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	7717	\begin{align*} -y+y^{\prime } x&=x^{3}+3 x^{2}-2 x \\ \end{align*}	✓	✓	✓	✓	0.129
1802	9282	\begin{align*} y^{\prime \prime } x +3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.129
1803	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*}	✓	✓	✓	✓	0.129
1804	15026	\begin{align*} {y^{\prime }}^{2}&=9 y^{4} \\ \end{align*}	✓	✓	✓	✓	0.129
1805	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.	✓	✓	✓	✓	0.129
1806	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.	✓	✓	✓	✓	0.129
1807	15713	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=x^{2} \\ y \left (0\right ) &= {\frac {11}{4}} \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.129
1808	20070	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \left (b x +a \right ) \\ \end{align*}	✓	✓	✓	✓	0.129
1809	21291	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.129
1810	23308	\begin{align*} 6 y^{\prime \prime \prime }-4 i y^{\prime \prime }+\left (3+i\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.129
1811	24435	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.129
1812	25059	\begin{align*} y^{\prime }-4 y&=1 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.129
1813	1325	\begin{align*} x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.130
1814	1775	\begin{align*} x^{2} \ln \left (x \right )^{2} y^{\prime \prime }-2 x \ln \left (x \right ) y^{\prime }+\left (2+\ln \left (x \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.130
1815	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*}	✓	✓	✓	✗	0.130
1816	2154	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=-{\mathrm e}^{x} \left (7+6 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.130
1817	4467	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }&=9 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.130
1818	6669	\begin{align*} 18 \,{\mathrm e}^{x}-3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.130
1819	7810	\begin{align*} y^{\prime \prime \prime \prime }&=5 x \\ \end{align*}	✓	✓	✓	✓	0.130
1820	8937	\begin{align*} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.130
1821	8956	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.130
1822	8958	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.130
1823	8978	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.130
1824	10496	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.130
1825	16450	\begin{align*} y^{\prime \prime }-\left (4+\frac {2}{x}\right ) y^{\prime }+\left (4+\frac {4}{x}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.130
1826	18180	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.130
1827	18469	\begin{align*} x^{\prime \prime }-2 x^{\prime }+2 x&=2 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.130
1828	20072	\begin{align*} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=\cos \left (x m \right ) \\ \end{align*}	✓	✓	✓	✓	0.130
1829	20359	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.130
1830	21284	\begin{align*} x^{\prime \prime \prime \prime }+x^{\prime \prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ x^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.130
1831	23427	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.130
1832	343	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime }&={\mathrm e}^{x}+2 x^{2}-5 \\ \end{align*}	✓	✓	✓	✓	0.131
1833	345	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-12 y^{\prime }&=x -2 x \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.131
1834	2149	\begin{align*} 4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y&=-{\mathrm e}^{x} \left (6 x^{2}+45 x +4\right ) \\ \end{align*}	✓	✓	✓	✓	0.131
1835	2314	\begin{align*} y^{\prime }+\frac {y}{\sqrt {t}}&={\mathrm e}^{\frac {\sqrt {t}}{2}} \\ \end{align*}	✓	✓	✓	✓	0.131
1836	2341	\begin{align*} 2 t y^{3}+3 t^{2} y^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.131
1837	10010	\begin{align*} \left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.131
1838	10487	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.131
1839	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*}	✓	✓	✓	✗	0.131
1840	14083	\begin{align*} x^{2} {y^{\prime }}^{2}-\left (x -1\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.131
1841	15706	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=-x^{2}+1 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.131
1842	20613	\begin{align*} \left (2 x^{3}-a \right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.131
1843	22812	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=12 t \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.131
1844	23413	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-7 y^{\prime } x +7 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.131
1845	1780	\begin{align*} y^{\prime \prime } x -\left (4 x +1\right ) y^{\prime }+\left (2+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.132
1846	2109	\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 ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.132
1847	3196	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.132
1848	6699	\begin{align*} 2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.132
1849	8623	\begin{align*} y^{\prime }+2 y&=0 \\ y \left (0\right ) &= {\frac {3}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.132
1850	10367	\begin{align*} {y^{\prime \prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	0.132
1851	10710	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.132
1852	11283	\begin{align*} y^{\prime \prime }&=\frac {20 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.132
1853	14348	\begin{align*} x^{\prime \prime \prime }+x^{\prime \prime }&=2 \,{\mathrm e}^{t}+3 t^{2} \\ \end{align*}	✓	✓	✓	✓	0.132
1854	15104	\begin{align*} y^{\left (6\right )}-y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.132
1855	15711	\begin{align*} y^{\prime \prime }+9 y&=18 \,{\mathrm e}^{3 x} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.132
1856	17561	\begin{align*} y^{\left (6\right )}+12 y^{\prime \prime \prime \prime }+48 y^{\prime \prime }+64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.132
1857	18176	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.132
1858	20164	\begin{align*} y^{\prime \prime \prime }&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.132
1859	22720	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+24 y&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.132
1860	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*}	✓	✓	✓	✗	0.132
1861	23411	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {9 y}{x^{4}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.132
1862	23426	\begin{align*} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.132
1863	23459	\begin{align*} y^{\prime \prime \prime }+y^{\prime }-2 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.132
1864	23521	\begin{align*} e i u^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.132
1865	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*}	✓	✓	✓	✓	0.132
1866	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*}	✓	✓	✓	✗	0.133
1867	2165	\begin{align*} 2 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-5 y^{\prime }-2 y&=18 \,{\mathrm e}^{x} \left (5+2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.133
1868	3208	\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.133
1869	6601	\begin{align*} y^{\prime \prime \prime }&=\cos \left (x \right )+1 \\ \end{align*}	✓	✓	✓	✓	0.133
1870	12720	\begin{align*} y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-a^{3} y-{\mathrm e}^{a x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.133
1871	14123	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=-3 \,{\mathrm e}^{2 x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.133
1872	15698	\begin{align*} y^{\prime \prime }+9 y&=2 \sin \left (3 x \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.133
1873	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*}	✓	✓	✓	✓	0.133
1874	17548	\begin{align*} 5 y^{\prime \prime \prime }-15 y^{\prime }+11 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.133
1875	18181	\begin{align*} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.133
1876	18465	\begin{align*} x^{\prime \prime }+x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.133
1877	19628	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= \operatorname {yd}_{0} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.133
1878	22748	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y&=2 \,{\mathrm e}^{3 x}-4 \,{\mathrm e}^{-5 x} \\ \end{align*}	✓	✓	✓	✓	0.133
1879	22788	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime }&=12 \,{\mathrm e}^{2 x}+24 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.133
1880	23421	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.133
1881	2108	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.134
1882	2172	\begin{align*} 2 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{x} \left (11+12 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.134
1883	3620	\begin{align*} 1-\sin \left (x \right ) y-\cos \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.134
1884	8499	\begin{align*} x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.134
1885	9287	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.134
1886	10476	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.134
1887	14340	\begin{align*} x^{\prime \prime }-t x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✗	0.134
1888	15096	\begin{align*} y^{\left (6\right )}-3 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.134
1889	15193	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.134
1890	15714	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 \sin \left (x \right ) \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.134
1891	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*}	✓	✓	✓	✗	0.134
1892	16481	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.134
1893	18462	\begin{align*} x^{\prime \prime }&=1 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.134
1894	460	\begin{align*} 3 x^{3} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.135
1895	1782	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.135
1896	4474	\begin{align*} y^{\prime \prime \prime \prime }-y&=4 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.135
1897	6695	\begin{align*} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.135
1898	9023	\begin{align*} x^{2}+y x +\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.135
1899	9283	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.135
1900	10497	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.135