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	2575	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.092
1402	3617	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=8 \sin \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	0.092
1403	4008	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x \left (x -3\right )}-\frac {y}{x^{3} \left (x +3\right )}&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.092
1404	7986	\begin{align*} y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
1405	8957	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.092
1406	10299	\begin{align*} x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
1407	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*}	✓	✓	✓	✗	0.092
1408	10906	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
1409	10917	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
1410	10920	\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*}	✓	✓	✓	✗	0.092
1411	11158	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
1412	14104	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=x \\ \end{align*}	✓	✓	✓	✓	0.092
1413	14341	\begin{align*} x^{\prime \prime }-2 a x^{\prime }+a^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
1414	15297	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.092
1415	16150	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.092
1416	18187	\begin{align*} 5 y^{\prime \prime \prime }-7 y^{\prime \prime }&=3 \\ \end{align*}	✓	✓	✓	✓	0.092
1417	19181	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
1418	21937	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+12 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
1419	23632	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.092
1420	24035	\begin{align*} 6 x^{2} y^{\prime \prime }-5 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.092
1421	24461	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 9 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.092
1422	24462	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+2 y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= -6 \\ y^{\prime \prime \prime }\left (0\right ) &= 14 \\ \end{align*}	✓	✓	✓	✓	0.092
1423	319	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.093
1424	1321	\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.093
1425	2132	\begin{align*} 3 y^{\prime \prime \prime }-y^{\prime \prime }-7 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= {\frac {14}{5}} \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	0.093
1426	6643	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.093
1427	7237	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=y x +2 x \sqrt {-x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	0.093
1428	9281	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.093
1429	10739	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.093
1430	10874	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.093
1431	10888	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.093
1432	11159	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.093
1433	20069	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-6 y^{\prime }+8 y&=x \\ \end{align*}	✓	✓	✓	✓	0.093
1434	20355	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2&=0 \\ \end{align*}	✓	✓	✓	✓	0.093
1435	22083	\begin{align*} y^{\prime \prime \prime }-y&=x \\ \end{align*}	✓	✓	✓	✓	0.093
1436	22151	\begin{align*} y^{\prime \prime \prime \prime }&=5 x \\ \end{align*}	✓	✓	✓	✓	0.093
1437	22228	\begin{align*} y^{\prime }-5 y&={\mathrm e}^{5 x} \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.093
1438	22229	\begin{align*} y^{\prime }-5 y&=0 \\ y \left (\pi \right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.093
1439	22652	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.093
1440	24438	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -7 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.093
1441	8015	\begin{align*} y^{\prime \prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.094
1442	9129	\begin{align*} y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.094
1443	9290	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.094
1444	10300	\begin{align*} x y \sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.094
1445	10500	\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*}	✓	✓	✓	✗	0.094
1446	11845	\begin{align*} y \sqrt {1+{y^{\prime }}^{2}}-a y y^{\prime }-a x&=0 \\ \end{align*}	✗	✓	✓	✗	0.094
1447	14342	\begin{align*} x^{\prime \prime }-\frac {\left (t +2\right ) x^{\prime }}{t}+\frac {\left (t +2\right ) x}{t^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.094
1448	18164	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.094
1449	19826	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.094
1450	20052	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.094
1451	21182	\begin{align*} x^{\prime \prime \prime }-x^{\prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.094
1452	23407	\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.094
1453	23408	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.094
1454	23410	\begin{align*} x^{2} \left (1-\ln \left (x \right )\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.094
1455	23673	\begin{align*} x^{3} \left (-x^{2}+1\right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.094
1456	25644	\begin{align*} y^{\prime }&=-\sin \left (t \right )+\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.094
1457	424	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.095
1458	956	\begin{align*} y^{\prime \prime \prime }&=y \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.095
1459	1320	\begin{align*} t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
1460	1774	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
1461	2577	\begin{align*} \left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.095
1462	2715	\begin{align*} y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=0 \\ 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 \\ y^{\prime \prime \prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.095
1463	3687	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
1464	3714	\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }&=6 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.095
1465	3954	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= A \\ y^{\prime }\left (0\right ) &= B \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.095
1466	4366	\begin{align*} \left (2 x +3\right ) y^{\prime }&=y+\sqrt {2 x +3} \\ \end{align*}	✓	✓	✓	✓	0.095
1467	8008	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=x^{2}+4 x +8 \\ \end{align*}	✓	✓	✓	✓	0.095
1468	8956	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.095
1469	9282	\begin{align*} y^{\prime \prime } x +3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
1470	10282	\begin{align*} a \sin \left (x \right ) y x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
1471	10283	\begin{align*} f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi &=0 \\ \end{align*}	✓	✓	✓	✓	0.095
1472	10301	\begin{align*} \pi y \sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
1473	10487	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
1474	10893	\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*}	✓	✓	✓	✗	0.095
1475	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*}	✓	✓	✓	✗	0.095
1476	10919	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
1477	11247	\begin{align*} u^{\prime \prime }+2 u^{\prime }+u&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
1478	17548	\begin{align*} 5 y^{\prime \prime \prime }-15 y^{\prime }+11 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
1479	17561	\begin{align*} y^{\left (6\right )}+12 y^{\prime \prime \prime \prime }+48 y^{\prime \prime }+64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
1480	18169	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime }&=3 \\ \end{align*}	✓	✓	✓	✓	0.095
1481	19762	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
1482	21196	\begin{align*} x^{\left (6\right )}-64 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
1483	21507	\begin{align*} y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.095
1484	22161	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ y^{\prime \prime }\left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.095
1485	22736	\begin{align*} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.095
1486	23421	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.095
1487	23635	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.095
1488	24023	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=x^{2}-x \\ \end{align*}	✓	✓	✓	✓	0.095
1489	25640	\begin{align*} y^{\prime \prime }+y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.095
1490	25643	\begin{align*} y^{\prime }&=-\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.095
1491	308	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+100 y^{\prime }-500 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 10 \\ y^{\prime \prime }\left (0\right ) &= 250 \\ \end{align*}	✓	✓	✓	✓	0.096
1492	317	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.096
1493	318	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.096
1494	472	\begin{align*} x^{3} \left (1-x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.096
1495	929	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.096
1496	1319	\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.096
1497	2138	\begin{align*} 4 y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.096
1498	3720	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.096
1499	6615	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime \prime }&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.096
1500	6698	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.096