2.3.7 Problems 601 to 700

Table 2.557: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
601	20591	\begin{align*} a y^{\prime \prime \prime }&=y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.057
602	21287	\begin{align*} x^{\prime }-x&=k \delta \left (t \right ) \\ x \left (0\right ) &= a \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.057
603	24494	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-16 y^{\prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.057
604	24517	\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+7 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.057
605	25388	\begin{align*} y_{1}^{\prime }&=y_{1} t +y_{2} t \\ y_{2}^{\prime }&=-y_{1} t -y_{2} t \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 4 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	0.057
606	25390	\begin{align*} y_{1}^{\prime }&=\left (2 t +1\right ) y_{1}+2 y_{2} t \\ y_{2}^{\prime }&=-2 y_{1} t +\left (1-2 t \right ) y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	0.057
607	25395	\begin{align*} y_{1}^{\prime }&=3 \sec \left (t \right ) y_{1}+5 \sec \left (t \right ) y_{2} \\ y_{2}^{\prime }&=-\sec \left (t \right ) y_{1}-3 \sec \left (t \right ) y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 2 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}	✗	✓	✗	✓	0.057
608	3104	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.058
609	3701	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-18 y^{\prime }-40 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.058
610	6595	\begin{align*} \left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2}&=4 x y \left (-y+y^{\prime } x \right )^{3} \\ \end{align*}	✗	✗	✓	✗	0.058
611	6774	\begin{align*} -k y-\left (-a b c +x \right ) y^{\prime }+\left (a b +a c +b c +a +b +c +1\right ) x y^{\prime \prime }+\left (3+a +b +c \right ) x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.058
612	12787	\begin{align*} y^{\prime \prime \prime \prime }+\left (1+\lambda \right ) a^{2} y^{\prime \prime }+\lambda \,a^{4} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.058
613	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*}	✗	✓	✓	✗	0.058
614	12815	\begin{align*} \nu ^{4} x^{4} y^{\prime \prime \prime \prime }+\left (4 \nu -2\right ) \nu ^{3} x^{3} y^{\prime \prime \prime }+\left (\nu -1\right ) \left (2 \nu -1\right ) \nu ^{2} x^{2} y^{\prime \prime }-\frac {b^{4} x^{\frac {2}{\nu }} y}{16}&=0 \\ \end{align*}	✗	✓	✓	✗	0.058
615	15146	\begin{align*} {y^{\prime \prime \prime }}^{2}+\sqrt {y}&=\sin \left (x \right ) \\ \end{align*}	✗	✗	✗	✗	0.058
616	16529	\begin{align*} y^{\prime \prime \prime \prime }-81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.058
617	18426	\begin{align*} {\mathrm e}^{t} x^{\prime }&=\frac {1}{y} \\ {\mathrm e}^{t} y^{\prime }&=\frac {1}{x} \\ \end{align*}	✗	✓	✓	✗	0.058
618	23365	\begin{align*} x^{\prime \prime }+y^{\prime }+6 x&=0 \\ y^{\prime \prime }-x^{\prime }+6 y&=0 \\ \end{align*} With initial conditions \begin{align*} x^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	0.058
619	24035	\begin{align*} 6 x^{2} y^{\prime \prime }-5 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.058
620	24418	\begin{align*} 4 y^{\prime \prime \prime }-13 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.058
621	24421	\begin{align*} x^{\prime \prime \prime }-7 x^{\prime }+6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.058
622	25394	\begin{align*} y_{1}^{\prime }&=\frac {4 t y_{1}}{t^{2}+1}+\frac {6 y_{2} t}{t^{2}+1}-3 t \\ y_{2}^{\prime }&=-\frac {2 t y_{1}}{t^{2}+1}-\frac {4 y_{2} t}{t^{2}+1}+t \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (1\right ) &= 1 \\ y_{2} \left (1\right ) &= -1 \\ \end{align*}	✗	✓	✓	✓	0.058
623	246	\begin{align*} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
624	3700	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
625	11279	\begin{align*} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
626	15421	\begin{align*} -a^{3} y+3 a^{2} y^{\prime }-3 a y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
627	18973	\begin{align*} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+4 y&=\cos \left (t \right ) \\ \end{align*}	✗	✗	✗	✗	0.059
628	19831	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
629	20196	\begin{align*} x^{2} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✗	✓	✓	✗	0.059
630	20699	\begin{align*} y^{\prime \prime \prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
631	21188	\begin{align*} x^{\prime \prime \prime \prime }-x^{\prime \prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.059
632	23259	\begin{align*} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
633	23472	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime } x +4 y&=x^{2} \\ \end{align*}	✗	✗	✗	✗	0.059
634	24419	\begin{align*} 4 y^{\prime \prime \prime }-49 y^{\prime }-60 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
635	24450	\begin{align*} y^{\left (5\right )}-16 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
636	24475	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
637	24489	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
638	311	\begin{align*} y^{\prime \prime }&=\left (-2+2 i \sqrt {3}\right ) y \\ \end{align*}	✓	✓	✓	✓	0.060
639	608	\begin{align*} x^{\prime }&=t x-y+{\mathrm e}^{t} z \\ y^{\prime }&=2 x+t^{2} y-z \\ z^{\prime }&={\mathrm e}^{-t} x+3 t y+t^{3} z \\ \end{align*}	✗	✗	✗	✗	0.060
640	1472	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
641	2121	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
642	2141	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
643	3086	\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
644	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*}	✓	✓	✓	✓	0.060
645	6619	\begin{align*} y^{\prime \prime \prime }&=a^{2} y \\ \end{align*}	✓	✓	✓	✓	0.060
646	6730	\begin{align*} a y+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
647	11073	\begin{align*} y^{\prime \prime }-4 y^{\prime } t +\left (4 t^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.060
648	11138	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
649	11227	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
650	13131	\begin{align*} x^{\prime }&=x \left (y-z\right ) \\ y^{\prime }&=y \left (z-x\right ) \\ z^{\prime }&=z \left (x-y\right ) \\ \end{align*}	✗	✗	✗	✗	0.060
651	13137	\begin{align*} \left (x-y\right ) \left (x-z\right ) x^{\prime }&=f \left (t \right ) \\ \left (-x+y\right ) \left (y-z\right ) y^{\prime }&=f \left (t \right ) \\ \left (z-x\right ) \left (z-y\right ) z^{\prime }&=f \left (t \right ) \\ \end{align*}	✗	✓	✓	✗	0.060
652	15672	\begin{align*} y^{\prime \prime \prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
653	18968	\begin{align*} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y&=0 \\ \end{align*}	✗	✗	✗	✗	0.060
654	18969	\begin{align*} y^{\prime \prime \prime }+t y^{\prime \prime }+t^{2} y^{\prime }+t^{2} y&=\ln \left (t \right ) \\ \end{align*}	✗	✗	✗	✗	0.060
655	19184	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
656	19784	\begin{align*} y^{2} y^{\prime \prime \prime }-\left (3 y y^{\prime }+2 x y^{2}\right ) y^{\prime \prime }+\left (2 {y^{\prime }}^{2}+2 y y^{\prime } x +3 y^{2} x^{2}\right ) y^{\prime }+x^{3} y^{3}&=0 \\ \end{align*}	✗	✓	✗	✗	0.060
657	21502	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
658	23552	\begin{align*} y^{\left (5\right )}-y^{\prime }-\frac {4 y}{x}&=0 \\ \end{align*}	✗	✗	✓	✓	0.060
659	24449	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
660	24491	\begin{align*} y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
661	24493	\begin{align*} 4 y^{\prime \prime \prime }+8 y^{\prime \prime }-11 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
662	24504	\begin{align*} 8 y^{\prime \prime \prime }-4 y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
663	24518	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
664	952	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
665	1465	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
666	4146	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
667	8198	\begin{align*} x^{\prime \prime }&=4 y+{\mathrm e}^{t} \\ y^{\prime \prime }&=4 x-{\mathrm e}^{t} \\ \end{align*}	✗	✓	✓	✓	0.061
668	8206	\begin{align*} y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }+158 y^{\prime \prime }-580 y^{\prime }+841 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
669	8917	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+6 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
670	10961	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.061
671	11263	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
672	11300	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.061
673	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*}	✗	✗	✗	✗	0.061
674	18971	\begin{align*} \left (x^{2}-2\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+3 y&=0 \\ \end{align*}	✗	✗	✗	✗	0.061
675	18975	\begin{align*} y^{\prime \prime \prime }+t y^{\prime \prime }+5 t^{2} y^{\prime }+2 y t^{3}&=\ln \left (t \right ) \\ \end{align*}	✗	✗	✗	✗	0.061
676	19754	\begin{align*} y^{\prime \prime \prime \prime }-a^{4} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
677	22669	\begin{align*} y^{\prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
678	24422	\begin{align*} 10 y^{\prime \prime \prime }+y^{\prime \prime }-7 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
679	24448	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+12 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
680	24500	\begin{align*} 18 y^{\prime \prime \prime }-33 y^{\prime \prime }+20 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
681	25148	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
682	290	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
683	939	\begin{align*} -4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
684	941	\begin{align*} y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
685	954	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
686	3704	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
687	6607	\begin{align*} a y+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
688	8921	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
689	8927	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
690	10653	\begin{align*} y^{\prime \prime }-4 y^{\prime } t +\left (4 t^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.062
691	10713	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
692	10848	\begin{align*} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.062
693	18974	\begin{align*} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+7 t^{2} y&=0 \\ \end{align*}	✗	✗	✗	✗	0.062
694	21183	\begin{align*} x^{\prime \prime \prime }+x^{\prime \prime }-2 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.062
695	24416	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
696	24497	\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
697	295	\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*}	✓	✓	✓	✓	0.063
698	1470	\begin{align*} \left (2-t \right ) y^{\prime \prime \prime }+\left (2 t -3\right ) y^{\prime \prime }-y^{\prime } t +y&=0 \\ \end{align*}	✗	✓	✓	✗	0.063
699	1474	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
700	2789	\begin{align*} x^{\prime }&=-b x y+m \\ y^{\prime }&=b x y-g y \\ \end{align*}	✗	✗	✗	✗	0.063