2.3.16 Problems 1501 to 1600

Table 2.563: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1501	7328	\begin{align*} y^{\prime \prime } x -2 \left (x +1\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.096
1502	7330	\begin{align*} x^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.096
1503	9288	\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.096
1504	10473	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.096
1505	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*}	✓	✓	✓	✓	0.096
1506	12783	\begin{align*} y^{\prime \prime \prime \prime }+4 y-f&=0 \\ \end{align*}	✓	✓	✓	✓	0.096
1507	14102	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.096
1508	16452	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}-4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.096
1509	18752	\begin{align*} x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.096
1510	21181	\begin{align*} x^{\prime \prime \prime }-x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ x \left (\infty \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.096
1511	23630	\begin{align*} y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.096
1512	1196	\begin{align*} 2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.097
1513	1778	\begin{align*} x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.097
1514	2714	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.097
1515	3103	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-6 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.097
1516	3712	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=4 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.097
1517	6715	\begin{align*} -y+y^{\prime } x +4 x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.097
1518	8165	\begin{align*} \left (y-x \right ) y^{\prime }&=y-x \\ \end{align*}	✓	✓	✓	✓	0.097
1519	8934	\begin{align*} y^{\prime \prime \prime }-y&=x \\ \end{align*}	✓	✓	✓	✓	0.097
1520	10870	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.097
1521	16451	\begin{align*} \left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.097
1522	16758	\begin{align*} y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.097
1523	18469	\begin{align*} x^{\prime \prime }-2 x^{\prime }+2 x&=2 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.097
1524	19828	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.097
1525	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*}	✓	✓	✓	✓	0.097
1526	21879	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+3 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.097
1527	22619	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.097
1528	23310	\begin{align*} 6 y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+y^{\prime \prime }-7 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.097
1529	25633	\begin{align*} y^{\prime \prime }-y^{\prime }&=1 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.097
1530	321	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.098
1531	930	\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.098
1532	1773	\begin{align*} y^{\prime \prime } x +\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.098
1533	1779	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.098
1534	2579	\begin{align*} t y^{\prime \prime }-\left (1+3 t \right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.098
1535	6736	\begin{align*} y-2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.098
1536	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*}	✓	✓	✓	✗	0.098
1537	11246	\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.098
1538	14097	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.098
1539	14111	\begin{align*} y^{\prime \prime \prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.098
1540	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*}	✓	✓	✓	✓	0.098
1541	16454	\begin{align*} y^{\prime \prime } x +\left (2 x +2\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.098
1542	18886	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.098
1543	19529	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.098
1544	22664	\begin{align*} y a^{2} b^{2}+\left (a^{2}+b^{2}\right ) y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.098
1545	23264	\begin{align*} y^{\prime \prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.098
1546	23311	\begin{align*} 3 y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y^{\prime \prime }-2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.098
1547	23998	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }&={\mathrm e}^{x}+1 \\ \end{align*}	✓	✓	✓	✓	0.098
1548	24024	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }&={\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.098
1549	24435	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.098
1550	25249	\begin{align*} t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.098
1551	25258	\begin{align*} t y^{\prime \prime }+\left (-1+t \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.098
1552	25260	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.098
1553	341	\begin{align*} y^{\prime \prime \prime }-y&={\mathrm e}^{x}+7 \\ \end{align*}	✓	✓	✓	✓	0.099
1554	1324	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.099
1555	1775	\begin{align*} x^{2} \ln \left (x \right )^{2} y^{\prime \prime }-2 x \ln \left (x \right ) y^{\prime }+\left (2+\ln \left (x \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.099
1556	3641	\begin{align*} y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1557	3708	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1558	3713	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y&=24 \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.099
1559	3729	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=4 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.099
1560	5762	\begin{align*} a \,{\mathrm e}^{b x} y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.099
1561	6632	\begin{align*} y^{\prime }+2 y^{\prime \prime }+y^{\prime \prime \prime }&=\left (x -1\right ) x \\ \end{align*}	✓	✓	✓	✓	0.099
1562	6695	\begin{align*} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1563	6727	\begin{align*} 4 \,{\mathrm e}^{-x} \cos \left (x \right )+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1564	6729	\begin{align*} y^{\prime \prime \prime \prime }&={\mathrm e}^{x} \cos \left (x \right )+y \\ \end{align*}	✓	✓	✓	✓	0.099
1565	7060	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1566	7329	\begin{align*} 3 y^{\prime \prime } x -2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.099
1567	7616	\begin{align*} 3 y^{\prime \prime \prime }+18 y^{\prime \prime }+13 y^{\prime }-19 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1568	7717	\begin{align*} -y+y^{\prime } x&=x^{3}+3 x^{2}-2 x \\ \end{align*}	✓	✓	✓	✓	0.099
1569	9103	\begin{align*} y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.099
1570	9284	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.099
1571	9446	\begin{align*} L i^{\prime }+R i&=E_{0} \delta \left (t \right ) \\ i \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.099
1572	9600	\begin{align*} y+2 y^{\prime }&=0 \\ y \left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.099
1573	10819	\begin{align*} u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u&=0 \\ \end{align*}	✓	✓	✓	✗	0.099
1574	10854	\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.099
1575	10924	\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*}	✓	✓	✓	✗	0.099
1576	14566	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1577	16450	\begin{align*} y^{\prime \prime }-\left (4+\frac {2}{x}\right ) y^{\prime }+\left (4+\frac {4}{x}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.099
1578	16456	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1579	16480	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 8 \\ y^{\prime \prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.099
1580	18369	\begin{align*} 2 y^{\prime \prime }+4 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.099
1581	18461	\begin{align*} x^{\prime \prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.099
1582	18465	\begin{align*} x^{\prime \prime }+x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.099
1583	19827	\begin{align*} 2 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1584	20078	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.099
1585	20356	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.099
1586	21190	\begin{align*} x^{\prime \prime \prime \prime }-8 x^{\prime \prime \prime }+23 x^{\prime \prime }-28 x^{\prime }+12 x&=0 \\ x \left (\infty \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.099
1587	23260	\begin{align*} y^{\prime \prime \prime }&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.099
1588	23426	\begin{align*} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.099
1589	23486	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.099
1590	23637	\begin{align*} y^{\prime \prime }-4 y&=-3 \,{\mathrm e}^{t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.099
1591	24617	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=6 x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.099
1592	5510	\begin{align*} x^{2} {y^{\prime }}^{2}+4 x y^{\prime } y-5 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1593	6699	\begin{align*} 2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1594	6703	\begin{align*} -8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1595	7326	\begin{align*} \left (-x +2\right ) x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.100
1596	9023	\begin{align*} x^{2}+y x +\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1597	9286	\begin{align*} y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1}&=0 \\ \end{align*}	✓	✓	✓	✗	0.100
1598	11239	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1599	15079	\begin{align*} x^{\left (6\right )}-x^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.100
1600	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*}	✓	✓	✓	✗	0.100