2.3.21 Problems 2001 to 2100

Table 2.573: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2001	18312	\begin{align*} y^{\prime \prime }+\left (\tan \left (x \right )-2 \cot \left (x \right )\right ) y^{\prime }+2 \cot \left (x \right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.144
2002	18468	\begin{align*} x^{\prime \prime }+6 x^{\prime }&=12 t +2 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.144
2003	19580	\begin{align*} y^{\prime } x&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.144
2004	21583	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+3 y^{\prime }+9 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.144
2005	22227	\begin{align*} y^{\prime }-5 y&=0 \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.144
2006	23997	\begin{align*} y^{\prime \prime \prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.144
2007	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*}	✓	✓	✓	✓	0.145
2008	3123	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&=x^{2}+8 \\ \end{align*}	✓	✓	✓	✓	0.145
2009	6603	\begin{align*} y^{\prime \prime \prime }&=\sin \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	0.145
2010	14099	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=2 \,{\mathrm e}^{-x}-x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.145
2011	14819	\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=4 t \,{\mathrm e}^{-3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.145
2012	19834	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.145
2013	19857	\begin{align*} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.145
2014	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*}	✓	✓	✓	✓	0.145
2015	20095	\begin{align*} y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.145
2016	20395	\begin{align*} x^{2} {y^{\prime }}^{2}+y y^{\prime } x -6 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.145
2017	20806	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.145
2018	21533	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.145
2019	23395	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.145
2020	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*}	✓	✓	✓	✓	0.146
2021	2724	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=t^{2} \\ \end{align*}	✓	✓	✓	✓	0.146
2022	8957	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.146
2023	11099	\begin{align*} y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.146
2024	11240	\begin{align*} y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.146
2025	11251	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.146
2026	15517	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.146
2027	18080	\begin{align*} x y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.146
2028	18101	\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.146
2029	18276	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=-2 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.146
2030	18755	\begin{align*} y^{\prime \prime }+a \left (y^{\prime } x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.146
2031	21306	\begin{align*} x^{\prime \prime \prime }+a x^{\prime \prime }+b x^{\prime }+c x&=0 \\ \end{align*}	✓	✓	✓	✓	0.146
2032	22651	\begin{align*} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.146
2033	23023	\begin{align*} x^{\prime \prime }+2 x^{\prime }+4 x&=0 \\ x \left (0\right ) &= 5 \\ x \left (\frac {\pi \sqrt {3}}{6}\right ) &= 2 \,{\mathrm e}^{-\frac {\pi \sqrt {3}}{6}} \\ \end{align*}	✓	✓	✓	✓	0.146
2034	11249	\begin{align*} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.147
2035	13998	\begin{align*} y^{2} \left (3 y-6 y^{\prime } x \right )-x \left (y-2 y^{\prime } x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.147
2036	14816	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.147
2037	20358	\begin{align*} y^{\prime }+2 y^{\prime \prime }+y^{\prime \prime \prime }&={\mathrm e}^{2 x}+x^{2}+x \\ \end{align*}	✓	✓	✓	✓	0.147
2038	20988	\begin{align*} u^{\prime }&=u^{3} \\ u \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.147
2039	21181	\begin{align*} x^{\prime \prime \prime }-x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ x \left (\infty \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.147
2040	23397	\begin{align*} x y^{\prime \prime \prime }-\frac {6 y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.147
2041	24692	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.147
2042	256	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 5 \\ y^{\prime \prime }\left (1\right ) &= -11 \\ \end{align*}	✓	✓	✓	✓	0.148
2043	340	\begin{align*} y^{\left (5\right )}+2 y^{\prime \prime \prime }+2 y^{\prime \prime }&=3 x^{2}-1 \\ \end{align*}	✓	✓	✓	✓	0.148
2044	1057	\begin{align*} 2 y^{\prime } x&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.148
2045	2148	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{-3 x} \left (6 x^{2}-23 x +32\right ) \\ \end{align*}	✓	✓	✓	✓	0.148
2046	2167	\begin{align*} 2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime }-y&=3 \,{\mathrm e}^{-\frac {x}{2}} \left (1-6 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.148
2047	2296	\begin{align*} 2 t y+y^{\prime }&=t \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.148
2048	3129	\begin{align*} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=\sin \left (x k \right ) \\ \end{align*}	✓	✓	✓	✓	0.148
2049	8924	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }-y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.148
2050	9113	\begin{align*} y^{\prime }-\frac {y}{x}&=x^{2} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.148
2051	10298	\begin{align*} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
2052	10804	\begin{align*} y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
2053	11036	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
2054	15189	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.148
2055	16997	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.148
2056	20363	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime }-6 y&={\mathrm e}^{2 x} \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✓	0.148
2057	22320	\begin{align*} y^{\prime \prime \prime }&=-24 \cos \left (\frac {\pi x}{2}\right ) \\ y \left (0\right ) &= -4 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.148
2058	23381	\begin{align*} 8 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
2059	23387	\begin{align*} 3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
2060	23415	\begin{align*} x \left (x -2\right ) y^{\prime \prime }-2 \left (x^{2}-3 x +3\right ) y^{\prime }+\left (x^{2}-4 x +6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
2061	23489	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.148
2062	24035	\begin{align*} 6 x^{2} y^{\prime \prime }-5 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
2063	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*}	✓	✓	✓	✓	0.148
2064	24865	\begin{align*} x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
2065	2150	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&={\mathrm e}^{-2 x} \left (3 x^{2}-17 x +2\right ) \\ \end{align*}	✓	✓	✓	✓	0.149
2066	4468	\begin{align*} y^{\left (5\right )}+4 y^{\prime \prime \prime }&=7+x \\ \end{align*}	✓	✓	✓	✓	0.149
2067	6925	\begin{align*} 2 y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.149
2068	7235	\begin{align*} \left ({\mathrm e}^{x}+1\right ) y^{\prime }+2 \,{\mathrm e}^{x} y&=\left ({\mathrm e}^{x}+1\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.149
2069	10499	\begin{align*} x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.149
2070	11171	\begin{align*} y^{\prime \prime } x -2 \left (x +1\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.149
2071	19189	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.149
2072	22252	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.149
2073	472	\begin{align*} x^{3} \left (1-x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.150
2074	3135	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=5 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.150
2075	3641	\begin{align*} y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.150
2076	6647	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=x \left (1-{\mathrm e}^{x} x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.150
2077	9290	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.150
2078	14571	\begin{align*} \left (x^{3}-x^{2}\right ) y^{\prime \prime }-\left (x^{3}+2 x^{2}-2 x \right ) y^{\prime }+\left (2 x^{2}+2 x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.150
2079	22052	\begin{align*} x y^{2}+\left (y^{2} x^{2}+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.150
2080	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*}	✓	✓	✓	✓	0.150
2081	23424	\begin{align*} y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.150
2082	2293	\begin{align*} y^{\prime }+\sin \left (t \right ) y&=0 \\ y \left (0\right ) &= {\frac {3}{2}} \\ \end{align*}	✓	✓	✓	✓	0.151
2083	5478	\begin{align*} x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.151
2084	8637	\begin{align*} 9 y^{\prime \prime }-6 y^{\prime }+y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.151
2085	8948	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.151
2086	11189	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.151
2087	12790	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y-32 \sin \left (2 x \right )+24 \cos \left (2 x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.151
2088	14565	\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.151
2089	14812	\begin{align*} y+y^{\prime }&=2 \sin \left (t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.151
2090	14998	\(\left [\begin {array}{cc} 3 & -1 \\ 1 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.151
2091	15310	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.151
2092	15699	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=x \,{\mathrm e}^{x}-3 x^{2} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.151
2093	21578	\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+16 y^{\prime \prime }&=96 \,{\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.151
2094	22173	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.151
2095	22625	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=3 \,{\mathrm e}^{x}-2 \\ \end{align*}	✓	✓	✓	✓	0.151
2096	22809	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.151
2097	2217	\begin{align*} 4 y^{\prime \prime \prime }-3 y^{\prime }-y&={\mathrm e}^{-\frac {x}{2}} \left (2-3 x \right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 15 \\ y^{\prime \prime }\left (0\right ) &= -17 \\ \end{align*}	✓	✓	✓	✓	0.152
2098	6697	\begin{align*} -8 y+3 y^{\prime } x +x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.152
2099	7238	\begin{align*} y^{\prime }+y \tanh \left (x \right )&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.152
2100	9288	\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.152