2.3.6 Problems 501 to 600

Table 2.561: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
501	15754	\begin{align*} y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x} \\ y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x} \\ \end{align*}	✗	✓	✓	✓	0.062
502	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
503	19183	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
504	19831	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
505	21236	\begin{align*} x^{\prime }+y&=3 t \\ y^{\prime }-t x^{\prime }&=0 \\ \end{align*}	✗	✓	✓	✓	0.062
506	22658	\begin{align*} y^{\prime \prime \prime \prime }+16 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
507	23990	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
508	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
509	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*}	✓	✓	✓	✓	0.062
510	306	\begin{align*} 9 y^{\prime \prime \prime }+11 y^{\prime \prime }+4 y^{\prime }-14 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
511	2712	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
512	6604	\begin{align*} y^{\prime \prime \prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.063
513	10047	\begin{align*} y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
514	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
515	14094	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
516	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*}	✗	✗	✗	✗	0.063
517	16533	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
518	16720	\begin{align*} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
519	17540	\begin{align*} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
520	18405	\begin{align*} x_{1}^{\prime }&=\frac {x_{1}^{2}}{x_{2}} \\ x_{2}^{\prime }&=x_{2}-x_{1} \\ \end{align*}	✗	✓	✓	✓	0.063
521	18426	\begin{align*} {\mathrm e}^{t} x^{\prime }&=\frac {1}{y} \\ {\mathrm e}^{t} y^{\prime }&=\frac {1}{x} \\ \end{align*}	✗	✓	✓	✗	0.063
522	18631	\begin{align*} x^{\prime }&=-2 t x+y \\ y^{\prime }&=3 x-y \\ \end{align*}	✗	✓	✓	✓	0.063
523	18635	\begin{align*} x^{\prime }&=x+y+4 \\ y^{\prime }&=-2 x+\sin \left (t \right ) y \\ \end{align*}	✗	✓	✗	✗	0.063
524	19182	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
525	19534	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
526	19826	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
527	21701	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+y^{\prime } x -y&=-\ln \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.063
528	23107	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+6 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
529	25143	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
530	25520	\begin{align*} y^{\prime \prime \prime \prime }&=16 y \\ \end{align*}	✓	✓	✓	✓	0.063
531	25920	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
532	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*}	✓	✓	✓	✓	0.064
533	942	\begin{align*} 6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.064
534	4150	\begin{align*} y^{\prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.064
535	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
536	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 (x^{4} a +n \left (n +1\right ) \left (n +3\right ) \left (-2+n \right )\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.064
537	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
538	12834	\begin{align*} \left (x -a \right )^{5} \left (x -b \right )^{5} y^{\left (5\right )}-c y&=0 \\ \end{align*}	✗	✗	✗	✗	0.064
539	16400	\begin{align*} y^{\prime \prime \prime \prime }&=-2 y^{\prime \prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.064
540	16527	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.064
541	18402	\begin{align*} x_{1}^{\prime }&=-2 t x_{1}^{2} \\ x_{2}^{\prime }&=\frac {x_{2}+t}{t} \\ \end{align*}	✗	✓	✓	✗	0.064
542	18424	\begin{align*} x^{\prime }&=\frac {y}{x-y} \\ y^{\prime }&=\frac {x}{x-y} \\ \end{align*}	✗	✓	✓	✓	0.064
543	21235	\begin{align*} x^{\prime }+t y&=-1 \\ x^{\prime }+y^{\prime }&=2 \\ \end{align*}	✗	✓	✓	✓	0.064
544	22314	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.064
545	22637	\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+2 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.064
546	22666	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.064
547	25925	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.064
548	4549	\begin{align*} x^{\prime }+4 x+2 y&=\frac {2}{{\mathrm e}^{t}-1} \\ 6 x-y^{\prime }+3 y&=\frac {3}{{\mathrm e}^{t}-1} \\ \end{align*}	✗	✓	✓	✓	0.065
549	6720	\begin{align*} -4 \left (1+3 x \right ) y+2 x \left (2+5 x \right ) y^{\prime }-2 x^{2} \left (2 x +1\right ) y^{\prime \prime }+x^{3} \left (x +1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.065
550	8920	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
551	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 x y_{1}-y_{2}+{\mathrm e}^{x} y_{3} \\ \end{align*}	✗	✗	✗	✗	0.065
552	13132	\begin{align*} x^{\prime }+y^{\prime }&=x y \\ y^{\prime }+z^{\prime }&=y z \\ x^{\prime }+z^{\prime }&=x z \\ \end{align*}	✗	✓	✗	✗	0.065
553	14422	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
554	14423	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
555	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
556	18403	\begin{align*} x_{1}^{\prime }&={\mathrm e}^{t -x_{1}} \\ x_{2}^{\prime }&=2 \,{\mathrm e}^{x_{1}} \\ \end{align*}	✗	✓	✓	✗	0.065
557	18409	\begin{align*} x^{\prime }&=\frac {y+t}{x+y} \\ y^{\prime }&=\frac {t +x}{x+y} \\ \end{align*}	✗	✓	✗	✗	0.065
558	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
559	19754	\begin{align*} y^{\prime \prime \prime \prime }-a^{4} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
560	20340	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
561	21957	\begin{align*} y^{\prime \prime \prime \prime }+x y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-y^{\prime } x +\sin \left (y\right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.065
562	23309	\begin{align*} 3 y^{\prime \prime \prime }+4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
563	25536	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
564	26107	\begin{align*} y^{\left (5\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
565	2709	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
566	4572	\begin{align*} x_{1}^{\prime }&=-x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-3 x_{1}+4 x_{2}+\frac {{\mathrm e}^{3 t}}{1+{\mathrm e}^{2 t}} \\ \end{align*}	✗	✓	✓	✗	0.066
567	6661	\begin{align*} a^{3} x^{3} y+3 a^{2} x^{2} y^{\prime }+3 a x y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.066
568	6685	\begin{align*} 2 x^{3} y+\left (-2 x^{3}+6\right ) y^{\prime }+x \left (-x^{2}+6\right ) y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.066
569	9294	\begin{align*} y^{\prime \prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
570	14096	\begin{align*} y^{\prime }-y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
571	15734	\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*} With initial conditions \begin{align*} y_{1} \left (-1\right ) &= 3 \\ y_{2} \left (-1\right ) &= -3 \\ \end{align*}	✗	✓	✓	✓	0.066
572	15736	\begin{align*} y_{1}^{\prime }&=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\ y_{2}^{\prime }&=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (1\right ) &= 1 \\ y_{2} \left (1\right ) &= -1 \\ \end{align*}	✗	✗	✗	✗	0.066
573	15737	\begin{align*} y_{1}^{\prime }&=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\ y_{2}^{\prime }&=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (2\right ) &= 1 \\ y_{2} \left (2\right ) &= -1 \\ \end{align*}	✗	✗	✗	✗	0.066
574	16487	\begin{align*} y^{\prime \prime \prime \prime }-10 y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
575	16535	\begin{align*} y^{\prime \prime \prime }-9 y^{\prime \prime }+31 y^{\prime }-39 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
576	16544	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
577	16550	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+16 y^{\prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
578	18406	\begin{align*} x^{\prime }&=\frac {{\mathrm e}^{-x}}{t} \\ y^{\prime }&=\frac {x \,{\mathrm e}^{-y}}{t} \\ \end{align*}	✗	✓	✓	✓	0.066
579	18407	\begin{align*} x^{\prime }&=\frac {y+t}{x+y} \\ y^{\prime }&=\frac {x-t}{x+y} \\ \end{align*}	✗	✓	✗	✗	0.066
580	18977	\begin{align*} \left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y&=0 \\ \end{align*}	✗	✗	✗	✗	0.066
581	19532	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
582	19762	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
583	19828	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
584	20699	\begin{align*} y^{\prime \prime \prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
585	20992	\begin{align*} x^{\prime }&=\left (3 t -1\right ) x-\left (1-t \right ) y+t \,{\mathrm e}^{t^{2}} \\ y^{\prime }&=-\left (t +2\right ) x+\left (-2+t \right ) y-{\mathrm e}^{t^{2}} \\ \end{align*}	✗	✓	✓	✗	0.066
586	21253	\begin{align*} x^{\prime }&=x \left (3-y\right ) \\ y^{\prime }&=y \left (x-5\right ) \\ \end{align*}	✗	✓	✓	✗	0.066
587	22114	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+2 y^{\prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
588	22680	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
589	1477	\begin{align*} y^{\left (6\right )}-y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
590	4573	\begin{align*} x_{1}^{\prime }&=-4 x_{1}-2 x_{2}+\frac {2}{{\mathrm e}^{t}-1} \\ x_{2}^{\prime }&=6 x_{1}+3 x_{2}-\frac {3}{{\mathrm e}^{t}-1} \\ \end{align*}	✗	✓	✓	✓	0.067
591	6625	\begin{align*} -3 y+y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
592	6769	\begin{align*} -a^{2} y+12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.067
593	6785	\begin{align*} y^{\left (6\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
594	12784	\begin{align*} y^{\prime \prime \prime \prime }+\lambda y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
595	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*}	✗	✓	✓	✗	0.067
596	19540	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
597	25650	\begin{align*} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\ \end{align*}	✗	✗	✓	✗	0.067
598	26105	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
599	246	\begin{align*} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.068
600	1480	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.068