2.3.17 Problems 1601 to 1700

Table 2.607: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1601	26530	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.138
1602	1784	\begin{align*} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.139
1603	10487	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.139
1604	14591	\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.139
1605	14616	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+6 y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.139
1606	15423	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.139
1607	15712	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.139
1608	16454	\begin{align*} x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.139
1609	17579	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.139
1610	19573	\begin{align*} y^{\prime }-y^{\prime \prime }+y^{\prime \prime \prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.139
1611	20084	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.139
1612	20085	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=x \,{\mathrm e}^{x}+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.139
1613	20358	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{2 x}+x^{2}+x \\ \end{align*}	✓	✓	✓	✓	0.139
1614	20491	\begin{align*} -8 y+7 x y^{\prime }-3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.139
1615	23019	\begin{align*} y^{\prime \prime }+3 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi \sqrt {3}}{6}\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.139
1616	23395	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.139
1617	23397	\begin{align*} x y^{\prime \prime \prime }-\frac {6 y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.139
1618	24553	\begin{align*} y^{\prime \prime \prime }-y&=x \\ \end{align*}	✓	✓	✓	✓	0.139
1619	26582	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.139
1620	6723	\begin{align*} \left (-x +a \right )^{3} \left (-x +b \right )^{3} y^{\prime \prime \prime }&=c y \\ \end{align*}	✗	✓	✓	✗	0.140
1621	10500	\begin{align*} x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.140
1622	14617	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }+13 y^{\prime }+30 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.140
1623	19842	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y&=x \\ \end{align*}	✓	✓	✓	✓	0.140
1624	19846	\begin{align*} y^{\prime \prime \prime \prime }-y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.140
1625	22637	\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+2 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.140
1626	23387	\begin{align*} 3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.140
1627	1467	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.141
1628	1777	\begin{align*} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.141
1629	1780	\begin{align*} x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.141
1630	2575	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.141
1631	3211	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.141
1632	6771	\begin{align*} -c^{4} y+16 \left (1+a -b \right ) \left (2+a -b \right ) y^{\prime \prime }+32 \left (2+a -b \right ) x y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.141
1633	15422	\begin{align*} y^{\left (5\right )}-4 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.141
1634	16451	\begin{align*} \left (x +1\right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.141
1635	16754	\begin{align*} y^{\prime \prime \prime }+8 y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.141
1636	19547	\begin{align*} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.141
1637	19837	\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.141
1638	19838	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x \\ \end{align*}	✓	✓	✓	✓	0.141
1639	20707	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.141
1640	22658	\begin{align*} y^{\prime \prime \prime \prime }+16 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.141
1641	26575	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=x^{2}+x \\ \end{align*}	✓	✓	✓	✓	0.141
1642	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*}	✓	✓	✓	✗	0.142
1643	16450	\begin{align*} y^{\prime \prime }-\left (4+\frac {2}{x}\right ) y^{\prime }+\left (4+\frac {4}{x}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.142
1644	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*}	✓	✓	✓	✓	0.142
1645	19607	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.142
1646	20050	\begin{align*} y^{\prime \prime \prime }-y&=\left (1+{\mathrm e}^{x}\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.142
1647	20095	\begin{align*} y+3 x y^{\prime }+9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.142
1648	21182	\begin{align*} x^{\prime \prime \prime }-x^{\prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.142
1649	22680	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.142
1650	23406	\begin{align*} x^{3} y^{\prime \prime }+\left (5 x^{3}-x^{2}\right ) y^{\prime }+2 \left (3 x^{3}-x^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.142
1651	26828	\begin{align*} 7 x^{\prime \prime }+14 x^{\prime }&=\left (t -\frac {1}{4}\right ) {\mathrm e}^{-2 t} \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= -{\frac {1}{56}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.142
1652	2573	\begin{align*} y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.143
1653	3208	\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.143
1654	3783	\begin{align*} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.143
1655	6774	\begin{align*} -k y-\left (-a b c +x \right ) y^{\prime }+\left (a b +a c +b c +a +b +c +1\right ) x y^{\prime \prime }+\left (3+a +b +c \right ) x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.143
1656	8014	\begin{align*} y^{\prime \prime \prime \prime }-y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.143
1657	12790	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y-32 \sin \left (2 x \right )+24 \cos \left (2 x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.143
1658	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*}	✓	✓	✓	✗	0.143
1659	23381	\begin{align*} 8 y-8 x y^{\prime }+4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.143
1660	27112	\(\left [\begin {array}{cc} 1 & 0 \\ -4 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.143
1661	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*}	✓	✓	✓	✗	0.144
1662	2140	\begin{align*} 4 y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+19 y^{\prime \prime }+32 y^{\prime }+12 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -3 \\ y^{\prime \prime }\left (0\right ) &= -{\frac {7}{2}} \\ y^{\prime \prime \prime }\left (0\right ) &= {\frac {31}{4}} \\ \end{align*}	✓	✓	✓	✓	0.144
1663	8008	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=x^{2}+4 x +8 \\ \end{align*}	✓	✓	✓	✓	0.144
1664	16730	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }&=8 \\ \end{align*}	✓	✓	✓	✓	0.144
1665	20072	\begin{align*} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=\cos \left (m x \right ) \\ \end{align*}	✓	✓	✓	✓	0.144
1666	23487	\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.144
1667	24015	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.144
1668	24525	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }&=12 \\ \end{align*}	✓	✓	✓	✓	0.144
1669	6785	\begin{align*} y^{\left (6\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.145
1670	7990	\begin{align*} y^{\left (5\right )}-4 y^{\prime \prime \prime }&=5 \\ \end{align*}	✓	✓	✓	✓	0.145
1671	10298	\begin{align*} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.145
1672	14592	\begin{align*} y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.145
1673	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*}	✓	✓	✓	✓	0.145
1674	24523	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=3 \\ \end{align*}	✓	✓	✓	✓	0.145
1675	24526	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }&=12 \\ \end{align*}	✓	✓	✓	✓	0.145
1676	24529	\begin{align*} y^{\prime \prime \prime }+9 y^{\prime \prime }&=11 \\ \end{align*}	✓	✓	✓	✓	0.145
1677	8928	\begin{align*} y^{\left (5\right )}+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.146
1678	11189	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.146
1679	14595	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+15 y^{\prime \prime }+20 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.146
1680	16445	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.146
1681	20579	\begin{align*} y^{\left (5\right )}-n^{2} y^{\prime \prime \prime }&={\mathrm e}^{a x} \\ \end{align*}	✓	✓	✓	✓	0.146
1682	23422	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.146
1683	3207	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{x}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.147
1684	14864	\begin{align*} x^{\prime }&=y+\frac {x \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \\ y^{\prime }&=-x+\frac {y \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \\ \end{align*}	✗	✗	✗	✗	0.147
1685	16813	\begin{align*} y^{\prime \prime }+y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.147
1686	17563	\begin{align*} y^{\prime \prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.147
1687	23390	\begin{align*} 2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-12 x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.147
1688	23424	\begin{align*} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.147
1689	1782	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1690	2724	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=t^{2} \\ \end{align*}	✓	✓	✓	✓	0.148
1691	3129	\begin{align*} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=\sin \left (k x \right ) \\ \end{align*}	✓	✓	✓	✓	0.148
1692	3784	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1693	3786	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}+4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1694	6772	\begin{align*} -a^{4} x^{3} y-x y^{\prime \prime }+2 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.148
1695	10759	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
1696	12721	\begin{align*} y^{\prime \prime \prime }+\operatorname {a2} y^{\prime \prime }+\operatorname {a1} y^{\prime }+\operatorname {a0} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1697	12761	\begin{align*} \left (-a^{2}+1\right ) x y^{\prime }+3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
1698	12812	\begin{align*} a y+12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
1699	16702	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=30 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.148
1700	17580	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.148