2.3.21 Problems 2001 to 2100

Table 2.585: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2001	9100	\begin{align*} y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.149
2002	10594	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.149
2003	10687	\begin{align*} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.149
2004	10698	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.149
2005	10852	\begin{align*} y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.149
2006	10938	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.149
2007	14597	\begin{align*} y^{\left (5\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.149
2008	21289	\begin{align*} x^{\prime \prime }&=\delta \left (-t +a \right ) \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.149
2009	21552	\begin{align*} y^{\prime \prime \prime \prime }&=5 x \\ \end{align*}	✓	✓	✓	✓	0.149
2010	22041	\begin{align*} y^{2}+y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.149
2011	22641	\begin{align*} y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }-16 y^{\prime \prime }+12 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.149
2012	398	\begin{align*} x^{\prime \prime }+6 x^{\prime }+45 x&=50 \cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.150
2013	827	\begin{align*} 2 y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.150
2014	5955	\begin{align*} x^{2} y^{\prime \prime }&=6 y \\ \end{align*}	✓	✓	✓	✓	0.150
2015	10608	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.150
2016	10692	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.150
2017	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*}	✓	✓	✓	✓	0.150
2018	19846	\begin{align*} y^{\prime \prime \prime \prime }-y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.150
2019	22053	\begin{align*} x y^{2}+x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.150
2020	24622	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=9 \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.150
2021	340	\begin{align*} y^{\left (5\right )}+2 y^{\prime \prime \prime }+2 y^{\prime \prime }&=3 x^{2}-1 \\ \end{align*}	✓	✓	✓	✓	0.151
2022	357	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&=1+x \,{\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.151
2023	1778	\begin{align*} x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.151
2024	2573	\begin{align*} y^{\prime \prime }-4 y^{\prime } t +\left (4 t^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.151
2025	2575	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.151
2026	3414	\begin{align*} {y^{\prime }}^{2}-3 y^{\prime }+2&=0 \\ \end{align*}	✓	✓	✓	✓	0.151
2027	3587	\begin{align*} y^{\prime \prime \prime }&=6 x \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.151
2028	3618	\begin{align*} t x^{\prime }+2 x&=4 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.151
2029	5909	\begin{align*} b \,x^{k} y+a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.151
2030	7327	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.151
2031	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*}	✓	✓	✓	✓	0.151
2032	10535	\begin{align*} \left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (-x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.151
2033	11133	\begin{align*} x^{2} y^{\prime \prime }+2 x \left (2+x \right ) y^{\prime }+2 \left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.151
2034	11146	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.151
2035	11223	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.151
2036	11252	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.151
2037	14596	\begin{align*} y^{\prime \prime \prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.151
2038	15187	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.151
2039	15195	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.151
2040	15496	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.151
2041	16730	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }&=8 \\ \end{align*}	✓	✓	✓	✓	0.151
2042	20374	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y&=16 x^{2}+256 \\ \end{align*}	✓	✓	✓	✓	0.151
2043	20593	\begin{align*} y^{\prime \prime \prime }&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.151
2044	25163	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.151
2045	399	\begin{align*} x^{\prime \prime }+10 x^{\prime }+650 x&=100 \cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.152
2046	535	\begin{align*} x^{\prime \prime }+4 x&=\cos \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.152
2047	1467	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.152
2048	1680	\begin{align*} 6 y^{2} x^{2}+4 y y^{\prime } x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.152
2049	5956	\begin{align*} x^{2} y^{\prime \prime }&=12 y \\ \end{align*}	✓	✓	✓	✓	0.152
2050	5980	\begin{align*} \left (b x +a \right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.152
2051	7073	\begin{align*} 3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.152
2052	10667	\begin{align*} t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.152
2053	10672	\begin{align*} t^{2} y^{\prime \prime }-t \left (1+t \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.152
2054	10866	\begin{align*} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.152
2055	11092	\begin{align*} t^{2} y^{\prime \prime }-t \left (1+t \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.152
2056	11175	\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.152
2057	11210	\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.152
2058	15486	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.152
2059	16540	\begin{align*} y^{\prime \prime \prime \prime }+26 y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= -28 \\ y^{\prime \prime }\left (0\right ) &= -102 \\ y^{\prime \prime \prime }\left (0\right ) &= 622 \\ \end{align*}	✓	✓	✓	✓	0.152
2060	848	\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.153
2061	10595	\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.153
2062	10659	\begin{align*} y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✗	0.153
2063	10683	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.153
2064	11014	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.153
2065	11087	\begin{align*} t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.153
2066	16702	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=30 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.153
2067	17563	\begin{align*} y^{\prime \prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.153
2068	17579	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.153
2069	23340	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+5 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.153
2070	25162	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=t \\ \end{align*}	✓	✓	✓	✓	0.153
2071	25997	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=t \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.153
2072	379	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y&=8 x^{{4}/{3}} \\ \end{align*}	✓	✓	✓	✓	0.154
2073	491	\begin{align*} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.154
2074	832	\begin{align*} 35 y^{\prime \prime }-y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.154
2075	847	\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.154
2076	2577	\begin{align*} \left (2 t +1\right ) y^{\prime \prime }-4 \left (1+t \right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.154
2077	3614	\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {4}{\left (x^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	0.154
2078	6615	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime \prime }&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.154
2079	6632	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=\left (x -1\right ) x \\ \end{align*}	✓	✓	✓	✓	0.154
2080	10617	\begin{align*} 9 \left (x +3\right ) x^{2} y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (4 x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.154
2081	10699	\begin{align*} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.154
2082	10702	\begin{align*} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.154
2083	10847	\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}	✓	✓	✓	✗	0.154
2084	10969	\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.154
2085	11145	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.154
2086	11222	\begin{align*} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.154
2087	11258	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.154
2088	11289	\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.154
2089	15321	\begin{align*} y^{\prime \prime }+9 y&=18 t \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.154
2090	18008	\begin{align*} x&=\sin \left (y^{\prime }\right )+y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.154
2091	18277	\begin{align*} y^{\prime \prime \prime \prime }-y&=8 \,{\mathrm e}^{x} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.154
2092	19573	\begin{align*} y^{\prime }-y^{\prime \prime }+y^{\prime \prime \prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.154
2093	23227	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.154
2094	831	\begin{align*} 6 y^{\prime \prime }-7 y^{\prime }-20 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.155
2095	10557	\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.155
2096	10856	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.155
2097	11108	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.155
2098	11117	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.155
2099	11229	\begin{align*} 2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.155
2100	14090	\begin{align*} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.155