2.3.19 Problems 1801 to 1900

Table 2.569: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1801	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.	✓	✓	✓	✓	0.109
1802	16446	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.109
1803	18985	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.109
1804	20081	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime }-6 y&={\mathrm e}^{2 x} \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✓	0.109
1805	23427	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.109
1806	23491	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.109
1807	24059	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=x^{3}+{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.109
1808	25068	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.109
1809	25641	\begin{align*} y^{\prime \prime }+B y^{\prime }+C y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.109
1810	335	\begin{align*} y-2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.110
1811	7916	\begin{align*} -y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.110
1812	7989	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&=5 \\ \end{align*}	✓	✓	✓	✓	0.110
1813	10245	\begin{align*} y^{\prime }&=\frac {1}{x} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.110
1814	16663	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=32 x \\ \end{align*}	✓	✓	✓	✓	0.110
1815	19539	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.110
1816	20363	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime }-6 y&={\mathrm e}^{2 x} \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✓	0.110
1817	21231	\begin{align*} x^{\prime \prime \prime }-2 x^{\prime \prime }+3 x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.110
1818	21880	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+5 y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.110
1819	23413	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-7 y^{\prime } x +7 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.110
1820	23647	\begin{align*} y^{\prime }-3 y&=2 \,{\mathrm e}^{t} \\ y \left (1\right ) &= {\mathrm e}^{3}-{\mathrm e} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.110
1821	23997	\begin{align*} y^{\prime \prime \prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.110
1822	24014	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=2 x \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.110
1823	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*}	✓	✓	✓	✓	0.111
1824	2576	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.111
1825	8985	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime }+3 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.111
1826	15437	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=2 x +3 \\ \end{align*}	✓	✓	✓	✓	0.111
1827	22816	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.111
1828	23419	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.111
1829	23511	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&=x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.111
1830	24464	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y \left (2\right ) &= 0 \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.111
1831	24777	\begin{align*} {y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.111
1832	959	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.112
1833	962	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.112
1834	4477	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime }&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.112
1835	6616	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime \prime }&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.112
1836	8936	\begin{align*} y^{\prime \prime \prime \prime }+16 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.112
1837	8978	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.112
1838	9386	\begin{align*} x^{2} y^{\prime \prime }+\left (-x +2\right ) y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.112
1839	16662	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=32 \,{\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.112
1840	16754	\begin{align*} y^{\prime \prime \prime }+8 y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.112
1841	17566	\begin{align*} 24 y^{\prime \prime \prime }-26 y^{\prime \prime }+9 y^{\prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.112
1842	19298	\begin{align*} y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.112
1843	19538	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.112
1844	21312	\begin{align*} x^{\prime \prime \prime \prime }+8 x^{\prime \prime \prime }+23 x^{\prime \prime }+2 x^{\prime }+12 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.112
1845	21984	\begin{align*} y x +y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.112
1846	23464	\begin{align*} y^{\prime \prime \prime \prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.112
1847	24001	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x -{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.112
1848	25160	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.112
1849	25264	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.112
1850	25322	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.112
1851	2724	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=t^{2} \\ \end{align*}	✓	✓	✓	✓	0.113
1852	4514	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=9 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.113
1853	11284	\begin{align*} y^{\prime \prime }&=\frac {12 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.113
1854	14951	\begin{align*} t^{2} y^{\prime \prime }-\left (t^{2}+2 t \right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.113
1855	17534	\begin{align*} t y^{\prime \prime }+2 y^{\prime }+t y&=0 \\ \end{align*}	✓	✓	✓	✓	0.113
1856	20491	\begin{align*} -8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.113
1857	22241	\begin{align*} y^{\prime }+2 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.113
1858	23648	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=27 t \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.113
1859	24480	\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }-11 y^{\prime \prime }-8 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.113
1860	24781	\begin{align*} x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.113
1861	25263	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.113
1862	960	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.114
1863	1684	\begin{align*} \left (x +y\right )^{2}+\left (x +y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.114
1864	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*}	✓	✓	✓	✓	0.114
1865	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*}	✓	✓	✓	✗	0.114
1866	15188	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.114
1867	16457	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.114
1868	16541	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+9 y^{\prime \prime }+9 y^{\prime }&=0 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 6 \\ y^{\prime \prime \prime }\left (0\right ) &= -60 \\ \end{align*}	✓	✓	✓	✓	0.114
1869	18172	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.114
1870	18219	\begin{align*} y^{\prime \prime \prime }-y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.114
1871	18906	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=18 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.114
1872	23523	\begin{align*} e i u^{\prime \prime \prime \prime }&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.114
1873	24040	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (3 x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.114
1874	24865	\begin{align*} x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.114
1875	25162	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=t \\ \end{align*}	✓	✓	✓	✓	0.114
1876	3929	\begin{align*} 3 y+y^{\prime }&=2 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.115
1877	3930	\begin{align*} y^{\prime }+2 y&=4 t \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.115
1878	4474	\begin{align*} y^{\prime \prime \prime \prime }-y&=4 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.115
1879	5508	\begin{align*} x^{2} {y^{\prime }}^{2}+3 x y^{\prime } y+2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1880	6617	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=-3 \,{\mathrm e}^{2 x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.115
1881	7239	\begin{align*} y^{\prime }+y \cos \left (x \right )&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.115
1882	8623	\begin{align*} y^{\prime }+2 y&=0 \\ y \left (0\right ) &= {\frac {3}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.115
1883	10049	\begin{align*} y y^{\prime \prime }&=x \\ \end{align*}	✗	✗	✗	✗	0.115
1884	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*}	✓	✓	✓	✗	0.115
1885	11280	\begin{align*} y^{\prime \prime }&=\frac {2 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.115
1886	11281	\begin{align*} y^{\prime \prime }&=\frac {6 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.115
1887	12827	\begin{align*} y^{\left (5\right )}+a y^{\prime \prime \prime \prime }-f&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1888	14113	\begin{align*} y-2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=4+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.115
1889	14570	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-4 \left (x +1\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.115
1890	15199	\begin{align*} y^{\prime \prime }-20 y^{\prime }+51 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -14 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.115
1891	16666	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=6 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.115
1892	16809	\begin{align*} y^{\prime \prime }+3 y^{\prime }&=\delta \left (t \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.115
1893	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*}	✓	✓	✓	✓	0.115
1894	18899	\begin{align*} y^{\prime \prime }-8 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.115
1895	19186	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1896	20077	\begin{align*} y^{\prime \prime \prime \prime }-a^{4} y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.115
1897	20613	\begin{align*} \left (2 x^{3}-a \right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1898	22132	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=2 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.115
1899	22227	\begin{align*} y^{\prime }-5 y&=0 \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.115
1900	22260	\begin{align*} y^{\prime }+z&=t \\ z^{\prime }-y&=0 \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ z \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.115