2.3.17 Problems 1601 to 1700

Table 2.583: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1601	366	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.142
1602	2191	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+8 y^{\prime \prime }+8 y^{\prime }+4 y&=-2 \,{\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.142
1603	6766	\begin{align*} 2 y^{\prime \prime }+4 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.142
1604	8955	\begin{align*} y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.142
1605	14568	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.142
1606	17012	\begin{align*} y^{\prime \prime \prime \prime }+\frac {25 y^{\prime \prime }}{2}-5 y^{\prime }+\frac {629 y}{16}&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ y^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.142
1607	19037	\begin{align*} x_{1}^{\prime }&=-x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.142
1608	19447	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.142
1609	22746	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=x^{5}+1 \\ \end{align*}	✓	✓	✓	✓	0.142
1610	24482	\begin{align*} y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.142
1611	26046	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.142
1612	541	\begin{align*} x^{\prime \prime }+6 x^{\prime }+25 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.143
1613	2157	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+8 y^{\prime }+16 y&=2 \,{\mathrm e}^{4 x} \left (13+15 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.143
1614	9282	\begin{align*} y^{\prime \prime } x +3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.143
1615	12792	\begin{align*} 4 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+11 y^{\prime \prime }-3 y^{\prime }-4 \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.143
1616	15099	\begin{align*} x^{3} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.143
1617	23412	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.143
1618	345	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-12 y^{\prime }&=x -2 x \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.144
1619	556	\begin{align*} t x^{\prime \prime }+\left (3 t -1\right ) x^{\prime }+3 x&=0 \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.144
1620	8857	\begin{align*} y^{\prime \prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.144
1621	8934	\begin{align*} y^{\prime \prime \prime }-y&=x \\ \end{align*}	✓	✓	✓	✓	0.144
1622	14613	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.144
1623	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*}	✓	✓	✓	✓	0.144
1624	19443	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.144
1625	19564	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=12 x -2 \\ \end{align*}	✓	✓	✓	✓	0.144
1626	20123	\begin{align*} y^{\prime \prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.144
1627	23426	\begin{align*} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.144
1628	26539	\begin{align*} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.144
1629	343	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime }&={\mathrm e}^{x}+2 x^{2}-5 \\ \end{align*}	✓	✓	✓	✓	0.145
1630	2160	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-2 y&=-3 \,{\mathrm e}^{2 x} \left (11+12 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.145
1631	2208	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{2 x} \left (-3 x^{2}-4 x +5\right ) \\ \end{align*}	✓	✓	✓	✓	0.145
1632	3190	\begin{align*} y^{\prime \prime \prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.145
1633	8930	\begin{align*} y^{\prime \prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.145
1634	14612	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.145
1635	16809	\begin{align*} y^{\prime \prime }+3 y^{\prime }&=\delta \left (t \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.145
1636	21310	\begin{align*} x^{\prime \prime \prime }+5 x^{\prime \prime }+9 x^{\prime }+5 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.145
1637	21879	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+3 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.145
1638	22246	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.145
1639	22479	\begin{align*} y^{\prime \prime \prime }&=3 \sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.145
1640	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*}	✓	✓	✓	✓	0.145
1641	23405	\begin{align*} x^{2} y^{\prime \prime }+\left (2 x^{2}-x \right ) y^{\prime }-2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.145
1642	23459	\begin{align*} y^{\prime \prime \prime }+y^{\prime }-2 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.145
1643	23519	\begin{align*} e i u^{\prime \prime \prime \prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.145
1644	24443	\begin{align*} 2 y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-2 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.145
1645	325	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=3 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.146
1646	2183	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-8 y^{\prime }-8 y&={\mathrm e}^{x} \left (8 \cos \left (x \right )+16 \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.146
1647	9287	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.146
1648	10012	\begin{align*} \frac {y^{\prime }}{x +y}&=0 \\ \end{align*}	✓	✓	✓	✓	0.146
1649	17579	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.146
1650	19571	\begin{align*} y^{\prime \prime \prime }-\frac {y^{\prime }}{4}&=x \\ \end{align*}	✓	✓	✓	✓	0.146
1651	19837	\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.146
1652	20071	\begin{align*} y^{\prime \prime \prime }-13 y^{\prime }+12 y&=x \\ \end{align*}	✓	✓	✓	✓	0.146
1653	26536	\begin{align*} y^{\prime \prime \prime \prime }-2 n^{2} y^{\prime \prime }+n^{4} y&=\cos \left (x n +\alpha \right ) \\ \end{align*}	✓	✓	✓	✓	0.146
1654	2184	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }-4 y&={\mathrm e}^{x} \left (2 \cos \left (2 x \right )-\sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.147
1655	8954	\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.147
1656	10578	\begin{align*} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.147
1657	19565	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=9 x^{2}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	0.147
1658	21231	\begin{align*} x^{\prime \prime \prime }-2 x^{\prime \prime }+3 x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.147
1659	25321	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.147
1660	2155	\begin{align*} 2 y^{\prime \prime \prime }-7 y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{2 x} \left (17+30 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.148
1661	7823	\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.148
1662	7826	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.148
1663	8952	\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1664	16446	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1665	17369	\begin{align*} t^{2} y^{\prime \prime }+4 y^{\prime } t -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1666	19574	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.148
1667	19607	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.148
1668	19759	\begin{align*} x^{\prime \prime \prime \prime }-6 x^{\prime \prime \prime }+11 x^{\prime \prime }-6 x^{\prime }&={\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	0.148
1669	19834	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.148
1670	20193	\begin{align*} y^{\prime \prime } x -\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
1671	21188	\begin{align*} x^{\prime \prime \prime \prime }-x^{\prime \prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.148
1672	23409	\begin{align*} y^{\prime \prime } x +\left (x -1\right ) y^{\prime }+\left (3-12 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
1673	23423	\begin{align*} y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
1674	23427	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
1675	24035	\begin{align*} 6 x^{2} y^{\prime \prime }-5 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1676	24451	\begin{align*} 4 y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }-3 y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1677	24453	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-6 y^{\prime \prime }-28 y^{\prime }-24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1678	356	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime }&=x^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ y^{\prime \prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.149
1679	555	\begin{align*} t x^{\prime \prime }+\left (-2+t \right ) x^{\prime }+x&=0 \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.149
1680	1778	\begin{align*} x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.149
1681	3117	\begin{align*} y^{\prime \prime \prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.149
1682	6605	\begin{align*} y^{\prime \prime \prime }&=y+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.149
1683	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*}	✓	✓	✓	✓	0.149
1684	19569	\begin{align*} y^{\prime \prime \prime }-8 y&=16 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.149
1685	19599	\begin{align*} x^{4} y^{\prime \prime }+\sin \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.149
1686	22252	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.149
1687	22625	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=3 \,{\mathrm e}^{x}-2 \\ \end{align*}	✓	✓	✓	✓	0.149
1688	25076	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=4 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.149
1689	2148	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{-3 x} \left (6 x^{2}-23 x +32\right ) \\ \end{align*}	✓	✓	✓	✓	0.150
1690	2150	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&={\mathrm e}^{-2 x} \left (3 x^{2}-17 x +2\right ) \\ \end{align*}	✓	✓	✓	✓	0.150
1691	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*}	✓	✓	✓	✓	0.150
1692	8928	\begin{align*} y^{\left (5\right )}+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.150
1693	14339	\begin{align*} x^{\prime \prime }+t x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✗	0.150
1694	14567	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.150
1695	19838	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x \\ \end{align*}	✓	✓	✓	✓	0.150
1696	20090	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.150
1697	23413	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-7 y^{\prime } x +7 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.150
1698	261	\begin{align*} y^{\prime \prime }+2 y&=6 x +4 \\ \end{align*}	✓	✓	✓	✓	0.151
1699	558	\begin{align*} t x^{\prime \prime }+2 \left (t -1\right ) x^{\prime }-2 x&=0 \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.151
1700	2156	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+3 y^{\prime }+9 y&=2 \,{\mathrm e}^{3 x} \left (11-24 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.151