2.3.15 Problems 1401 to 1500

Table 2.603: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1401	10801	\begin{align*} x y^{\prime \prime }+2 y^{\prime }+4 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.122
1402	10821	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.122
1403	11159	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.122
1404	13039	\begin{align*} \left (y^{2}-{y^{\prime }}^{2} x^{2}+x^{2} y y^{\prime \prime }\right )^{2}-4 x y \left (x y^{\prime }-y\right )^{3}&=0 \\ \end{align*}	✗	✗	✓	✗	0.122
1405	16481	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.122
1406	18139	\begin{align*} y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-6 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.122
1407	20190	\begin{align*} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+3 \left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.122
1408	22115	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-4 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.122
1409	22118	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+32 y^{\prime \prime }-64 y^{\prime }+64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.122
1410	22496	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.122
1411	23491	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.122
1412	26823	\begin{align*} x^{\prime \prime }-2 x^{\prime }-3 x&=3 t^{2}+7 t +3 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.122
1413	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*}	✓	✓	✓	✗	0.123
1414	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*}	✓	✓	✓	✗	0.123
1415	12720	\begin{align*} y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-a^{3} y-{\mathrm e}^{a x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.123
1416	14588	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.123
1417	16448	\begin{align*} 2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.123
1418	19448	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.123
1419	22674	\begin{align*} y^{\left (5\right )}-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.123
1420	24035	\begin{align*} 6 x^{2} y^{\prime \prime }-5 x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.123
1421	11239	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.124
1422	11845	\begin{align*} y \sqrt {1+{y^{\prime }}^{2}}-a y y^{\prime }-a x&=0 \\ \end{align*}	✗	✓	✓	✗	0.124
1423	20357	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime }&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	0.124
1424	20665	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.124
1425	22679	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.124
1426	24574	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=4 \\ \end{align*}	✓	✓	✓	✓	0.124
1427	25923	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.124
1428	2107	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-7 y^{\prime \prime }-y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -6 \\ y^{\prime \prime }\left (0\right ) &= 10 \\ y^{\prime \prime \prime }\left (0\right ) &= -36 \\ \end{align*}	✓	✓	✓	✓	0.125
1429	6688	\begin{align*} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.125
1430	6706	\begin{align*} -2 \left (x^{2}+4\right ) y+x \left (x^{2}+8\right ) y^{\prime }-4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.125
1431	6732	\begin{align*} y+y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1432	6797	\begin{align*} 3 y^{2}+18 x y y^{\prime }+9 {y^{\prime }}^{2} x^{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*}	✗	✓	✓	✗	0.125
1433	7810	\begin{align*} y^{\prime \prime \prime \prime }&=5 x \\ \end{align*}	✓	✓	✓	✓	0.125
1434	7836	\begin{align*} x^{3} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.125
1435	11216	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1436	15690	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 5 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.125
1437	16447	\begin{align*} x^{2} y^{\prime \prime }-6 x y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1438	18983	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1439	19169	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1440	19451	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.125
1441	19453	\begin{align*} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.125
1442	20053	\begin{align*} y^{\prime \prime \prime }+8 y&=x^{4}+2 x +1 \\ \end{align*}	✓	✓	✓	✓	0.125
1443	20054	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.125
1444	20077	\begin{align*} y^{\prime \prime \prime \prime }-a^{4} y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.125
1445	21196	\begin{align*} x^{\left (6\right )}-64 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1446	23464	\begin{align*} y^{\prime \prime \prime \prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.125
1447	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*}	✓	✓	✓	✓	0.125
1448	26104	\begin{align*} y^{\prime \prime \prime }-y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.125
1449	3192	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.126
1450	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*}	✗	✓	✓	✗	0.126
1451	19569	\begin{align*} y^{\prime \prime \prime }-8 y&=16 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.126
1452	23405	\begin{align*} x^{2} y^{\prime \prime }+\left (2 x^{2}-x \right ) y^{\prime }-2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.126
1453	23421	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.126
1454	26546	\begin{align*} 3 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.126
1455	26827	\begin{align*} x^{\prime \prime }+x&=2 \,{\mathrm e}^{t} \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.126
1456	961	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
1457	3490	\begin{align*} y^{\prime \prime \prime }-12 y^{\prime }+16 y&=32 x -8 \\ \end{align*}	✓	✓	✓	✓	0.127
1458	10496	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
1459	10734	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
1460	11158	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
1461	16449	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
1462	19443	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
1463	19571	\begin{align*} y^{\prime \prime \prime }-\frac {y^{\prime }}{4}&=x \\ \end{align*}	✓	✓	✓	✓	0.127
1464	20363	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime }-6 y&={\mathrm e}^{2 x} \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✓	0.127
1465	23260	\begin{align*} y^{\prime \prime \prime }&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.127
1466	24479	\begin{align*} y^{\prime \prime \prime }+7 y^{\prime \prime }+19 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= -12 \\ \end{align*}	✓	✓	✓	✓	0.127
1467	26580	\begin{align*} y^{\prime \prime \prime }-y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.127
1468	26792	\begin{align*} y^{\prime \prime \prime }+\alpha y^{\prime \prime }+\beta y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
1469	332	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=3 x -1 \\ \end{align*}	✓	✓	✓	✓	0.128
1470	3152	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.128
1471	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*}	✗	✓	✓	✗	0.128
1472	6730	\begin{align*} a y+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.128
1473	10498	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.128
1474	15150	\begin{align*} 3 y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.128
1475	18132	\begin{align*} y^{\left (6\right )}+2 y^{\left (5\right )}+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.128
1476	19189	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.128
1477	19564	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=12 x -2 \\ \end{align*}	✓	✓	✓	✓	0.128
1478	23427	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.128
1479	24487	\begin{align*} 4 y+4 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.128
1480	24692	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.128
1481	26527	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }&=4 \\ \end{align*}	✓	✓	✓	✓	0.128
1482	26825	\begin{align*} x^{\prime \prime }+2 x^{\prime }&=6 t^{2}+6 t -3 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= -{\frac {3}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.128
1483	269	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.129
1484	957	\begin{align*} y^{\prime \prime \prime \prime }&=y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+2 y \\ 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 ) &= 15 \\ \end{align*}	✓	✓	✓	✓	0.129
1485	4454	\begin{align*} y^{\left (6\right )}-64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.129
1486	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*}	✗	✓	✓	✗	0.129
1487	7991	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.129
1488	10803	\begin{align*} x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.129
1489	12811	\begin{align*} 12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.129
1490	17566	\begin{align*} 24 y^{\prime \prime \prime }-26 y^{\prime \prime }+9 y^{\prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.129
1491	19036	\begin{align*} x_{1}^{\prime }&=5 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.129
1492	19164	\begin{align*} 2 x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+12 x y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.129
1493	19574	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.129
1494	20700	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.129
1495	24480	\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }-11 y^{\prime \prime }-8 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.129
1496	1785	\begin{align*} x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.130
1497	10491	\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*}	✓	✓	✓	✗	0.130
1498	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*}	✓	✓	✓	✗	0.130
1499	15421	\begin{align*} -a^{3} y+3 a^{2} y^{\prime }-3 a y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.130
1500	17565	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 8 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.130