2.3.6 Problems 501 to 600

Table 2.585: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
501	21780	\begin{align*} x^{\prime }&=\sin \left (x\right )-4 y \\ y^{\prime }&=\sin \left (2 x\right )-5 y \\ \end{align*}	✗	✗	✗	✗	0.057
502	22890	\begin{align*} x^{\prime \prime }+2 y^{\prime }+8 x&=32 t \\ y^{\prime \prime }+3 x^{\prime }-2 y&=60 \,{\mathrm e}^{-t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 6 \\ x^{\prime }\left (0\right ) &= 0 \\ y \left (0\right ) &= -24 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	0.057
503	416	\begin{align*} x^{2} y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.058
504	2145	\begin{align*} y^{\prime \prime \prime \prime }+64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.058
505	3100	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }-20 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.058
506	7047	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.058
507	8970	\begin{align*} y^{\prime \prime \prime }-y x&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✗	0.058
508	14870	\begin{align*} x^{\prime }&=x-x^{2} \\ y^{\prime }&=2 y-y^{2} \\ \end{align*}	✗	✓	✓	✗	0.058
509	15146	\begin{align*} {y^{\prime \prime \prime }}^{2}+\sqrt {y}&=\sin \left (x \right ) \\ \end{align*}	✗	✗	✗	✗	0.058
510	16397	\begin{align*} y^{\prime \prime \prime }&=y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.058
511	18711	\begin{align*} x^{\prime }&=-\left (x-y\right ) \left (1-x-y\right ) \\ y^{\prime }&=x \left (y+2\right ) \\ \end{align*}	✗	✗	✗	✗	0.058
512	18714	\begin{align*} x^{\prime }&=-x+2 x y \\ y^{\prime }&=y-x^{2}-y^{2} \\ \end{align*}	✗	✓	✓	✗	0.058
513	21784	\begin{align*} x^{\prime }&=2 x y \\ y^{\prime }&=3 y^{2}-x^{2} \\ \end{align*}	✗	✓	✓	✗	0.058
514	26777	\begin{align*} x^{\prime }&=5 x+y \cos \left (y\right )-\frac {x^{3}}{3} \\ y^{\prime }&=3 x+2 y+\frac {x^{4}}{12}-y^{3} {\mathrm e}^{y} \\ \end{align*}	✗	✗	✗	✗	0.058
515	27600	\begin{align*} y^{2} y^{\prime \prime \prime }&={y^{\prime }}^{3} \\ \end{align*}	✗	✓	✓	✗	0.058
516	27626	\begin{align*} y^{\left (5\right )}-10 y^{\prime \prime \prime }+9 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.058
517	27630	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.058
518	950	\begin{align*} 2 y^{\prime \prime \prime }-y^{\prime \prime }-5 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
519	2112	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
520	2119	\begin{align*} 4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
521	2143	\begin{align*} y^{\prime \prime \prime \prime }+64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
522	7058	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-11 y^{\prime \prime }-12 y^{\prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
523	7978	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
524	8058	\begin{align*} \left (1+2 y+3 y^{2}\right ) y^{\prime \prime \prime }+6 y^{\prime } \left (y^{\prime \prime }+{y^{\prime }}^{2}+3 y y^{\prime \prime }\right )&=x \\ \end{align*}	✗	✓	✗	✗	0.059
525	8060	\begin{align*} y y^{\prime \prime \prime }+3 y^{\prime } y^{\prime \prime }-2 y y^{\prime \prime }-2 {y^{\prime }}^{2}+y y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}	✗	✓	✗	✗	0.059
526	9294	\begin{align*} y^{\prime \prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
527	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*}	✗	✓	✗	✗	0.059
528	12776	\begin{align*} \left (x -a \right )^{3} \left (x -b \right )^{3} y^{\prime \prime \prime }-c y&=0 \\ \end{align*}	✗	✓	✓	✗	0.059
529	13097	\begin{align*} x^{\prime \prime }+a \left (x^{\prime }-y^{\prime }\right )+b_{1} x&=c_{1} {\mathrm e}^{i \omega t} \\ y^{\prime \prime }+a \left (y^{\prime }-x^{\prime }\right )+b_{2} y&=c_{2} {\mathrm e}^{i \omega t} \\ \end{align*}	✗	✓	✓	✗	0.059
530	16486	\begin{align*} y^{\prime \prime \prime }-9 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
531	16529	\begin{align*} y^{\prime \prime \prime \prime }-81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
532	16971	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
533	17549	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
534	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
535	19531	\begin{align*} y^{\prime \prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
536	19540	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
537	20196	\begin{align*} x^{2} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✗	✓	✓	✗	0.059
538	20591	\begin{align*} a y^{\prime \prime \prime }&=y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.059
539	21308	\begin{align*} x^{\prime \prime \prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
540	23340	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+5 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
541	23342	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
542	23472	\begin{align*} y^{\prime \prime \prime }-3 x y^{\prime \prime }+4 y&=x^{2} \\ \end{align*}	✗	✗	✗	✗	0.059
543	25146	\begin{align*} y^{\prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
544	25148	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
545	26106	\begin{align*} y^{\prime \prime \prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
546	26496	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
547	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*}	✓	✓	✓	✓	0.059
548	26801	\begin{align*} y^{\prime \prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
549	27625	\begin{align*} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.059
550	288	\begin{align*} y^{\prime \prime \prime \prime }&=16 y \\ \end{align*}	✓	✓	✓	✓	0.060
551	2114	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
552	2117	\begin{align*} 2 y^{\prime \prime \prime }+3 y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
553	3076	\begin{align*} 2 y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-20 y^{\prime \prime }+27 y^{\prime }+18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
554	7065	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
555	7612	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+7 y^{\prime }+15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
556	9293	\begin{align*} y^{\prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
557	12715	\begin{align*} y^{\prime \prime \prime }+x^{2 c -2} y^{\prime }+\left (c -1\right ) x^{2 c -3} y&=0 \\ \end{align*}	✗	✓	✓	✗	0.060
558	12822	\begin{align*} y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y-\lambda \left (a x -b \right ) \left (-a^{2} y+y^{\prime \prime }\right )&=0 \\ \end{align*}	✗	✓	✓	✗	0.060
559	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
560	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
561	19532	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
562	19762	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
563	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 x y y^{\prime }+3 x^{2} y^{2}\right ) y^{\prime }+x^{3} y^{3}&=0 \\ \end{align*}	✗	✓	✗	✗	0.060
564	19826	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
565	23341	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.060
566	23552	\begin{align*} y^{\left (5\right )}-y^{\prime }-\frac {4 y}{x}&=0 \\ \end{align*}	✗	✗	✓	✓	0.060
567	27771	\begin{align*} y^{\prime \prime \prime }-x y^{\prime \prime }+\left (x -2\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.060
568	1474	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
569	2116	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+16 y^{\prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
570	3084	\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-15 y^{\prime \prime \prime }-19 y^{\prime \prime }+30 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
571	3701	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-18 y^{\prime }-40 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
572	8915	\begin{align*} y^{\prime \prime \prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
573	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*}	✗	✓	✓	✗	0.061
574	13096	\begin{align*} a_{1} x^{\prime \prime }+b_{1} x^{\prime }+c_{1} x-A y^{\prime }&=B \,{\mathrm e}^{i \omega t} \\ a_{2} y^{\prime \prime }+b_{2} y^{\prime }+c_{2} y+A x^{\prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.061
575	13122	\begin{align*} x^{\prime }&=-y+x \left (x^{2}+y^{2}-1\right ) \\ y^{\prime }&=x+y \left (x^{2}+y^{2}-1\right ) \\ \end{align*}	✗	✗	✗	✗	0.061
576	15681	\begin{align*} y^{\prime \prime \prime \prime }+\left (-3-i\right ) y^{\prime \prime \prime }+\left (4+3 i\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
577	18971	\begin{align*} \left (x^{2}-2\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+3 y&=0 \\ \end{align*}	✗	✗	✗	✗	0.061
578	18975	\begin{align*} y^{\prime \prime \prime }+t y^{\prime \prime }+5 t^{2} y^{\prime }+2 t^{3} y&=\ln \left (t \right ) \\ \end{align*}	✗	✗	✗	✗	0.061
579	20339	\begin{align*} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.061
580	284	\begin{align*} -4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
581	285	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
582	952	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
583	2120	\begin{align*} 27 y^{\prime \prime \prime }+27 y^{\prime \prime }+9 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
584	3699	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
585	3702	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
586	7611	\begin{align*} z^{\prime \prime \prime }+2 z^{\prime \prime }-4 z^{\prime }-8 z&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
587	7669	\begin{align*} x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
588	7983	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+9 y^{\prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
589	12743	\begin{align*} x^{2} y^{\prime \prime \prime }-3 \left (x -m \right ) x y^{\prime \prime }+\left (2 x^{2}+4 \left (n -m \right ) x +m \left (2 m -1\right )\right ) y^{\prime }-2 n \left (2 x -2 m +1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.062
590	12759	\begin{align*} x^{3} y^{\prime \prime \prime }+\left (a \,x^{2 \nu }+1-\nu ^{2}\right ) x y^{\prime }+\left (b \,x^{3 \nu }+a \left (\nu -1\right ) x^{2 \nu }+\nu ^{2}-1\right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	0.062
591	12794	\begin{align*} y^{\prime \prime \prime \prime } x -\left (6 x^{2}+1\right ) y^{\prime \prime \prime }+12 x^{3} y^{\prime \prime }-\left (9 x^{2}-7\right ) x^{2} y^{\prime }+2 \left (x^{2}-3\right ) x^{3} y&=0 \\ \end{align*}	✗	✓	✓	✗	0.062
592	13125	\begin{align*} {x^{\prime }}^{2}+x^{\prime } t +a y^{\prime }-x&=0 \\ x^{\prime } y^{\prime }+t y^{\prime }-y&=0 \\ \end{align*}	✗	✓	✓	✓	0.062
593	16972	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
594	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
595	19529	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
596	19754	\begin{align*} y^{\prime \prime \prime \prime }-a^{4} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
597	20578	\begin{align*} a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
598	21251	\begin{align*} x^{\prime }&=2 x-2 x y \\ y^{\prime }&=-y+x y \\ \end{align*}	✗	✓	✓	✗	0.062
599	21700	\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y&=4 \ln \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.062
600	24096	\begin{align*} x^{2} y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.062