2.3.18 Problems 1701 to 1800

Table 2.567: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1701	8928	\begin{align*} y^{\left (5\right )}+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.121
1702	10495	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.121
1703	11158	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.121
1704	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*}	✓	✓	✓	✗	0.121
1705	15077	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=x^{2}-{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.121
1706	15080	\begin{align*} x^{\prime \prime \prime \prime }-2 x^{\prime \prime }+x&=t^{2}-3 \\ \end{align*}	✓	✓	✓	✓	0.121
1707	15695	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.121
1708	15703	\begin{align*} y^{\prime \prime }-9 y&=2+x \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.121
1709	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*}	✓	✓	✓	✓	0.121
1710	18028	\begin{align*} {y^{\prime }}^{2}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.121
1711	22132	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=2 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.121
1712	23405	\begin{align*} x^{2} y^{\prime \prime }+\left (2 x^{2}-x \right ) y^{\prime }-2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.121
1713	24510	\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-9 y^{\prime \prime \prime }-13 y^{\prime \prime }+8 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.121
1714	25163	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.121
1715	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*}	✓	✓	✓	✓	0.122
1716	7191	\begin{align*} 2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x}&=\sqrt {x} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.122
1717	10817	\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.122
1718	10998	\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*}	✓	✓	✓	✗	0.122
1719	13050	\begin{align*} 2 y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.122
1720	14567	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.122
1721	14950	\begin{align*} x^{\prime \prime \prime \prime }-5 x^{\prime \prime }+4 x&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.122
1722	15218	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.122
1723	20094	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.122
1724	20190	\begin{align*} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+3 \left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.122
1725	21552	\begin{align*} y^{\prime \prime \prime \prime }&=5 x \\ \end{align*}	✓	✓	✓	✓	0.122
1726	1777	\begin{align*} y^{\prime \prime } x -\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.123
1727	2576	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.123
1728	2658	\begin{align*} t^{2} y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y&=0 \\ \end{align*} Series expansion around \(t=0\).	✗	✗	✓	✗	0.123
1729	3126	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y&={\mathrm e}^{4 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.123
1730	3201	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-2 x} \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.123
1731	4164	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.123
1732	9827	\begin{align*} x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.123
1733	10918	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.123
1734	13182	\(\left [\begin {array}{cc} 5 & 1 \\ -9 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.123
1735	13183	\(\left [\begin {array}{cc} 11 & 9 \\ -16 & -13 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.123
1736	14570	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-4 \left (x +1\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.123
1737	14830	\begin{align*} t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 t x^{\prime }-6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.123
1738	16451	\begin{align*} \left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.123
1739	19838	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x \\ \end{align*}	✓	✓	✓	✓	0.123
1740	19842	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y&=x \\ \end{align*}	✓	✓	✓	✓	0.123
1741	20356	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.123
1742	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 \(x=-1\).	✗	✗	✓	✗	0.123
1743	24438	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -7 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.123
1744	24467	\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+3 y^{\prime }-9 y&=0 \\ y \left (0\right ) &= -1 \\ y \left (1\right ) &= 0 \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.123
1745	2714	\begin{align*} y^{\prime \prime \prime \prime }-y&=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 ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.124
1746	3192	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.124
1747	3194	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&={\mathrm e}^{2 x} \left (x -3\right ) \\ \end{align*}	✓	✓	✓	✓	0.124
1748	8830	\begin{align*} y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.124
1749	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*}	✓	✓	✓	✓	0.124
1750	14814	\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.124
1751	16452	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}-4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.124
1752	19837	\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.124
1753	22794	\begin{align*} i^{\prime \prime \prime \prime }+9 i^{\prime \prime }&=20 \,{\mathrm e}^{-t} \\ i \left (0\right ) &= 0 \\ i^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.124
1754	2110	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.125
1755	2316	\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\cos \left (t \right ) \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.125
1756	6637	\begin{align*} -3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&={\mathrm e}^{-x}+3 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.125
1757	6731	\begin{align*} y^{\prime \prime \prime \prime }&=x^{3}+a^{4} y \\ \end{align*}	✓	✓	✓	✓	0.125
1758	7916	\begin{align*} -y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1759	11299	\begin{align*} x^{2} y^{\prime \prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.125
1760	15192	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.125
1761	15264	\begin{align*} y^{\prime \prime \prime }&=2 y^{\prime \prime }-4 y^{\prime }+\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.125
1762	18089	\begin{align*} y^{\prime \prime \prime }&=x +\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.125
1763	24461	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 9 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.125
1764	24484	\begin{align*} y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
1765	25337	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{t}+\frac {\left (1-t \right ) y}{t^{3}}&=0 \\ \end{align*} Series expansion around \(t=0\).	✗	✗	✓	✗	0.125
1766	6911	\begin{align*} x +y+1+\left (2 x +2 y+2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.126
1767	8936	\begin{align*} y^{\prime \prime \prime \prime }+16 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.126
1768	11280	\begin{align*} y^{\prime \prime }&=\frac {2 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.126
1769	14044	\begin{align*} {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.126
1770	16447	\begin{align*} x^{2} y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.126
1771	19544	\begin{align*} y^{\prime \prime \prime \prime }&=\sin \left (x \right )+24 \\ \end{align*}	✓	✓	✓	✓	0.126
1772	20058	\begin{align*} y^{\prime \prime \prime \prime }+y&=x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.126
1773	21959	\begin{align*} {y^{\prime \prime }}^{{3}/{2}}+y&=x \\ \end{align*}	✗	✓	✓	✗	0.126
1774	23409	\begin{align*} y^{\prime \prime } x +\left (x -1\right ) y^{\prime }+\left (3-12 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.126
1775	1779	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
1776	6693	\begin{align*} -y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
1777	7236	\begin{align*} x \ln \left (x \right ) y^{\prime }+y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.127
1778	15220	\begin{align*} y+2 y^{\prime }&={\mathrm e}^{-\frac {t}{2}} \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.127
1779	16457	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
1780	18221	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=\cos \left (2 x \right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.127
1781	19763	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.127
1782	20050	\begin{align*} y^{\prime \prime \prime }-y&=\left ({\mathrm e}^{x}+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.127
1783	22810	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=4 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.127
1784	492	\begin{align*} x^{3} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.128
1785	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*}	✓	✓	✓	✓	0.128
1786	3152	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.128
1787	6617	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=-3 \,{\mathrm e}^{2 x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.128
1788	10498	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.128
1789	14948	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.128
1790	15105	\begin{align*} y^{\left (6\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime }&=x +{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.128
1791	15200	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.128
1792	15437	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=2 x +3 \\ \end{align*}	✓	✓	✓	✓	0.128
1793	15697	\begin{align*} y^{\prime \prime }-9 y&=2 \sin \left (3 x \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.128
1794	17560	\begin{align*} y^{\left (6\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.128
1795	18214	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.128
1796	18467	\begin{align*} x^{\prime \prime }+x&=t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.128
1797	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*}	✓	✓	✓	✓	0.128
1798	23491	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.128
1799	24506	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+5 y^{\prime \prime }-8 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.128
1800	4477	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime }&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.129