2.3.15 Problems 1401 to 1500

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

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1401	11239	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1402	11245	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1403	11248	\begin{align*} u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u&=0 \\ \end{align*}	✓	✓	✓	✗	0.102
1404	11301	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1405	12783	\begin{align*} y^{\prime \prime \prime \prime }+4 y-f&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1406	14708	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1407	14748	\begin{align*} \left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.102
1408	15091	\begin{align*} y^{\prime \prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.102
1409	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*}	✓	✓	✓	✓	0.102
1410	17543	\begin{align*} y^{\prime \prime \prime \prime }+16 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1411	17555	\begin{align*} y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1412	18170	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }&=4 \\ \end{align*}	✓	✓	✓	✓	0.102
1413	19573	\begin{align*} y^{\prime }-y^{\prime \prime }+y^{\prime \prime \prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.102
1414	20104	\begin{align*} -8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1415	20193	\begin{align*} y^{\prime \prime } x -\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.102
1416	21280	\begin{align*} x^{\prime }+x&={\mathrm e}^{t} \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.102
1417	22746	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=x^{5}+1 \\ \end{align*}	✓	✓	✓	✓	0.102
1418	23260	\begin{align*} y^{\prime \prime \prime }&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.102
1419	24452	\begin{align*} 4 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }-23 y^{\prime \prime }+12 y^{\prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1420	3180	\begin{align*} y^{\prime \prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.103
1421	6615	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime \prime }&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.103
1422	6643	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.103
1423	9108	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=2 x \csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.103
1424	10912	\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*}	✓	✓	✓	✗	0.103
1425	10917	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
1426	11232	\begin{align*} x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
1427	17746	\begin{align*} 9 y^{\prime \prime \prime }+36 y^{\prime \prime }+40 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
1428	18367	\begin{align*} y^{\prime \prime \prime \prime }-\lambda ^{4} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime \prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.103
1429	18461	\begin{align*} x^{\prime \prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.103
1430	25142	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.103
1431	25249	\begin{align*} t^{2} y^{\prime \prime }-3 y^{\prime } t +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
1432	25258	\begin{align*} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.103
1433	3614	\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {4}{\left (x^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	0.104
1434	6632	\begin{align*} y^{\prime }+2 y^{\prime \prime }+y^{\prime \prime \prime }&=\left (x -1\right ) x \\ \end{align*}	✓	✓	✓	✓	0.104
1435	7231	\begin{align*} y^{\prime }+2 y x -x \,{\mathrm e}^{-x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
1436	10541	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.104
1437	10848	\begin{align*} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.104
1438	10851	\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*}	✓	✓	✓	✗	0.104
1439	10888	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
1440	11102	\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
1441	12727	\begin{align*} 18 \,{\mathrm e}^{x}-3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
1442	13626	\begin{align*} \left (A x y+B \,x^{2}+x k \right ) y^{\prime }&=A y^{2}+B x y+\left (A b +k \right ) y+B b x +b k \\ \end{align*}	✓	✓	✓	✓	0.104
1443	14126	\begin{align*} y^{\prime }+2 y^{\prime \prime }+y^{\prime \prime \prime }&=x^{2}-x \\ \end{align*}	✓	✓	✓	✓	0.104
1444	17556	\begin{align*} y^{\left (5\right )}+4 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
1445	17747	\begin{align*} 9 y^{\prime \prime \prime }+12 y^{\prime \prime }+13 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
1446	18190	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=1 \\ \end{align*}	✓	✓	✓	✓	0.104
1447	19570	\begin{align*} y^{\prime \prime \prime \prime }-y&=-x^{3}+1 \\ \end{align*}	✓	✓	✓	✓	0.104
1448	21203	\begin{align*} t^{3} x^{\prime \prime \prime }+4 t^{2} x^{\prime \prime }+3 t x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
1449	23311	\begin{align*} 3 y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y^{\prime \prime }-2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
1450	24427	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-13 y^{\prime \prime }+38 y^{\prime }-24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
1451	25060	\begin{align*} y^{\prime }-4 y&={\mathrm e}^{4 t} \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.104
1452	1324	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.105
1453	1326	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
1454	2206	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&={\mathrm e}^{2 x} \left (10+3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.105
1455	3611	\begin{align*} x^{2} y^{\prime }-4 y x&=x^{7} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.105
1456	8934	\begin{align*} y^{\prime \prime \prime }-y&=x \\ \end{align*}	✓	✓	✓	✓	0.105
1457	10900	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.105
1458	14951	\begin{align*} t^{2} y^{\prime \prime }-\left (t^{2}+2 t \right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.105
1459	18168	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.105
1460	18571	\begin{align*} 2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
1461	20065	\begin{align*} y^{\prime }+2 y^{\prime \prime }+y^{\prime \prime \prime }&={\mathrm e}^{2 x}+x^{2}+x \\ \end{align*}	✓	✓	✓	✓	0.105
1462	20079	\begin{align*} y^{\prime \prime \prime \prime }-y&={\mathrm e}^{x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.105
1463	24426	\begin{align*} 4 y^{\prime \prime \prime \prime }-15 y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
1464	24482	\begin{align*} y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
1465	24509	\begin{align*} -4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
1466	25253	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.105
1467	25262	\begin{align*} t^{2} y^{\prime \prime }-2 y^{\prime } t +\left (t^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
1468	1322	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.106
1469	2315	\begin{align*} \frac {y}{t}+y^{\prime }&=\cos \left (t \right )+\frac {\sin \left (t \right )}{t} \\ \end{align*}	✓	✓	✓	✓	0.106
1470	6627	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.106
1471	8959	\begin{align*} x^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.106
1472	9101	\begin{align*} y^{\prime }+y x&=x \\ \end{align*}	✓	✓	✓	✓	0.106
1473	10803	\begin{align*} x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.106
1474	10854	\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.106
1475	14124	\begin{align*} y-2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.106
1476	14952	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.106
1477	18171	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.106
1478	19608	\begin{align*} y^{\prime \prime }+\frac {n y^{\prime }}{x^{2}}+\frac {q y}{x^{3}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.106
1479	24498	\begin{align*} 4 y^{\prime \prime \prime }+28 y^{\prime \prime }+61 y^{\prime }+37 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.106
1480	24499	\begin{align*} 4 y^{\prime \prime \prime }+12 y^{\prime \prime }+13 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.106
1481	24505	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-4 y^{\prime \prime }-4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.106
1482	24508	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.106
1483	25156	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.106
1484	25160	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.106
1485	317	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.107
1486	10819	\begin{align*} u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u&=0 \\ \end{align*}	✓	✓	✓	✗	0.107
1487	10850	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.107
1488	14615	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+9 y^{\prime }-5 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.107
1489	17558	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.107
1490	19814	\begin{align*} \left (x^{2}-2 y x \right ) y^{\prime }+x^{2}-3 y x +2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.107
1491	20077	\begin{align*} y^{\prime \prime \prime \prime }-a^{4} y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.107
1492	22510	\begin{align*} \left (y^{2}+2 y x \right ) \left (x^{2}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.107
1493	22781	\begin{align*} x^{\prime \prime \prime \prime }-x&=8 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.107
1494	23952	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.107
1495	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.	✓	✓	✓	✓	0.107
1496	25162	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=t \\ \end{align*}	✓	✓	✓	✓	0.107
1497	7986	\begin{align*} y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.108
1498	14566	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.108
1499	14697	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.108
1500	15196	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.108