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	24805	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.121
2002	1782	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.122
2003	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 \(t=0\).	✗	✗	✓	✗	0.122
2004	3190	\begin{align*} y^{\prime \prime \prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.122
2005	3624	\begin{align*} y^{\prime }+\frac {2 y}{x}&=4 x \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.122
2006	3799	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime }&=\sin \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.122
2007	4520	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=54 t \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.122
2008	7238	\begin{align*} y^{\prime }+y \tanh \left (x \right )&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.122
2009	8928	\begin{align*} y^{\left (5\right )}+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.122
2010	10733	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.122
2011	14123	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=-3 \,{\mathrm e}^{2 x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.122
2012	16772	\begin{align*} y^{\prime \prime }-9 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 9 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.122
2013	18173	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.122
2014	20395	\begin{align*} x^{2} {y^{\prime }}^{2}+x y^{\prime } y-6 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.122
2015	23653	\begin{align*} y^{\prime \prime }-10 y^{\prime }+21 y&=21 t^{2}+t +13 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.122
2016	25163	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.122
2017	25627	\begin{align*} y^{\prime \prime }+16 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.122
2018	957	\begin{align*} y^{\prime \prime \prime \prime }&=y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+2 y \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 15 \\ \end{align*}	✓	✓	✓	✓	0.123
2019	12845	\begin{align*} y^{\prime \prime }+a \,x^{r} y^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	0.123
2020	18966	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+3 y&=t \\ \end{align*}	✓	✓	✓	✗	0.123
2021	23308	\begin{align*} 6 y^{\prime \prime \prime }-4 i y^{\prime \prime }+\left (3+i\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.123
2022	23425	\begin{align*} y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.123
2023	23644	\begin{align*} y^{\prime \prime }+10 y^{\prime }+26 y&=37 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.123
2024	23652	\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=16 t \,{\mathrm e}^{-t}-15 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -9 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.123
2025	23660	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=3 \,{\mathrm e}^{2 t} t -4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.123
2026	3117	\begin{align*} y^{\prime \prime \prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.124
2027	9827	\begin{align*} x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.124
2028	12917	\begin{align*} y y^{\prime \prime }-a x&=0 \\ \end{align*}	✗	✗	✗	✗	0.124
2029	14626	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+y^{\prime }-6 y&=-18 x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	0.124
2030	15203	\begin{align*} 4 y^{\prime \prime }+40 y^{\prime }+101 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.124
2031	16133	\begin{align*} y^{\prime \prime }-4 y&={\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.124
2032	16661	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=10 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.124
2033	17570	\begin{align*} 2 y^{\left (5\right )}+7 y^{\prime \prime \prime \prime }+17 y^{\prime \prime \prime }+17 y^{\prime \prime }+5 y^{\prime }&=0 \\ y \left (0\right ) &= -3 \\ y^{\prime }\left (0\right ) &= {\frac {15}{2}} \\ y^{\prime \prime }\left (0\right ) &= {\frac {17}{4}} \\ y^{\prime \prime \prime }\left (0\right ) &= -{\frac {385}{8}} \\ y^{\prime \prime \prime \prime }\left (0\right ) &= {\frac {1217}{16}} \\ \end{align*}	✓	✓	✓	✓	0.124
2034	17735	\begin{align*} t y^{\prime \prime }+2 y^{\prime }+t y&=0 \\ \end{align*}	✓	✓	✓	✓	0.124
2035	22146	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x}+1 \\ \end{align*}	✓	✓	✓	✓	0.124
2036	23387	\begin{align*} 3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.124
2037	23459	\begin{align*} y^{\prime \prime \prime }+y^{\prime }-2 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.124
2038	23650	\begin{align*} y^{\prime \prime }-3 y^{\prime }-4 y&=25 t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.124
2039	25060	\begin{align*} y^{\prime }-4 y&={\mathrm e}^{4 t} \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.124
2040	336	\begin{align*} y^{\left (5\right )}+5 y^{\prime \prime \prime \prime }-y&=17 \\ \end{align*}	✓	✓	✓	✓	0.125
2041	491	\begin{align*} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.125
2042	1467	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
2043	6570	\begin{align*} X \left (x , y\right )^{3} y^{\prime \prime }&=1 \\ \end{align*}	✗	✗	✗	✗	0.125
2044	6655	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=x^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.125
2045	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*}	✓	✓	✓	✓	0.125
2046	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.	✓	✓	✓	✓	0.125
2047	10244	\begin{align*} y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.125
2048	11189	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.125
2049	11294	\begin{align*} y^{\prime \prime }&=\left (\frac {1}{x}-\frac {3}{16 x^{2}}\right ) y \\ \end{align*}	✓	✓	✓	✓	0.125
2050	14952	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.125
2051	15105	\begin{align*} y^{\left (6\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime }&=x +{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.125
2052	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.	✓	✓	✓	✓	0.125
2053	15201	\begin{align*} 3 y^{\prime \prime }+8 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.125
2054	16665	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=30 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.125
2055	17371	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
2056	17376	\begin{align*} t y^{\prime \prime }+2 y^{\prime }+16 t y&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
2057	17532	\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
2058	19035	\begin{align*} x_{1}^{\prime }&=-4 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.125
2059	21187	\begin{align*} x^{\prime \prime \prime \prime }-x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ x^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.125
2060	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.	✓	✓	✓	✓	0.125
2061	22712	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=3 x^{2}-4 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.125
2062	22779	\begin{align*} y^{\prime \prime \prime }-4 y&=4 x +2+3 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.125
2063	23417	\begin{align*} y^{\prime \prime }-\left (1+\frac {3}{2 x}\right ) y^{\prime }+\frac {3 y}{2 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.125
2064	23657	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=3 t^{3}-9 t^{2}-5 t +1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.125
2065	25186	\begin{align*} y^{\prime \prime }-2 y&=t y \\ \end{align*}	✓	✓	✓	✓	0.125
2066	414	\begin{align*} y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.126
2067	6776	\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*}	✓	✓	✓	✓	0.126
2068	6942	\begin{align*} y-3 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.126
2069	14009	\begin{align*} x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.126
2070	14748	\begin{align*} \left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.126
2071	15198	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.126
2072	15517	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.126
2073	18753	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.126
2074	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.	✓	✓	✓	✓	0.126
2075	23390	\begin{align*} 2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-12 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.126
2076	23489	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.126
2077	23633	\begin{align*} y^{\prime }-3 y&=13 \cos \left (2 t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.126
2078	25637	\begin{align*} y^{\prime \prime }+a^{2} y&=1 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.126
2079	3939	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=4 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.127
2080	4370	\begin{align*} y^{\prime }&=\left (\sin \left (x \right )^{2}-y\right ) \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.127
2081	6775	\begin{align*} -4 y-2 y^{\prime } x +4 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
2082	6941	\begin{align*} 3 y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
2083	7236	\begin{align*} x \ln \left (x \right ) y^{\prime }+y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.127
2084	8804	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=4 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.127
2085	9113	\begin{align*} y^{\prime }-\frac {y}{x}&=x^{2} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.127
2086	14077	\begin{align*} x^{2} {y^{\prime }}^{2}-2 \left (y x +2 y^{\prime }\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
2087	14565	\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.127
2088	14954	\begin{align*} \left (-t^{2}+t \right ) x^{\prime \prime }+\left (-t^{2}+2\right ) x^{\prime }+\left (2-t \right ) x&=0 \\ \end{align*}	✓	✓	✓	✗	0.127
2089	16151	\begin{align*} y^{\prime \prime }+16 y&=t \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.127
2090	18755	\begin{align*} y^{\prime \prime }+a \left (y^{\prime } x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.127
2091	20050	\begin{align*} y^{\prime \prime \prime }-y&=\left ({\mathrm e}^{x}+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.127
2092	20085	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=x \,{\mathrm e}^{x}+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.127
2093	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*}	✓	✓	✓	✓	0.127
2094	21199	\begin{align*} x^{\prime \prime \prime }-x^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.127
2095	25158	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.127
2096	3940	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=30 \,{\mathrm e}^{-3 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.128
2097	5759	\begin{align*} -\left (a^{2}-b \,{\mathrm e}^{x}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.128
2098	6646	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.128
2099	7212	\begin{align*} y^{\prime \prime }+y \,{\mathrm e}^{2 x}&=n^{2} y \\ \end{align*}	✓	✓	✓	✗	0.128
2100	10734	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.128