2.3.17 Problems 1601 to 1700

Table 2.577: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1601	2139	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-8 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -2 \\ y^{\prime \prime }\left (0\right ) &= 6 \\ y^{\prime \prime \prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.123
1602	8139	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.123
1603	10550	\begin{align*} 2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (1-2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.123
1604	10994	\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.123
1605	15203	\begin{align*} 4 y^{\prime \prime }+40 y^{\prime }+101 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.123
1606	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*}	✓	✓	✓	✓	0.123
1607	16998	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.123
1608	22640	\begin{align*} y^{\prime \prime \prime \prime }-20 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.123
1609	22667	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.123
1610	24524	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+4 y&=14 \\ \end{align*}	✓	✓	✓	✓	0.123
1611	368	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=2 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.124
1612	2795	\begin{align*} x^{\prime }&=x-y^{2} \\ y^{\prime }&=x^{2}-y \\ z^{\prime }&={\mathrm e}^{z}-x \\ \end{align*}	✗	✓	✓	✗	0.124
1613	18260	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x}-1 \\ \end{align*}	✓	✓	✓	✓	0.124
1614	18261	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime }&=x +2 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.124
1615	25258	\begin{align*} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.124
1616	366	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.125
1617	382	\begin{align*} y^{\prime \prime }+y&=2 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.125
1618	543	\begin{align*} x^{\prime \prime }-4 x&=3 t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.125
1619	1783	\begin{align*} \left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.125
1620	2136	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= -2 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.125
1621	3128	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.125
1622	3196	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.125
1623	3208	\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.125
1624	10245	\begin{align*} y^{\prime }&=\frac {1}{x} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.125
1625	10499	\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*}	✓	✓	✓	✗	0.125
1626	10622	\begin{align*} \left (1-x \right )^{2} x^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.125
1627	10809	\begin{align*} x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1628	10811	\begin{align*} y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.125
1629	10822	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.125
1630	15096	\begin{align*} y^{\left (6\right )}-3 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.125
1631	15198	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.125
1632	18752	\begin{align*} x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1633	19444	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1634	22083	\begin{align*} y^{\prime \prime \prime }-y&=x \\ \end{align*}	✓	✓	✓	✓	0.125
1635	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*}	✓	✓	✓	✓	0.125
1636	22672	\begin{align*} s^{\prime \prime \prime \prime }+2 s^{\prime \prime }-8 s&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1637	24049	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=16 \,{\mathrm e}^{2 x} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.125
1638	24058	\begin{align*} y^{\prime \prime }+y&=x^{2} \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi ^{2}}{4} \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 2 \pi \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.125
1639	24534	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }&=12 \\ \end{align*}	✓	✓	✓	✓	0.125
1640	24611	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.125
1641	542	\begin{align*} x^{\prime \prime }-6 x^{\prime }+8 x&=2 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.126
1642	2137	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+7 y^{\prime \prime }+6 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= -8 \\ y^{\prime \prime }\left (0\right ) &= -14 \\ y^{\prime \prime \prime }\left (0\right ) &= -62 \\ \end{align*}	✓	✓	✓	✓	0.126
1643	2452	\begin{align*} t^{3} y^{\prime \prime }-y^{\prime } t -\left (t^{2}+\frac {5}{4}\right ) y&=0 \\ \end{align*} Series expansion around \(t=0\).	✗	✗	✓	✗	0.126
1644	8934	\begin{align*} y^{\prime \prime \prime }-y&=x \\ \end{align*}	✓	✓	✓	✓	0.126
1645	10779	\begin{align*} 2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.126
1646	11208	\begin{align*} 2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.126
1647	13181	\(\left [\begin {array}{cc} 3 & -1 \\ 1 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.126
1648	15193	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.126
1649	18751	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.126
1650	21804	\begin{align*} \left (x -y\right ) y^{\prime }&=-x +y \\ \end{align*}	✓	✓	✓	✓	0.126
1651	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*}	✓	✓	✓	✓	0.126
1652	24530	\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime }&=11 \\ \end{align*}	✓	✓	✓	✓	0.126
1653	24533	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }&=12 \\ \end{align*}	✓	✓	✓	✓	0.126
1654	325	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=3 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.127
1655	375	\begin{align*} y^{\prime \prime }-4 y&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.127
1656	538	\begin{align*} x^{\prime \prime }+4 x^{\prime }+3 x&=1 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.127
1657	1780	\begin{align*} y^{\prime \prime } x -\left (4 x +1\right ) y^{\prime }+\left (2+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.127
1658	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 \(x=0\).	✗	✗	✓	✗	0.127
1659	7618	\begin{align*} y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+15 y^{\prime \prime }+4 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
1660	10497	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
1661	11302	\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.127
1662	17558	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
1663	19453	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.127
1664	20356	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.127
1665	20707	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.127
1666	24017	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{x} \sin \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.127
1667	24683	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=12 x -2 \\ \end{align*}	✓	✓	✓	✓	0.127
1668	25913	\begin{align*} 2 y^{\prime \prime }-9 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
1669	424	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.128
1670	537	\begin{align*} x^{\prime \prime }+9 x&=1 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.128
1671	3201	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-2 x} \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.128
1672	10621	\begin{align*} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (3+2 x \right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.128
1673	10820	\begin{align*} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.128
1674	10903	\begin{align*} y^{\prime \prime } x -\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.128
1675	11036	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.128
1676	11099	\begin{align*} y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.128
1677	11172	\begin{align*} 3 y^{\prime \prime } x -2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.128
1678	15194	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.128
1679	16447	\begin{align*} x^{2} y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.128
1680	18179	\begin{align*} y^{\prime \prime \prime \prime }-2 n^{2} y^{\prime \prime }+n^{4} y&=\cos \left (x n +\alpha \right ) \\ \end{align*}	✓	✓	✓	✓	0.128
1681	19565	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=9 x^{2}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	0.128
1682	20139	\begin{align*} y^{\left (5\right )}-m^{2} y^{\prime \prime \prime }&={\mathrm e}^{a x} \\ \end{align*}	✓	✓	✓	✓	0.128
1683	20195	\begin{align*} \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.128
1684	20358	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{2 x}+x^{2}+x \\ \end{align*}	✓	✓	✓	✓	0.128
1685	25260	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.128
1686	3714	\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }&=6 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.129
1687	9290	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.129
1688	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*}	✓	✓	✓	✗	0.129
1689	10618	\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.129
1690	10658	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.129
1691	11255	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.129
1692	11260	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.129
1693	16449	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.129
1694	17568	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= 4 \\ y^{\prime \prime \prime }\left (0\right ) &= -24 \\ \end{align*}	✓	✓	✓	✓	0.129
1695	18101	\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.129
1696	22649	\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*}	✓	✓	✓	✓	0.129
1697	343	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime }&={\mathrm e}^{x}+2 x^{2}-5 \\ \end{align*}	✓	✓	✓	✓	0.130
1698	1782	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.130
1699	9286	\begin{align*} y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1}&=0 \\ \end{align*}	✓	✓	✓	✗	0.130
1700	10620	\begin{align*} x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (-3 x +4\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.130