2.3.20 Problems 1901 to 2000

Table 2.571: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1901	23424	\begin{align*} y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.115
1902	25259	\begin{align*} y^{\prime \prime }-\tan \left (t \right ) y^{\prime }-\sec \left (t \right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.115
1903	25337	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{t}+\frac {\left (1-t \right ) y}{t^{3}}&=0 \\ \end{align*} Series expansion around \(t=0\).	✗	✗	✓	✗	0.115
1904	25634	\begin{align*} y^{\prime \prime }+y&=\cos \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.115
1905	360	\begin{align*} y^{\prime \prime \prime \prime }-y&=5 \\ 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 ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.116
1906	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*}	✓	✓	✓	✓	0.116
1907	8937	\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*}	✓	✓	✓	✓	0.116
1908	9109	\begin{align*} y-x +x y \cot \left (x \right )+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.116
1909	10156	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y {y^{\prime }}^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	0.116
1910	12792	\begin{align*} 4 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+11 y^{\prime \prime }-3 y^{\prime }-4 \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.116
1911	15220	\begin{align*} y+2 y^{\prime }&={\mathrm e}^{-\frac {t}{2}} \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.116
1912	18466	\begin{align*} x^{\prime \prime }-x^{\prime }&=1 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.116
1913	20094	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.116
1914	22173	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.116
1915	23414	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{4}/{3}}}-\frac {6}{x^{2}}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.116
1916	24069	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y&=x^{5}+2 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.116
1917	24487	\begin{align*} 4 y+4 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.116
1918	25638	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=1 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.116
1919	232	\begin{align*} y y^{\prime \prime }&=6 x^{4} \\ \end{align*}	✗	✗	✗	✗	0.117
1920	6637	\begin{align*} -3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&={\mathrm e}^{-x}+3 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.117
1921	14354	\begin{align*} x^{\prime \prime }-2 x^{\prime }+2 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.117
1922	14424	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 y^{\prime } x -8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.117
1923	15100	\begin{align*} x^{\prime \prime \prime \prime }+x&=t^{3} \\ \end{align*}	✓	✓	✓	✓	0.117
1924	16803	\begin{align*} y^{\prime \prime }&=\delta \left (t -3\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.117
1925	19581	\begin{align*} x^{2} y^{\prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.117
1926	19832	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.117
1927	20058	\begin{align*} y^{\prime \prime \prime \prime }+y&=x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.117
1928	21881	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+42 y^{\prime \prime }-104 y^{\prime }+169 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.117
1929	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*}	✓	✓	✓	✗	0.117
1930	24845	\begin{align*} 6 x {y^{\prime }}^{2}-\left (2 y+3 x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.117
1931	25064	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.117
1932	249	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.118
1933	961	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.118
1934	2128	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -2 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.118
1935	3800	\begin{align*} y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y&=8 \,{\mathrm e}^{-x}+1 \\ \end{align*}	✓	✓	✓	✓	0.118
1936	4467	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }&=9 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.118
1937	6925	\begin{align*} 2 y x +\left (y^{2}+x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.118
1938	9311	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.118
1939	9312	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.118
1940	11299	\begin{align*} x^{2} y^{\prime \prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.118
1941	18216	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=x^{2}+x \\ \end{align*}	✓	✓	✓	✓	0.118
1942	18220	\begin{align*} y-2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.118
1943	20054	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.118
1944	20065	\begin{align*} y^{\prime }+2 y^{\prime \prime }+y^{\prime \prime \prime }&={\mathrm e}^{2 x}+x^{2}+x \\ \end{align*}	✓	✓	✓	✓	0.118
1945	22817	\begin{align*} t y^{\prime \prime }-t y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.118
1946	23376	\begin{align*} 2 y-2 y^{\prime } x +3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.118
1947	23422	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.118
1948	24857	\begin{align*} x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.118
1949	25065	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.118
1950	25256	\begin{align*} t y^{\prime \prime }-2 \left (t +1\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.118
1951	958	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.119
1952	3180	\begin{align*} y^{\prime \prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.119
1953	4515	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=2 t^{2}+1 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.119
1954	5760	\begin{align*} -\left (a^{2}-{\mathrm e}^{2 x}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.119
1955	7240	\begin{align*} x^{\prime }&=\cos \left (y \right )-x \tan \left (y \right ) \\ \end{align*}	✓	✓	✓	✓	0.119
1956	7991	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.119
1957	8499	\begin{align*} x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.119
1958	9309	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=1 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.119
1959	11283	\begin{align*} y^{\prime \prime }&=\frac {20 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.119
1960	17580	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.119
1961	18213	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=x^{2}+x \\ \end{align*}	✓	✓	✓	✓	0.119
1962	18227	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&={\mathrm e}^{x}+1 \\ \end{align*}	✓	✓	✓	✓	0.119
1963	19537	\begin{align*} a^{4} y+2 a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.119
1964	19542	\begin{align*} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+48 y^{\prime \prime }+16 y^{\prime }-96 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.119
1965	20358	\begin{align*} y^{\prime }+2 y^{\prime \prime }+y^{\prime \prime \prime }&={\mathrm e}^{2 x}+x^{2}+x \\ \end{align*}	✓	✓	✓	✓	0.119
1966	20700	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.119
1967	22810	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=4 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.119
1968	23395	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.119
1969	23651	\begin{align*} y^{\prime \prime }+13 y^{\prime }+36 y&=10-72 t \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.119
1970	25063	\begin{align*} y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.119
1971	3936	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.120
1972	9110	\begin{align*} y^{\prime }-y x&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.120
1973	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*}	✓	✓	✓	✗	0.120
1974	15077	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=x^{2}-{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.120
1975	15192	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.120
1976	15215	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 t} t^{2} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.120
1977	16581	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.120
1978	16583	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.120
1979	19036	\begin{align*} x_{1}^{\prime }&=5 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.120
1980	19037	\begin{align*} x_{1}^{\prime }&=-x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.120
1981	19536	\begin{align*} a^{4} y+2 a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.120
1982	22625	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=3 \,{\mathrm e}^{x}-2 \\ \end{align*}	✓	✓	✓	✓	0.120
1983	22791	\begin{align*} s^{\prime \prime \prime \prime }-2 s^{\prime \prime }+s&=100 \cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.120
1984	23381	\begin{align*} 8 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.120
1985	24045	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{x} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.120
1986	25257	\begin{align*} y^{\prime \prime }-2 \sec \left (t \right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.120
1987	3935	\begin{align*} y^{\prime \prime }+4 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.121
1988	6657	\begin{align*} -a^{3} y+3 a^{2} y^{\prime }-3 a y^{\prime \prime }+y^{\prime \prime \prime }&={\mathrm e}^{a x} \\ \end{align*}	✓	✓	✓	✓	0.121
1989	12837	\begin{align*} y^{\prime \prime }-6 y^{2}-x&=0 \\ \end{align*}	✗	✗	✗	✗	0.121
1990	14348	\begin{align*} x^{\prime \prime \prime }+x^{\prime \prime }&=2 \,{\mathrm e}^{t}+3 t^{2} \\ \end{align*}	✓	✓	✓	✓	0.121
1991	15104	\begin{align*} y^{\left (6\right )}-y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.121
1992	15200	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.121
1993	15264	\begin{align*} y^{\prime \prime \prime }&=2 y^{\prime \prime }-4 y^{\prime }+\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.121
1994	16148	\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.121
1995	16159	\begin{align*} y^{2} y^{\prime \prime }&=8 x^{2} \\ \end{align*}	✗	✗	✗	✗	0.121
1996	16582	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.121
1997	16776	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=t^{2} {\mathrm e}^{3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.121
1998	18898	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=t \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.121
1999	22720	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+24 y&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.121
2000	23397	\begin{align*} x y^{\prime \prime \prime }-\frac {6 y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.121