2.3.5 Problems 401 to 500

Table 2.541: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
401	1469	\begin{align*} t y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }+t y&=0 \\ \end{align*}	✗	✓	✓	✗	0.042
402	4144	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.042
403	4146	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.042
404	6642	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.042
405	6645	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.042
406	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*}	✗	✓	✓	✗	0.042
407	6722	\begin{align*} -4 \left (3 x^{2}+1\right ) y+2 x \left (5 x^{2}+2\right ) y^{\prime }-2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.042
408	6734	\begin{align*} y-2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.042
409	7271	\begin{align*} y^{\prime \prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.042
410	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*}	✗	✓	✓	✗	0.042
411	13045	\begin{align*} x^{2} y^{\prime \prime \prime }+y^{\prime \prime } x +\left (2 y x -1\right ) y^{\prime }+y^{2}-f \left (x \right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.042
412	13046	\begin{align*} x^{2} y^{\prime \prime \prime }+x \left (y-1\right ) y^{\prime \prime }+x {y^{\prime }}^{2}+\left (1-y\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✗	✗	0.042
413	13088	\begin{align*} t x^{\prime }-t y^{\prime }-2 y&=0 \\ t x^{\prime \prime }+2 x^{\prime }+t x&=0 \\ \end{align*}	✗	✓	✓	✗	0.042
414	13127	\begin{align*} x^{\prime \prime }&=a \,{\mathrm e}^{2 x}-{\mathrm e}^{-x}+{\mathrm e}^{-2 x} \cos \left (y\right )^{2} \\ y^{\prime \prime }&={\mathrm e}^{-2 x} \sin \left (y\right ) \cos \left (y\right )-\frac {\sin \left (y\right )}{\cos \left (y\right )^{3}} \\ \end{align*}	✗	✗	✗	✗	0.042
415	14096	\begin{align*} y^{\prime }-y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.042
416	18144	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.042
417	18145	\begin{align*} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.042
418	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*}	✗	✓	✓	✗	0.042
419	18983	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.042
420	20040	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.042
421	22658	\begin{align*} y^{\prime \prime \prime \prime }+16 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.042
422	23107	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+6 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.042
423	23309	\begin{align*} 3 y^{\prime \prime \prime }+4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.042
424	23436	\begin{align*} y^{\prime \prime \prime \prime }-\ln \left (x +1\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.042
425	25391	\begin{align*} y_{1}^{\prime }&=y_{1}+y_{2} \\ y_{2}^{\prime }&=\frac {y_{1}}{t}+\frac {y_{2}}{t} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (1\right ) &= -3 \\ y_{2} \left (1\right ) &= 4 \\ \end{align*}	✗	✓	✓	✓	0.042
426	25392	\begin{align*} y_{1}^{\prime }&=\frac {y_{1}}{t}+1 \\ y_{2}^{\prime }&=\frac {y_{2}}{t}+t \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (1\right ) &= 1 \\ y_{2} \left (1\right ) &= 2 \\ \end{align*}	✗	✓	✓	✗	0.042
427	282	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.043
428	3700	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.043
429	3705	\begin{align*} y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.043
430	4447	\begin{align*} y^{\prime \prime \prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.043
431	6623	\begin{align*} y^{\prime }-y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.043
432	6628	\begin{align*} 4 y+4 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.043
433	6639	\begin{align*} 2 a^{2} y-a^{2} y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.043
434	6797	\begin{align*} 3 y^{2}+18 x y^{\prime } y+9 x^{2} {y^{\prime }}^{2}+9 x^{2} y y^{\prime \prime }+3 x^{3} y^{\prime } y^{\prime \prime }+x^{3} y y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.043
435	7066	\begin{align*} y^{\prime \prime \prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.043
436	7272	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-6 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.043
437	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*}	✗	✓	✗	✗	0.043
438	8153	\begin{align*} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\ \end{align*}	✗	✗	✓	✗	0.043
439	9291	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.043
440	9293	\begin{align*} y^{\prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.043
441	10051	\begin{align*} y^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.043
442	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*}	✗	✗	✗	✗	0.043
443	12752	\begin{align*} x^{2} y^{\prime \prime \prime }-2 \left (x^{2}-x \right ) y^{\prime \prime }+\left (x^{2}-2 x +\frac {1}{4}-\nu ^{2}\right ) y^{\prime }+\left (\nu ^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.043
444	12770	\begin{align*} x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-4 \left (1+3 x \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.043
445	12772	\begin{align*} x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-4 \left (3 x^{2}+1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.043
446	12834	\begin{align*} \left (x -a \right )^{5} \left (-b +x \right )^{5} y^{\left (5\right )}-c y&=0 \\ \end{align*}	✗	✗	✗	✗	0.043
447	13085	\begin{align*} 2 x^{\prime }+y^{\prime }-3 x&=0 \\ x^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{2 t} \\ \end{align*}	✗	✓	✓	✓	0.043
448	13086	\begin{align*} x^{\prime }+x-y^{\prime }&=2 t \\ x^{\prime \prime }+y^{\prime }-9 x+3 y&=\sin \left (2 t \right ) \\ \end{align*}	✗	✓	✓	✓	0.043
449	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*}	✗	✗	✗	✗	0.043
450	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*}	✗	✗	✗	✗	0.043
451	14093	\begin{align*} -y-2 y^{\prime }+2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.043
452	14171	\begin{align*} 2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 x^{2} {y^{\prime }}^{2}+36 x y^{\prime } y+6 y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	0.043
453	15755	\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*}	✗	✓	✓	✓	0.043
454	18968	\begin{align*} t \left (-1+t \right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y&=0 \\ \end{align*}	✗	✗	✗	✗	0.043
455	19217	\begin{align*} y^{\prime }&=\frac {y^{2}}{z} \\ z^{\prime }&=\frac {z^{2}}{y} \\ \end{align*}	✗	✓	✓	✗	0.043
456	21236	\begin{align*} x^{\prime }+y&=3 t \\ y^{\prime }-t x^{\prime }&=0 \\ \end{align*}	✗	✓	✓	✓	0.043
457	22085	\begin{align*} y^{\prime \prime \prime \prime }+x^{2} y^{\prime \prime \prime }+y^{\prime \prime } x -{\mathrm e}^{x} y^{\prime }+2 y&=x^{2}+x +1 \\ \end{align*}	✗	✗	✗	✗	0.043
458	22123	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.043
459	23943	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.043
460	25387	\begin{align*} y_{1}^{\prime }&=y_{2} t \\ y_{2}^{\prime }&=-y_{1} t \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	0.043
461	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*}	✗	✓	✓	✓	0.043
462	301	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.044
463	937	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.044
464	949	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.044
465	1471	\begin{align*} t^{2} \left (t +3\right ) y^{\prime \prime \prime }-3 t \left (t +2\right ) y^{\prime \prime }+6 \left (t +1\right ) y^{\prime }-6 y&=0 \\ \end{align*}	✗	✓	✓	✗	0.044
466	4145	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.044
467	6668	\begin{align*} -3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.044
468	8915	\begin{align*} y^{\prime \prime \prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.044
469	8917	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+6 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.044
470	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*}	✗	✗	✗	✗	0.044
471	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*}	✗	✓	✓	✗	0.044
472	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*}	✗	✓	✓	✓	0.044
473	17421	\begin{align*} {y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2}&=0 \\ \end{align*}	✗	✓	✗	✗	0.044
474	18142	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.044
475	20329	\begin{align*} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.044
476	22637	\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+2 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.044
477	22645	\begin{align*} y^{\left (6\right )}-4 y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.044
478	22666	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.044
479	22680	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.044
480	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*}	✗	✓	✓	✓	0.044
481	23990	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.044
482	25389	\begin{align*} y_{1}^{\prime }&=\frac {y_{1}}{t}+y_{2} \\ y_{2}^{\prime }&=-y_{1}+\frac {y_{2}}{t} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (\pi \right ) &= 1 \\ y_{2} \left (\pi \right ) &= -1 \\ \end{align*}	✗	✓	✓	✓	0.044
483	3704	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.045
484	4446	\begin{align*} y^{\prime \prime \prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.045
485	6625	\begin{align*} -3 y+y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.045
486	6759	\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*}	✗	✓	✓	✗	0.045
487	7056	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.045
488	8829	\begin{align*} a^{2} y^{\prime \prime \prime \prime }&=y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.045
489	8920	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.045
490	9297	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.045
491	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*}	✗	✓	✓	✗	0.045
492	20138	\begin{align*} a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.045
493	20335	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.045
494	20340	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.045
495	21700	\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y&=4 \ln \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.045
496	22336	\begin{align*} {| y^{\prime }|}+1&=0 \\ \end{align*}	✗	✓	✗	✗	0.045
497	25396	\begin{align*} y_{1}^{\prime }&=y_{1} t +y_{2} t +4 t \\ y_{2}^{\prime }&=-y_{1} t -y_{2} t +4 t \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 4 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	0.045
498	284	\begin{align*} -4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.046
499	289	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.046
500	302	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.046