2.3.19 Problems 1801 to 1900

Table 2.611: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1801	10301	\begin{align*} \pi y \sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.158
1802	10696	\begin{align*} x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.158
1803	16666	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=6 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.158
1804	17575	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.158
1805	19560	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.158
1806	19591	\begin{align*} x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.158
1807	23417	\begin{align*} y^{\prime \prime }-\left (1+\frac {3}{2 x}\right ) y^{\prime }+\frac {3 y}{2 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.158
1808	23673	\begin{align*} x^{3} \left (-x^{2}+1\right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.158
1809	24001	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x -{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.158
1810	24683	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=12 x -2 \\ \end{align*}	✓	✓	✓	✓	0.158
1811	26440	\begin{align*} y^{\prime \prime \prime }&=x \,{\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.158
1812	26532	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.158
1813	26572	\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*}	✓	✓	✓	✓	0.158
1814	341	\begin{align*} y^{\prime \prime \prime }-y&={\mathrm e}^{x}+7 \\ \end{align*}	✓	✓	✓	✓	0.159
1815	532	\begin{align*} x^{\prime \prime }-x^{\prime }-2 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.159
1816	1778	\begin{align*} x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.159
1817	6588	\begin{align*} 2 \left (x -y^{\prime }\right ) y^{\prime }-x \left (x +4 y^{\prime }\right ) y^{\prime \prime }+2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2}&=2 y \\ \end{align*}	✗	✗	✗	✗	0.159
1818	8953	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.159
1819	10970	\begin{align*} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.159
1820	11294	\begin{align*} y^{\prime \prime }&=\left (\frac {1}{x}-\frac {3}{16 x^{2}}\right ) y \\ \end{align*}	✓	✓	✓	✓	0.159
1821	17369	\begin{align*} t^{2} y^{\prime \prime }+4 t y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.159
1822	18367	\begin{align*} y^{\prime \prime \prime \prime }-\lambda ^{4} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime \prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.159
1823	20582	\begin{align*} n \,x^{3} y^{\prime \prime \prime }&=-x y^{\prime }+y \\ \end{align*}	✓	✓	✓	✗	0.159
1824	25250	\begin{align*} t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.159
1825	27587	\begin{align*} {y^{\prime \prime }}^{2}-y^{\prime } y^{\prime \prime \prime }&=\frac {{y^{\prime }}^{2}}{x^{2}} \\ \end{align*}	✗	✓	✓	✗	0.159
1826	3765	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=12 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.160
1827	3798	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.160
1828	22665	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.160
1829	23096	\begin{align*} 4 x^{\prime }+2 y^{\prime }+3 x&=E \sin \left (t \right ) \\ 4 x+2 x^{\prime }+3 y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.160
1830	24040	\begin{align*} y^{\prime \prime }+x y^{\prime }+\left (3 x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.160
1831	24527	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+14 y^{\prime }-8 y&=2 \\ \end{align*}	✓	✓	✓	✓	0.160
1832	25251	\begin{align*} 4 t^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.160
1833	26538	\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*}	✓	✓	✓	✓	0.160
1834	27048	\begin{align*} x^{\prime }+4 x-y&=0 \\ x^{\prime }+y^{\prime }&=t \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.160
1835	147	\begin{align*} x y^{\prime \prime }&=y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.161
1836	3135	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=5 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.161
1837	6631	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.161
1838	8532	\begin{align*} x^{3} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.161
1839	16663	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=32 x \\ \end{align*}	✓	✓	✓	✓	0.161
1840	18166	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=3 \\ \end{align*}	✓	✓	✓	✓	0.161
1841	18588	\begin{align*} \frac {y^{\prime }}{-\sin \left (y\right )+\frac {x}{y}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.161
1842	19622	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y&=0 \\ \end{align*} Series expansion around \(x=\infty \).	✗	✗	✓	✓	0.161
1843	20088	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&={\mathrm e}^{x}+\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.161
1844	22636	\begin{align*} y^{\prime \prime \prime }-16 y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.161
1845	24528	\begin{align*} y^{\prime \prime \prime }+9 y^{\prime }&=11 \\ \end{align*}	✓	✓	✓	✓	0.161
1846	24530	\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime }&=11 \\ \end{align*}	✓	✓	✓	✓	0.161
1847	533	\begin{align*} x^{\prime \prime }+8 x^{\prime }+15 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.162
1848	8955	\begin{align*} y-\left (x +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.162
1849	11238	\begin{align*} x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.162
1850	17534	\begin{align*} t y^{\prime \prime }+2 y^{\prime }+y t&=0 \\ \end{align*}	✓	✓	✓	✓	0.162
1851	18165	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.162
1852	19857	\begin{align*} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.162
1853	20749	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.162
1854	25260	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.162
1855	26003	\begin{align*} x^{\prime }+y&=3 \,{\mathrm e}^{2 t} \\ x+y^{\prime }&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.162
1856	26443	\begin{align*} y^{\prime \prime \prime }&=x +\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.162
1857	2574	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.163
1858	3197	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime }&=x^{2}+\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.163
1859	13181	\(\left [\begin {array}{cc} 3 & -1 \\ 1 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.163
1860	24533	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }&=12 \\ \end{align*}	✓	✓	✓	✓	0.163
1861	24534	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }&=12 \\ \end{align*}	✓	✓	✓	✓	0.163
1862	26832	\begin{align*} x^{\prime \prime }-x^{\prime }-6 x&=6 \,{\mathrm e}^{3 t}+2 \,{\mathrm e}^{-2 t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= {\frac {4}{5}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.163
1863	2578	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.164
1864	2658	\begin{align*} t^{2} y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 y t&=0 \\ \end{align*} Series expansion around \(t=0\).	✗	✗	✓	✗	0.164
1865	3623	\begin{align*} y^{\prime }+\frac {m y}{x}&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.164
1866	3713	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y&=24 \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.164
1867	6759	\begin{align*} a^{4} x^{4} y+4 a^{3} x^{3} y^{\prime }+6 a^{2} x^{2} y^{\prime \prime }+4 a x y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.164
1868	8952	\begin{align*} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.164
1869	15685	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=3+\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.164
1870	16466	\begin{align*} y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y&={\mathrm e}^{3 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.164
1871	17372	\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.164
1872	22161	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ y^{\prime \prime }\left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.164
1873	22649	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.164
1874	23243	\begin{align*} y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y&=2 x^{2}+3 \\ \end{align*}	✓	✓	✓	✗	0.164
1875	24531	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }&=12 \\ \end{align*}	✓	✓	✓	✓	0.164
1876	25258	\begin{align*} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.164
1877	7186	\begin{align*} y^{\prime \prime }+\frac {a y}{x^{{3}/{2}}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.165
1878	10282	\begin{align*} a \sin \left (x \right ) y x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.165
1879	27056	\begin{align*} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.165
1880	27711	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+5 x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.165
1881	6610	\begin{align*} y^{\prime \prime \prime }&=y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.166
1882	6639	\begin{align*} 2 a^{2} y-a^{2} y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.166
1883	7802	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=1+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.166
1884	9282	\begin{align*} x y^{\prime \prime }+3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.166
1885	16579	\begin{align*} -8 y+7 x y^{\prime }-3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.166
1886	24612	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.166
1887	25142	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.166
1888	25262	\begin{align*} t^{2} y^{\prime \prime }-2 t y^{\prime }+\left (t^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.166
1889	542	\begin{align*} x^{\prime \prime }-6 x^{\prime }+8 x&=2 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.167
1890	1484	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.167
1891	3198	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }+2 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✗	0.167
1892	6641	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.167
1893	6668	\begin{align*} -3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.167
1894	11280	\begin{align*} y^{\prime \prime }&=\frac {2 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.167
1895	17735	\begin{align*} t y^{\prime \prime }+2 y^{\prime }+y t&=0 \\ \end{align*}	✓	✓	✓	✓	0.167
1896	21180	\begin{align*} x^{\prime \prime \prime }+4 x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -1 \\ x^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.167
1897	24633	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.167
1898	26603	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=2 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.167
1899	27049	\begin{align*} x^{\prime }+y^{\prime }+x-y&=0 \\ x^{\prime }+2 y^{\prime }+x&=1 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.167
1900	335	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.168