y \cos \left (y\right ) \\ y^{\prime }&=3 x-2 y-x \,y^{2} \\ \end{align*}	✗	✓	✗	✗	0.102
642	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*}	✓	✓	✓	✓	0.102
643	472	\begin{align*} x^{3} \left (1-x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+x y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.103
644	941	\begin{align*} y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
645	942	\begin{align*} 6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
646	8920	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
647	10858	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
648	12749	\begin{align*} x^{2} y^{\prime \prime \prime }-2 \left (n +1\right ) x y^{\prime \prime }+\left (a \,x^{2}+6 n \right ) y^{\prime }-2 a x y&=0 \\ \end{align*}	✗	✓	✓	✗	0.103
649	13087	\begin{align*} x^{\prime }-x+2 y&=0 \\ x^{\prime \prime }-2 y^{\prime }&=2 t -\cos \left (2 t \right ) \\ \end{align*}	✗	✓	✓	✗	0.103
650	13088	\begin{align*} x^{\prime } t -t y^{\prime }-2 y&=0 \\ t x^{\prime \prime }+2 x^{\prime }+t x&=0 \\ \end{align*}	✗	✓	✓	✗	0.103
651	13092	\begin{align*} x^{\prime \prime }+x+y&=-5 \\ y^{\prime \prime }-4 x-3 y&=-3 \\ \end{align*}	✗	✓	✓	✓	0.103
652	13121	\begin{align*} x^{\prime }&=x+y-x \left (x^{2}+y^{2}\right ) \\ y^{\prime }&=-x+y-y \left (x^{2}+y^{2}\right ) \\ \end{align*}	✗	✗	✗	✗	0.103
653	18088	\begin{align*} y^{\prime \prime \prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.103
654	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*}	✓	✓	✓	✓	0.103
655	19182	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
656	22674	\begin{align*} y^{\left (5\right )}-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
657	25320	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.103
658	25636	\begin{align*} y^{\prime }-a y&=t \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.103
659	26543	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.103
660	26773	\begin{align*} x^{\prime }&=-\frac {2 x}{3}+\frac {\sin \left (2 y\right )}{2}-x^{3} y \\ y^{\prime }&=-y-2 x+x^{4}-y^{7} \\ \end{align*}	✗	✗	✗	✗	0.103
661	26781	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
662	26784	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+18 y^{\prime \prime }+34 y^{\prime }+20 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
663	26787	\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*}	✓	✓	✓	✓	0.103
664	26799	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+16 y^{\prime \prime }+24 y^{\prime }+20 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
665	1465	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
666	3091	\begin{align*} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
667	10851	\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*}	✓	✓	✓	✗	0.104
668	10874	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.104
669	13116	\begin{align*} x^{\prime }&=\left (a y+b \right ) x \\ y^{\prime }&=\left (c x+d \right ) y \\ \end{align*}	✗	✓	✓	✗	0.104
670	13118	\begin{align*} x^{\prime }&=h \left (a -x\right ) \left (c -x-y\right ) \\ y^{\prime }&=k \left (b -y\right ) \left (c -x-y\right ) \\ \end{align*}	✗	✓	✓	✗	0.104
671	14102	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.104
672	18409	\begin{align*} x^{\prime }&=\frac {y+t}{x+y} \\ y^{\prime }&=\frac {t +x}{x+y} \\ \end{align*}	✗	✓	✗	✗	0.104
673	19762	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
674	21182	\begin{align*} x^{\prime \prime \prime }-x^{\prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.104
675	21199	\begin{align*} x^{\prime \prime \prime }-x^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.104
676	25251	\begin{align*} 4 t^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
677	252	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+8 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.105
678	746	\begin{align*} \left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
679	4450	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
680	9294	\begin{align*} y^{\prime \prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
681	10476	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
682	10491	\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*}	✓	✓	✓	✗	0.105
683	10492	\begin{align*} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.105
684	10790	\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
685	10906	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
686	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*}	✓	✓	✓	✗	0.105
687	10917	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
688	10960	\begin{align*} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.105
689	11300	\begin{align*} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.105
690	12716	\begin{align*} y^{\prime \prime \prime }-\left (6 k^{2} \sin \left (x \right )^{2}+a \right ) y^{\prime }+b y&=0 \\ \end{align*}	✗	✗	✗	✗	0.105
691	14566	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
692	16400	\begin{align*} y^{\prime \prime \prime \prime }&=-2 y^{\prime \prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.105
693	18425	\begin{align*} x^{\prime }&=\sin \left (x\right ) \cos \left (y\right ) \\ y^{\prime }&=\cos \left (x\right ) \sin \left (y\right ) \\ \end{align*}	✗	✓	✓	✗	0.105
694	18712	\begin{align*} x^{\prime }&=y \left (2-x-y\right ) \\ y^{\prime }&=-x-y-2 x y \\ \end{align*}	✗	✗	✗	✗	0.105
695	20063	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
696	21231	\begin{align*} x^{\prime \prime \prime }-2 x^{\prime \prime }+3 x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
697	22115	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-4 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
698	25689	\begin{align*} y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }+158 y^{\prime \prime }-580 y^{\prime }+841 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
699	25918	\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
700	25921	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-9 y^{\prime \prime }+8 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105