2.3.17 Problems 1601 to 1700

Table 2.565: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1601	20359	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.100
1602	21415	\begin{align*} y^{2}+x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1603	23145	\begin{align*} y^{\prime } y&=x^{3} y^{2}+x y^{2} \\ \end{align*}	✓	✓	✓	✓	0.100
1604	23522	\begin{align*} e i u^{\prime \prime \prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.100
1605	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*}	✓	✓	✓	✓	0.100
1606	24776	\begin{align*} x {y^{\prime }}^{2}-2 \left (2 x +y\right ) y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1607	2574	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.101
1608	3709	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1609	6700	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1610	7331	\begin{align*} x \left (x +1\right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.101
1611	8014	\begin{align*} y^{\prime \prime \prime \prime }-y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.101
1612	9280	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1613	10503	\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*}	✓	✓	✓	✗	0.101
1614	10895	\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*}	✓	✓	✓	✗	0.101
1615	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*}	✓	✓	✓	✗	0.101
1616	16577	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1617	16702	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=30 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.101
1618	16730	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }&=8 \\ \end{align*}	✓	✓	✓	✓	0.101
1619	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*}	✓	✓	✓	✓	0.101
1620	19830	\begin{align*} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1621	21202	\begin{align*} x^{\prime \prime \prime \prime }-3 x^{\prime \prime \prime }+2 x^{\prime }-5 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1622	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*}	✓	✓	✓	✓	0.101
1623	22478	\begin{align*} y^{\prime \prime \prime \prime }&=\frac {x}{3} \\ \end{align*}	✓	✓	✓	✓	0.101
1624	23405	\begin{align*} x^{2} y^{\prime \prime }+\left (2 x^{2}-x \right ) y^{\prime }-2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.101
1625	23480	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.101
1626	24055	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=2 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -{\frac {1}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.101
1627	24555	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y&=3 \,{\mathrm e}^{-x}-4 x -6 \\ \end{align*}	✓	✓	✓	✓	0.101
1628	25252	\begin{align*} t^{2} y^{\prime \prime }+2 t y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1629	25690	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 y^{\prime } x -78 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1630	1322	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.102
1631	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*}	✓	✓	✓	✓	0.102
1632	3798	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.102
1633	4164	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1634	4450	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1635	6669	\begin{align*} 18 \,{\mathrm e}^{x}-3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1636	8050	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.102
1637	8139	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.102
1638	8933	\begin{align*} y^{\prime \prime \prime \prime }-k^{4} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.102
1639	9402	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.102
1640	9527	\begin{align*} x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.102
1641	10921	\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*}	✓	✓	✓	✗	0.102
1642	14124	\begin{align*} y-2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.102
1643	14343	\begin{align*} t^{2} x^{\prime \prime }+t x^{\prime }+\left (t^{2}-\frac {1}{4}\right ) x&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1644	15091	\begin{align*} y^{\prime \prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.102
1645	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*}	✓	✓	✓	✓	0.102
1646	16576	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1647	18188	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }&=-6 \\ \end{align*}	✓	✓	✓	✓	0.102
1648	18468	\begin{align*} x^{\prime \prime }+6 x^{\prime }&=12 t +2 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.102
1649	18885	\begin{align*} 9 y^{\prime \prime }+12 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.102
1650	18897	\begin{align*} y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.102
1651	20106	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1652	20665	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1653	22781	\begin{align*} x^{\prime \prime \prime \prime }-x&=8 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.102
1654	23634	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.102
1655	23994	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime }&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.102
1656	313	\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*}	✓	✓	✓	✓	0.103
1657	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*}	✓	✓	✓	✗	0.103
1658	3765	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=12 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.103
1659	6705	\begin{align*} 8 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
1660	6749	\begin{align*} -2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.103
1661	7190	\begin{align*} x^{3} y^{\prime \prime }+y&=x^{{3}/{2}} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.103
1662	10817	\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.103
1663	12727	\begin{align*} 18 \,{\mathrm e}^{x}-3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
1664	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*}	✓	✓	✓	✓	0.103
1665	16578	\begin{align*} x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 y^{\prime } x -18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
1666	18163	\begin{align*} y^{\prime \prime \prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.103
1667	19533	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
1668	19541	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
1669	20053	\begin{align*} y^{\prime \prime \prime }+8 y&=x^{4}+2 x +1 \\ \end{align*}	✓	✓	✓	✓	0.103
1670	21505	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
1671	23429	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.103
1672	23430	\begin{align*} y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.103
1673	24037	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.103
1674	24463	\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 ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= -5 \\ y^{\prime \prime \prime }\left (0\right ) &= 9 \\ \end{align*}	✓	✓	✓	✓	0.103
1675	24618	\begin{align*} y^{\prime \prime \prime }+12 y^{\prime \prime }+48 y^{\prime }+64 y&=8 x \,{\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.103
1676	24663	\begin{align*} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }-8 y^{\prime \prime }&=48 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.103
1677	25155	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.103
1678	25250	\begin{align*} t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.103
1679	25610	\begin{align*} y^{\prime \prime \prime \prime }-y&=t^{3} {\mathrm e}^{5 t} \\ \end{align*}	✓	✓	✓	✓	0.103
1680	320	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
1681	6702	\begin{align*} 2 y-2 y^{\prime } x +3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
1682	6731	\begin{align*} y^{\prime \prime \prime \prime }&=x^{3}+a^{4} y \\ \end{align*}	✓	✓	✓	✓	0.104
1683	14126	\begin{align*} y^{\prime }+2 y^{\prime \prime }+y^{\prime \prime \prime }&=x^{2}-x \\ \end{align*}	✓	✓	✓	✓	0.104
1684	17372	\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
1685	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*}	✓	✓	✓	✓	0.104
1686	17571	\begin{align*} y^{\left (5\right )}+8 y^{\prime \prime \prime \prime }&=0 \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 48 \\ y^{\prime \prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.104
1687	18189	\begin{align*} 3 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.104
1688	20104	\begin{align*} -8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
1689	20139	\begin{align*} y^{\left (5\right )}-m^{2} y^{\prime \prime \prime }&={\mathrm e}^{a x} \\ \end{align*}	✓	✓	✓	✓	0.104
1690	23409	\begin{align*} y^{\prime \prime } x +\left (x -1\right ) y^{\prime }+\left (3-12 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.104
1691	23640	\begin{align*} y^{\prime \prime }-9 y^{\prime }+18 y&=54 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.104
1692	24015	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.104
1693	24619	\begin{align*} y^{\prime \prime \prime }+9 y^{\prime \prime }+27 y^{\prime }+27 y&=15 x^{2} {\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.104
1694	24775	\begin{align*} x^{2} {y^{\prime }}^{2}-7 x y^{\prime } y+12 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.104
1695	25253	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.104
1696	266	\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.105
1697	933	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.105
1698	1785	\begin{align*} y^{\prime \prime } x -\left (4 x +1\right ) y^{\prime }+\left (2+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.105
1699	2680	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{t} t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.105
1700	3721	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=9 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.105