2.3.21 Problems 2001 to 2100

Table 2.615: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2001	3202	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime }&=x^{2} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.177
2002	3800	\begin{align*} y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y&=8 \,{\mathrm e}^{-x}+1 \\ \end{align*}	✓	✓	✓	✓	0.177
2003	10915	\begin{align*} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.177
2004	14614	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -8 \\ y^{\prime \prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.177
2005	16150	\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.	✓	✓	✓	✓	0.177
2006	21552	\begin{align*} y^{\prime \prime \prime \prime }&=5 x \\ \end{align*}	✓	✓	✓	✓	0.177
2007	23392	\begin{align*} 7 x^{4} y^{\prime \prime \prime \prime }-2 x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 x y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.177
2008	25162	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=t \\ \end{align*}	✓	✓	✓	✓	0.177
2009	25249	\begin{align*} t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.177
2010	26625	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.177
2011	26846	\begin{align*} x^{\prime }+x-2 y&=0 \\ y^{\prime }+x+4 y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.177
2012	1781	\begin{align*} 4 x^{2} \sin \left (x \right ) y^{\prime \prime }-4 x \left (\sin \left (x \right )+x \cos \left (x \right )\right ) y^{\prime }+\left (2 x \cos \left (x \right )+3 \sin \left (x \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.178
2013	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*}	✓	✓	✓	✓	0.178
2014	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*}	✓	✓	✓	✓	0.178
2015	2207	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y&=-{\mathrm e}^{3 x} \left (17 x^{2}+67 x +9\right ) \\ \end{align*}	✓	✓	✓	✓	0.178
2016	6665	\begin{align*} 2 y \left (2 f \left (x \right ) g \left (x \right )+g^{\prime }\left (x \right )\right )+\left (4 g \left (x \right )+f^{\prime }\left (x \right )+2 {f^{\prime }\left (x \right )}^{2}\right ) y^{\prime }+3 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.178
2017	7212	\begin{align*} y^{\prime \prime }+y \,{\mathrm e}^{2 x}&=n^{2} y \\ \end{align*}	✓	✓	✓	✗	0.178
2018	9285	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.178
2019	9287	\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.178
2020	10822	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.178
2021	11264	\begin{align*} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.178
2022	15138	\begin{align*} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.178
2023	15703	\begin{align*} y^{\prime \prime }-9 y&=x +2 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.178
2024	17371	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.178
2025	17532	\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.178
2026	17582	\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.178
2027	17602	\begin{align*} y^{\left (6\right )}+y^{\prime \prime \prime \prime }&=-24 \\ \end{align*}	✓	✓	✓	✓	0.178
2028	18088	\begin{align*} y^{\prime \prime \prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.178
2029	23022	\begin{align*} y^{\prime \prime }+3 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y \left (\frac {\pi \sqrt {3}}{3}\right ) &= 5 \,{\mathrm e}^{-\frac {\pi \sqrt {3}}{2}} \\ \end{align*}	✓	✓	✓	✓	0.178
2030	25256	\begin{align*} t y^{\prime \prime }-2 \left (t +1\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.178
2031	25263	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.178
2032	26536	\begin{align*} y^{\prime \prime \prime \prime }-2 n^{2} y^{\prime \prime }+n^{4} y&=\cos \left (n x +\alpha \right ) \\ \end{align*}	✓	✓	✓	✓	0.178
2033	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*}	✓	✓	✓	✓	0.178
2034	567	\begin{align*} x^{\prime \prime }+2 x^{\prime }+x&=t +\delta \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.179
2035	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*}	✓	✓	✓	✓	0.179
2036	2171	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y&={\mathrm e}^{x} \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✓	0.179
2037	6654	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.179
2038	6656	\begin{align*} -a^{3} y+3 a^{2} y^{\prime }-3 a y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.179
2039	7200	\begin{align*} u^{\prime \prime }-\frac {a^{2} u}{x^{{2}/{3}}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.179
2040	8933	\begin{align*} y^{\prime \prime \prime \prime }-k^{4} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.179
2041	13180	\(\left [\begin {array}{cc} -1 & 4 \\ -1 & 3 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.179
2042	16457	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.179
2043	19608	\begin{align*} y^{\prime \prime }+\frac {n y^{\prime }}{x^{2}}+\frac {q y}{x^{3}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.179
2044	26604	\begin{align*} y^{\prime \prime \prime \prime }-y&=8 \,{\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= 4 \\ y^{\prime \prime \prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.179
2045	1684	\begin{align*} \left (x +y\right )^{2}+\left (x +y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.180
2046	6743	\begin{align*} a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.180
2047	9105	\begin{align*} y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.180
2048	11281	\begin{align*} y^{\prime \prime }&=\frac {6 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.180
2049	14345	\begin{align*} x^{\prime \prime \prime }+x^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.180
2050	24621	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=16 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.180
2051	27623	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.180
2052	27762	\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.180
2053	934	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.181
2054	1462	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y&=t \\ \end{align*}	✓	✓	✓	✓	0.181
2055	4467	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }&=9 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.181
2056	6642	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.181
2057	6653	\begin{align*} -4 y+6 y^{\prime }-4 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.181
2058	11208	\begin{align*} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.181
2059	15696	\begin{align*} 2 y+y^{\prime }&=4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.181
2060	17375	\begin{align*} 4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (36 t^{2}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.181
2061	17598	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }-11 y^{\prime }+30 y&={\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	0.181
2062	17599	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-10 y^{\prime }-24 y&={\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	0.181
2063	23632	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.181
2064	26697	\begin{align*} y^{\prime \prime \prime \prime }-\lambda ^{4} y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.181
2065	345	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-12 y^{\prime }&=x -2 x \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.182
2066	1487	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.182
2067	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*}	✓	✓	✓	✓	0.182
2068	9288	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.182
2069	10820	\begin{align*} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.182
2070	11249	\begin{align*} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.182
2071	11283	\begin{align*} y^{\prime \prime }&=\frac {20 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.182
2072	17363	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.182
2073	20702	\begin{align*} y^{\prime \prime \prime }+y&=\left (1+{\mathrm e}^{x}\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.182
2074	21197	\begin{align*} x^{\prime \prime \prime \prime }+3 x^{\prime \prime \prime }+2 x^{\prime \prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.182
2075	25344	\begin{align*} t^{2} y^{\prime \prime }+5 t y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.182
2076	26724	\begin{align*} x y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.182
2077	27553	\begin{align*} y^{\prime \prime \prime } {y^{\prime }}^{2}&={y^{\prime \prime \prime }}^{3} \\ \end{align*}	✓	✓	✓	✓	0.182
2078	27752	\begin{align*} x y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.182
2079	2152	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y&={\mathrm e}^{x} \left (15 x^{2}+34 x +14\right ) \\ \end{align*}	✓	✓	✓	✓	0.183
2080	9281	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.183
2081	10574	\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-3 x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.183
2082	10811	\begin{align*} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.183
2083	10974	\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.183
2084	17376	\begin{align*} t y^{\prime \prime }+2 y^{\prime }+16 y t&=0 \\ \end{align*}	✓	✓	✓	✓	0.183
2085	20374	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y&=16 x^{2}+256 \\ \end{align*}	✓	✓	✓	✓	0.183
2086	23393	\begin{align*} x^{5} y^{\left (5\right )}+3 x^{3} y^{\prime \prime \prime }-9 x^{2} y^{\prime \prime }+18 x y^{\prime }-18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.183
2087	25255	\begin{align*} t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.183
2088	2452	\begin{align*} t^{3} y^{\prime \prime }-t y^{\prime }-\left (t^{2}+\frac {5}{4}\right ) y&=0 \\ \end{align*} Series expansion around \(t=0\).	✗	✗	✓	✗	0.184
2089	3954	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= A \\ y^{\prime }\left (0\right ) &= B \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.184
2090	6748	\begin{align*} -2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.184
2091	7820	\begin{align*} 2 y+y^{\prime }&=2 \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.184
2092	9284	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.184
2093	9290	\begin{align*} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.184
2094	10909	\begin{align*} x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.184
2095	11083	\begin{align*} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.184
2096	11210	\begin{align*} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.184
2097	17576	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+30 y^{\prime \prime }-56 y^{\prime }+49 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ y^{\prime \prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.184
2098	17600	\begin{align*} y^{\prime \prime \prime }-13 y^{\prime }+12 y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.184
2099	20593	\begin{align*} y^{\prime \prime \prime }&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.184
2100	20612	\begin{align*} y^{\prime \prime }-a x y^{\prime }+a^{2} \left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.184