2.3.16 Problems 1501 to 1600

Table 2.581: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1501	20146	\begin{align*} x^{4} y^{\prime \prime }+y^{\prime } x +y&=\frac {1}{x} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.131
1502	21193	\begin{align*} x^{\left (5\right )}+x^{\prime \prime \prime \prime }-x^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.131
1503	22119	\begin{align*} y^{\left (6\right )}-5 y^{\prime \prime \prime \prime }+16 y^{\prime \prime \prime }-16 y^{\prime }-32 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.131
1504	23350	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.131
1505	24450	\begin{align*} y^{\left (5\right )}-16 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.131
1506	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*}	✓	✓	✓	✓	0.131
1507	553	\begin{align*} x^{\prime \prime }+9 x&=6 \cos \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.132
1508	2572	\begin{align*} y^{\prime \prime }-\frac {2 \left (1+t \right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1}&=0 \\ \end{align*}	✓	✓	✓	✗	0.132
1509	2658	\begin{align*} t^{2} y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y&=0 \\ \end{align*} Series expansion around \(t=0\).	✗	✗	✓	✗	0.132
1510	10710	\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*}	✓	✓	✓	✗	0.132
1511	10900	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (3+2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.132
1512	16664	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.132
1513	19444	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.132
1514	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*}	✓	✓	✓	✓	0.132
1515	22736	\begin{align*} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.132
1516	24492	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+5 y^{\prime \prime }+5 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.132
1517	26532	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.132
1518	1782	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.133
1519	4450	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.133
1520	7820	\begin{align*} 2 y+y^{\prime }&=2 \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.133
1521	8960	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.133
1522	10734	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.133
1523	14113	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=4+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.133
1524	16133	\begin{align*} y^{\prime \prime }-4 y&={\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.133
1525	23992	\begin{align*} y^{\prime \prime \prime }-y&=1 \\ \end{align*}	✓	✓	✓	✓	0.133
1526	2207	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y&=-{\mathrm e}^{3 x} \left (17 x^{2}+67 x +9\right ) \\ \end{align*}	✓	✓	✓	✓	0.134
1527	10854	\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.134
1528	11159	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.134
1529	12827	\begin{align*} y^{\left (5\right )}+a y^{\prime \prime \prime \prime }-f&=0 \\ \end{align*}	✓	✓	✓	✓	0.134
1530	14341	\begin{align*} x^{\prime \prime }-2 a x^{\prime }+a^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	0.134
1531	14774	\begin{align*} x^{\prime }+y^{\prime }-x-2 y&=2 \,{\mathrm e}^{t} \\ x^{\prime }+y^{\prime }-3 x-4 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✗	0.134
1532	23430	\begin{align*} y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.134
1533	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*}	✓	✓	✓	✓	0.134
1534	567	\begin{align*} x^{\prime \prime }+2 x^{\prime }+x&=t +\delta \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.135
1535	2153	\begin{align*} 4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y&=-{\mathrm e}^{-2 x} \left (1-15 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.135
1536	2162	\begin{align*} 4 y^{\prime \prime \prime \prime }-11 y^{\prime \prime }-9 y^{\prime }-2 y&=-{\mathrm e}^{x} \left (1-6 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.135
1537	8953	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.135
1538	16538	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 6 \\ y^{\prime \prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.135
1539	16665	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=30 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.135
1540	19448	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.135
1541	23260	\begin{align*} y^{\prime \prime \prime }&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.135
1542	23408	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.135
1543	23421	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.135
1544	23486	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.135
1545	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*}	✓	✓	✓	✓	0.135
1546	24426	\begin{align*} 4 y^{\prime \prime \prime \prime }-15 y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.135
1547	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*}	✓	✓	✓	✓	0.135
1548	26457	\begin{align*} x y^{\prime \prime \prime }+y^{\prime \prime }-x -1&=0 \\ \end{align*}	✓	✓	✓	✓	0.135
1549	531	\begin{align*} x^{\prime \prime }+9 x&=0 \\ x \left (0\right ) &= 3 \\ x^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.136
1550	7353	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+13 y^{\prime \prime }-18 y^{\prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.136
1551	16457	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.136
1552	16790	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.136
1553	19451	\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.136
1554	19453	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.136
1555	21506	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.136
1556	22260	\begin{align*} y^{\prime }+z&=t \\ z^{\prime }-y&=0 \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ z \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.136
1557	24454	\begin{align*} 27 y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+8 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.136
1558	1467	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.137
1559	11121	\begin{align*} x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.137
1560	16661	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=10 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.137
1561	22781	\begin{align*} x^{\prime \prime \prime \prime }-x&=8 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.137
1562	23407	\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.137
1563	459	\begin{align*} x^{2} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.138
1564	16151	\begin{align*} y^{\prime \prime }+16 y&=t \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.138
1565	19036	\begin{align*} x_{1}^{\prime }&=5 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.138
1566	19842	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y&=x \\ \end{align*}	✓	✓	✓	✓	0.138
1567	23410	\begin{align*} x^{2} \left (1-\ln \left (x \right )\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.138
1568	26441	\begin{align*} y^{\prime \prime \prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.138
1569	2154	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=-{\mathrm e}^{x} \left (7+6 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.139
1570	2165	\begin{align*} 2 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-5 y^{\prime }-2 y&=18 \,{\mathrm e}^{x} \left (5+2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.139
1571	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*}	✓	✓	✓	✓	0.139
1572	8207	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 y^{\prime } x -78 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.139
1573	11216	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.139
1574	14340	\begin{align*} x^{\prime \prime }-t x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✗	0.139
1575	16148	\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.139
1576	16541	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+9 y^{\prime \prime }+9 y^{\prime }&=0 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 6 \\ y^{\prime \prime \prime }\left (0\right ) &= -60 \\ \end{align*}	✓	✓	✓	✓	0.139
1577	21505	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.139
1578	22132	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=2 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.139
1579	322	\begin{align*} y^{\prime \prime }+16 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.140
1580	559	\begin{align*} t x^{\prime \prime }-2 x^{\prime }+t x&=0 \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.140
1581	10759	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.140
1582	15678	\begin{align*} y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.140
1583	18366	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ y \left (0\right ) &= -1 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.140
1584	21202	\begin{align*} x^{\prime \prime \prime \prime }-3 x^{\prime \prime \prime }+2 x^{\prime }-5 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.140
1585	23464	\begin{align*} y^{\prime \prime \prime \prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.140
1586	24449	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.140
1587	375	\begin{align*} y^{\prime \prime }-4 y&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.141
1588	382	\begin{align*} y^{\prime \prime }+y&=2 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.141
1589	2576	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.141
1590	13925	\begin{align*} y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.141
1591	14123	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=-3 \,{\mathrm e}^{2 x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.141
1592	14569	\begin{align*} \left (x^{2}-x +1\right ) y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.141
1593	14952	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.141
1594	16455	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.141
1595	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*}	✓	✓	✓	✓	0.141
1596	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*}	✓	✓	✓	✓	0.141
1597	22181	\begin{align*} \left (x +1\right )^{3} y^{\prime \prime }+\left (x^{2}-1\right ) \left (x +1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=-1\).	✗	✗	✓	✗	0.141
1598	24036	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.141
1599	24478	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+10 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.141
1600	25078	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=4 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.141