2.3.20 Problems 1901 to 2000

Table 2.583: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1901	19570	\begin{align*} y^{\prime \prime \prime \prime }-y&=-x^{3}+1 \\ \end{align*}	✓	✓	✓	✓	0.142
1902	19574	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.142
1903	20840	\begin{align*} x^{\prime \prime }-x^{\prime }-6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.142
1904	20915	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{2 t} t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.142
1905	24050	\begin{align*} y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+54 y^{\prime \prime }-108 y^{\prime }+81 y&=x^{2} {\mathrm e}^{3 x} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.142
1906	25160	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.142
1907	25186	\begin{align*} y^{\prime \prime }-2 y&=t y \\ \end{align*}	✓	✓	✓	✓	0.142
1908	274	\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.143
1909	9106	\begin{align*} y^{\prime } x -3 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.143
1910	12761	\begin{align*} \left (-a^{2}+1\right ) x y^{\prime }+3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.143
1911	15202	\begin{align*} 2 y^{\prime \prime }+20 y^{\prime }+51 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.143
1912	16451	\begin{align*} \left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.143
1913	18571	\begin{align*} 2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.143
1914	19564	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=12 x -2 \\ \end{align*}	✓	✓	✓	✓	0.143
1915	25255	\begin{align*} t y^{\prime \prime }-y^{\prime }+4 y t^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.143
1916	356	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime }&=x^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ y^{\prime \prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.144
1917	557	\begin{align*} t x^{\prime \prime }-\left (4 t +1\right ) x^{\prime }+2 \left (2 t +1\right ) x&=0 \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.144
1918	558	\begin{align*} t x^{\prime \prime }+2 \left (t -1\right ) x^{\prime }-2 x&=0 \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.144
1919	3135	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=5 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.144
1920	3610	\begin{align*} y^{\prime }+\frac {2 y}{x}&=5 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.144
1921	3709	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.144
1922	5899	\begin{align*} a \,x^{2} y+2 y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.144
1923	6627	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.144
1924	8957	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.144
1925	10575	\begin{align*} 6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.144
1926	10959	\begin{align*} 2 y^{\prime \prime }+5 y^{\prime } x +\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.144
1927	15105	\begin{align*} y^{\left (6\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime }&=x +{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.144
1928	16458	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.144
1929	19189	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.144
1930	20916	\begin{align*} y^{\prime \prime }-3 y^{\prime }-4 y&=t^{2} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.144
1931	23991	\begin{align*} y^{\left (8\right )}-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.144
1932	25142	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.144
1933	25259	\begin{align*} y^{\prime \prime }-\tan \left (t \right ) y^{\prime }-\sec \left (t \right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.144
1934	26048	\begin{align*} x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }-3 y x&=1 \\ \end{align*}	✓	✓	✓	✗	0.144
1935	255	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\ y \left (1\right ) &= 6 \\ y^{\prime }\left (1\right ) &= 14 \\ y^{\prime \prime }\left (1\right ) &= 22 \\ \end{align*}	✓	✓	✓	✓	0.145
1936	823	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.145
1937	2107	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-7 y^{\prime \prime }-y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -6 \\ y^{\prime \prime }\left (0\right ) &= 10 \\ y^{\prime \prime \prime }\left (0\right ) &= -36 \\ \end{align*}	✓	✓	✓	✓	0.145
1938	8928	\begin{align*} y^{\left (5\right )}+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.145
1939	8936	\begin{align*} y^{\prime \prime \prime \prime }+16 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.145
1940	10773	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.145
1941	10830	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.145
1942	10886	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.145
1943	10905	\begin{align*} y^{\prime \prime } x -\left (4 x +1\right ) y^{\prime }+\left (2+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.145
1944	10956	\begin{align*} y^{\prime \prime }+3 y^{\prime } x +\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.145
1945	11038	\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.145
1946	11109	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.145
1947	11111	\begin{align*} 4 y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.145
1948	11181	\begin{align*} y^{\prime \prime }-y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.145
1949	11285	\begin{align*} y^{\prime \prime }-\frac {y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.145
1950	12298	\begin{align*} a \,{\mathrm e}^{b x} y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.145
1951	15191	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+37 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.145
1952	15222	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=t^{2} \\ y \left (0\right ) &= -12 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.145
1953	242	\begin{align*} 6 y^{\prime \prime }-7 y^{\prime }-20 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.146
1954	330	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=1+x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.146
1955	824	\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.146
1956	5890	\begin{align*} -y+y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.146
1957	7615	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.146
1958	7617	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.146
1959	10781	\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.146
1960	10972	\begin{align*} 2 \left (x +3\right ) x^{2} y^{\prime \prime }+x \left (5 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.146
1961	15298	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.146
1962	17560	\begin{align*} y^{\left (6\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.146
1963	18177	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=\sin \left (2 x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.146
1964	25257	\begin{align*} y^{\prime \prime }-2 \sec \left (t \right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.146
1965	26050	\begin{align*} {y^{\prime }}^{3}-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.146
1966	324	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=2 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.147
1967	397	\begin{align*} x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.147
1968	2313	\begin{align*} \frac {y}{t}+y^{\prime }&=\frac {1}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	0.147
1969	2716	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.147
1970	6643	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.147
1971	10697	\begin{align*} x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.147
1972	15204	\begin{align*} y^{\prime \prime }+6 y^{\prime }+34 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.147
1973	15508	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.147
1974	25911	\begin{align*} y^{\prime \prime }+2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.147
1975	377	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.148
1976	539	\begin{align*} x^{\prime \prime }+3 x^{\prime }+2 x&=t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.148
1977	828	\begin{align*} 4 y^{\prime \prime }+8 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1978	3129	\begin{align*} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=\sin \left (k x \right ) \\ \end{align*}	✓	✓	✓	✓	0.148
1979	3370	\begin{align*} x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 y^{\prime } x -\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.148
1980	3708	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1981	6731	\begin{align*} y^{\prime \prime \prime \prime }&=x^{3}+a^{4} y \\ \end{align*}	✓	✓	✓	✓	0.148
1982	9105	\begin{align*} y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1983	9561	\begin{align*} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.148
1984	10539	\begin{align*} 2 y^{\prime \prime }+5 y^{\prime } x +\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
1985	10554	\begin{align*} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1986	10580	\begin{align*} 4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
1987	10670	\begin{align*} t y^{\prime \prime }+y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
1988	10721	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
1989	10762	\begin{align*} \left (-x +3\right ) y-x \left (4-x \right ) y^{\prime }+2 \left (-x +2\right ) x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
1990	10764	\begin{align*} 4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
1991	11112	\begin{align*} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
1992	14089	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1993	15186	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.148
1994	16457	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1995	17561	\begin{align*} y^{\left (6\right )}+12 y^{\prime \prime \prime \prime }+48 y^{\prime \prime }+64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1996	17564	\begin{align*} y^{\prime \prime \prime \prime }+16 y^{\prime \prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.148
1997	18313	\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.148
1998	25917	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.148
1999	5880	\begin{align*} f \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.149
2000	6633	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.149