2.3.20 Problems 1901 to 2000

Table 2.613: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1901	537	\begin{align*} x^{\prime \prime }+9 x&=1 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.168
1902	564	\begin{align*} x^{\prime \prime }+4 x&=\delta \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.168
1903	2210	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✓	0.168
1904	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*}	✓	✓	✓	✓	0.168
1905	6626	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.168
1906	6630	\begin{align*} -15 y-7 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.168
1907	15710	\begin{align*} y^{\prime \prime }+9 y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.168
1908	16577	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.168
1909	16578	\begin{align*} x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 x y^{\prime }-18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.168
1910	16661	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=10 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.168
1911	18163	\begin{align*} y^{\prime \prime \prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.168
1912	20866	\begin{align*} -y+x y^{\prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.168
1913	21199	\begin{align*} x^{\prime \prime \prime }-x^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.168
1914	22083	\begin{align*} y^{\prime \prime \prime }-y&=x \\ \end{align*}	✓	✓	✓	✓	0.168
1915	23094	\begin{align*} 4 x^{\prime }-2 y&=\cos \left (2 t \right ) \\ x-2 y^{\prime }&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.168
1916	23391	\begin{align*} x^{5} y^{\left (5\right )}-2 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.168
1917	24684	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime }&=12 x -2 \\ \end{align*}	✓	✓	✓	✓	0.168
1918	26836	\begin{align*} x^{\prime \prime }+4 x&=4 \cos \left (2 t \right )-\frac {\sin \left (2 t \right )}{2} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= {\frac {1}{8}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.168
1919	26852	\begin{align*} x^{\prime }&=4 y+z \\ y^{\prime }&=z \\ z^{\prime }&=4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 5 \\ y \left (0\right ) &= 0 \\ z \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.168
1920	27046	\begin{align*} x^{\prime }+4 y^{\prime }-y&=0 \\ x^{\prime }+2 y&={\mathrm e}^{-t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.168
1921	6645	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.169
1922	10673	\begin{align*} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.169
1923	17370	\begin{align*} t^{2} y^{\prime \prime }+6 t y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.169
1924	22119	\begin{align*} y^{\left (6\right )}-5 y^{\prime \prime \prime \prime }+16 y^{\prime \prime \prime }-16 y^{\prime }-32 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.169
1925	22645	\begin{align*} y^{\left (6\right )}-4 y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.169
1926	22647	\begin{align*} 4 y^{\prime \prime \prime \prime }-20 y^{\prime \prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.169
1927	27759	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2}+y x \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.169
1928	543	\begin{align*} x^{\prime \prime }-4 x&=3 t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.170
1929	2162	\begin{align*} 4 y^{\prime \prime \prime \prime }-11 y^{\prime \prime }-9 y^{\prime }-2 y&=-{\mathrm e}^{x} \left (1-6 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.170
1930	6628	\begin{align*} 4 y+4 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.170
1931	16665	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=30 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.170
1932	19546	\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*}	✓	✓	✓	✓	0.170
1933	26843	\begin{align*} x^{\prime \prime }+4 x^{\prime }&=8 \sqrt {2}\, \sin \left (t +\frac {\pi }{4}\right ) \\ x \left (0\right ) &= -{\frac {40}{17}} \\ x^{\prime }\left (0\right ) &= {\frac {24}{17}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.170
1934	531	\begin{align*} x^{\prime \prime }+9 x&=0 \\ x \left (0\right ) &= 3 \\ x^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.171
1935	538	\begin{align*} x^{\prime \prime }+4 x^{\prime }+3 x&=1 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.171
1936	553	\begin{align*} x^{\prime \prime }+9 x&=6 \cos \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.171
1937	2154	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=-{\mathrm e}^{x} \left (7+6 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.171
1938	2155	\begin{align*} 2 y^{\prime \prime \prime }-7 y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{2 x} \left (17+30 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.171
1939	20197	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.171
1940	20750	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.171
1941	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*}	✓	✓	✓	✓	0.171
1942	23389	\begin{align*} 2 x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.171
1943	24649	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.171
1944	25254	\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.171
1945	26835	\begin{align*} x^{\prime \prime }+9 x&=18 \cos \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 9 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.171
1946	27131	\(\left [\begin {array}{cc} 0 & 2 i \\ 2 i & 4 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.171
1947	2153	\begin{align*} 4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y&=-{\mathrm e}^{-2 x} \left (1-15 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.172
1948	6635	\begin{align*} -3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
1949	9283	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
1950	10283	\begin{align*} f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi &=0 \\ \end{align*}	✓	✓	✓	✓	0.172
1951	10779	\begin{align*} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
1952	18972	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
1953	23511	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&=x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.172
1954	24682	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=12 x \\ \end{align*}	✓	✓	✓	✓	0.172
1955	24688	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=16 x^{3}+20 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.172
1956	25253	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.172
1957	26844	\begin{align*} x^{\prime \prime }+4 x^{\prime }&=8 \sqrt {2}\, \sin \left (2 t +\frac {\pi }{4}\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.172
1958	6667	\begin{align*} 4 y^{\prime \prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.173
1959	10550	\begin{align*} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.173
1960	11284	\begin{align*} y^{\prime \prime }&=\frac {12 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.173
1961	12530	\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.173
1962	18167	\begin{align*} y^{\prime \prime \prime \prime }-y&=1 \\ \end{align*}	✓	✓	✓	✓	0.173
1963	23635	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.173
1964	24650	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+9 y^{\prime }&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.173
1965	2576	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.174
1966	3370	\begin{align*} x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 x y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.174
1967	3709	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
1968	4450	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
1969	6612	\begin{align*} 4 y-2 y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
1970	6786	\begin{align*} a y+y^{\left (6\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
1971	9286	\begin{align*} y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1}&=0 \\ \end{align*}	✓	✓	✓	✗	0.174
1972	10150	\begin{align*} x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
1973	10965	\begin{align*} y^{\prime \prime }+3 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
1974	11299	\begin{align*} x^{2} y^{\prime \prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.174
1975	19544	\begin{align*} y^{\prime \prime \prime \prime }&=\sin \left (x \right )+24 \\ \end{align*}	✓	✓	✓	✓	0.174
1976	25160	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.174
1977	27758	\begin{align*} y^{\prime \prime }&=x y^{\prime }-y^{2} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.174
1978	2158	\begin{align*} 8 y^{\prime \prime \prime }-12 y^{\prime \prime }+6 y^{\prime }-y&={\mathrm e}^{\frac {x}{2}} \left (1+4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.175
1979	3708	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
1980	6651	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
1981	8207	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 x y^{\prime }-78 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
1982	8936	\begin{align*} y^{\prime \prime \prime \prime }+16 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.175
1983	10329	\begin{align*} x^{\prime }+y^{\prime }-x&=t +y \\ x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✗	0.175
1984	10658	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
1985	10809	\begin{align*} x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
1986	23388	\begin{align*} x^{4} y^{\prime \prime \prime \prime }-5 x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 x y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
1987	24532	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime }&=12 \\ \end{align*}	✓	✓	✓	✓	0.175
1988	24681	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=4 x^{3}+2 x \\ \end{align*}	✓	✓	✓	✓	0.175
1989	26601	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=-2 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.175
1990	26837	\begin{align*} x^{\prime \prime }+2 x^{\prime }+3 x&=\cos \left (t \right ) t \\ x \left (0\right ) &= -{\frac {1}{4}} \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.175
1991	27040	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=8 \delta \left (t \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.175
1992	27047	\begin{align*} x^{\prime }+2 x-y^{\prime }&=0 \\ x^{\prime }+x+y&=t^{2} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.175
1993	6618	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.176
1994	8956	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.176
1995	16443	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }-83 y-25&=0 \\ \end{align*}	✓	✓	✓	✗	0.176
1996	19161	\begin{align*} 40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )}&=0 \\ \end{align*}	✗	✓	✓	✗	0.176
1997	25156	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.176
1998	25264	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.176
1999	27132	\(\left [\begin {array}{cc} 3 & 4 i \\ 4 i & -5 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.176
2000	2165	\begin{align*} 2 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-5 y^{\prime }-2 y&=18 \,{\mathrm e}^{x} \left (5+2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.177