2.3.15 Problems 1401 to 1500

Table 2.579: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1401	4142	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.124
1402	7063	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.124
1403	7611	\begin{align*} z^{\prime \prime \prime }+2 z^{\prime \prime }-4 z^{\prime }-8 z&=0 \\ \end{align*}	✓	✓	✓	✓	0.124
1404	7669	\begin{align*} x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.124
1405	10790	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.124
1406	10911	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.124
1407	10918	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.124
1408	16660	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=12 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.124
1409	24425	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.124
1410	7068	\begin{align*} y^{\prime }+2 y^{\prime \prime \prime }+y^{\left (5\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1411	7612	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+7 y^{\prime }+15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1412	10998	\begin{align*} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.125
1413	11135	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.125
1414	11219	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1415	15262	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=5 \\ \end{align*}	✓	✓	✓	✓	0.125
1416	16450	\begin{align*} y^{\prime \prime }-\left (4+\frac {2}{x}\right ) y^{\prime }+\left (4+\frac {4}{x}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.125
1417	16452	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}-4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1418	16539	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 13 \\ y^{\prime \prime }\left (0\right ) &= 86 \\ \end{align*}	✓	✓	✓	✓	0.125
1419	24416	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1420	24418	\begin{align*} 4 y^{\prime \prime \prime }-13 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1421	24424	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1422	24448	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+12 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1423	147	\begin{align*} y^{\prime \prime } x&=y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.126
1424	336	\begin{align*} y^{\left (5\right )}+5 y^{\prime \prime \prime \prime }-y&=17 \\ \end{align*}	✓	✓	✓	✓	0.126
1425	2140	\begin{align*} 4 y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+19 y^{\prime \prime }+32 y^{\prime }+12 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -3 \\ y^{\prime \prime }\left (0\right ) &= -{\frac {7}{2}} \\ y^{\prime \prime \prime }\left (0\right ) &= {\frac {31}{4}} \\ \end{align*}	✓	✓	✓	✓	0.126
1426	4149	\begin{align*} y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.126
1427	7802	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x}+1 \\ \end{align*}	✓	✓	✓	✓	0.126
1428	8532	\begin{align*} x^{3} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.126
1429	10787	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.126
1430	10810	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.126
1431	10870	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.126
1432	19450	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.126
1433	24422	\begin{align*} 10 y^{\prime \prime \prime }+y^{\prime \prime }-7 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.126
1434	24491	\begin{align*} y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.126
1435	532	\begin{align*} x^{\prime \prime }-x^{\prime }-2 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.127
1436	542	\begin{align*} x^{\prime \prime }-6 x^{\prime }+8 x&=2 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.127
1437	1780	\begin{align*} y^{\prime \prime } x -\left (4 x +1\right ) y^{\prime }+\left (2+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.127
1438	1783	\begin{align*} \left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.127
1439	2574	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.127
1440	2577	\begin{align*} \left (2 t +1\right ) y^{\prime \prime }-4 \left (1+t \right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.127
1441	7833	\begin{align*} x^{\prime \prime }+4 x^{\prime }+4 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.127
1442	8014	\begin{align*} y^{\prime \prime \prime \prime }-y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.127
1443	10817	\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.127
1444	10921	\begin{align*} x^{2} y^{\prime \prime }-2 x \left (2+x \right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.127
1445	11239	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
1446	16663	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=32 x \\ \end{align*}	✓	✓	✓	✓	0.127
1447	16666	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=6 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.127
1448	18983	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
1449	19449	\begin{align*} y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1}&=0 \\ \end{align*}	✓	✓	✓	✗	0.127
1450	22083	\begin{align*} y^{\prime \prime \prime }-y&=x \\ \end{align*}	✓	✓	✓	✓	0.127
1451	22652	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.127
1452	23404	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
1453	360	\begin{align*} y^{\prime \prime \prime \prime }-y&=5 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.128
1454	424	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.128
1455	537	\begin{align*} x^{\prime \prime }+9 x&=1 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.128
1456	538	\begin{align*} x^{\prime \prime }+4 x^{\prime }+3 x&=1 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.128
1457	7666	\begin{align*} x^{\prime \prime \prime }-x^{\prime \prime }+x^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.128
1458	10733	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.128
1459	11232	\begin{align*} x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.128
1460	11278	\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*}	✓	✓	✓	✗	0.128
1461	14124	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.128
1462	15138	\begin{align*} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.128
1463	16445	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.128
1464	19446	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.128
1465	23264	\begin{align*} y^{\prime \prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.128
1466	23349	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.128
1467	24447	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.128
1468	543	\begin{align*} x^{\prime \prime }-4 x&=3 t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.129
1469	8923	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.129
1470	12783	\begin{align*} y^{\prime \prime \prime \prime }+4 y-f&=0 \\ \end{align*}	✓	✓	✓	✓	0.129
1471	14129	\begin{align*} -2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.129
1472	14566	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.129
1473	21573	\begin{align*} y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+54 y^{\prime \prime }+108 y^{\prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.129
1474	22784	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.129
1475	23429	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.129
1476	24441	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.129
1477	24444	\begin{align*} 4 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }-2 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.129
1478	24481	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.129
1479	26572	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.129
1480	6602	\begin{align*} \sin \left (x \right )+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.130
1481	6679	\begin{align*} 2 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=a \\ \end{align*}	✓	✓	✓	✓	0.130
1482	8959	\begin{align*} x^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.130
1483	10367	\begin{align*} {y^{\prime \prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	0.130
1484	10888	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.130
1485	10895	\begin{align*} x^{2} y^{\prime \prime }+2 x \left (x -1\right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.130
1486	11189	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.130
1487	12797	\begin{align*} 2 y^{\prime \prime }+4 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.130
1488	18982	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }-4 y^{\prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.130
1489	21186	\begin{align*} x^{\prime \prime \prime \prime }-6 x^{\prime \prime }+5 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.130
1490	21195	\begin{align*} x^{\left (6\right )}-x^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.130
1491	21508	\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.130
1492	22619	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.130
1493	23762	\begin{align*} y^{\prime \prime }&=0 \\ y \left (0\right ) &= \operatorname {c1} \\ y \left (L \right ) &= \operatorname {c2} \\ \end{align*}	✓	✓	✓	✓	0.130
1494	25064	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.130
1495	1684	\begin{align*} \left (x +y\right )^{2}+\left (x +y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.131
1496	2579	\begin{align*} t y^{\prime \prime }-\left (1+3 t \right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.131
1497	7609	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-6 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.131
1498	13056	\begin{align*} 9 {y^{\prime \prime }}^{2} y^{\left (5\right )}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+40 y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.131
1499	14614	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -8 \\ y^{\prime \prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.131
1500	17561	\begin{align*} y^{\left (6\right )}+12 y^{\prime \prime \prime \prime }+48 y^{\prime \prime }+64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.131