2.3.80 Problems 7901 to 8000

Table 2.733: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7901	4560	\begin{align*} 2 x^{\prime }+x-5 y^{\prime }-4 y&=28 \,{\mathrm e}^{t} \operatorname {Heaviside}\left (t -2\right ) \\ 3 x^{\prime }-2 x-4 y^{\prime }+y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.585
7902	7775	\begin{align*} x^{\prime \prime }-3 x^{\prime }+2 x&=\sin \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.585
7903	10086	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x -x&=0 \\ \end{align*}	✓	✓	✓	✗	0.585
7904	16659	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=3 x^{4} \\ \end{align*}	✓	✓	✓	✓	0.585
7905	19361	\begin{align*} x^{2} y^{\prime \prime }&=2 x y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.585
7906	19652	\begin{align*} x^{\prime }&=-x-2 y \\ y^{\prime }&=4 x-5 y \\ \end{align*}	✓	✓	✓	✓	0.585
7907	20076	\begin{align*} y^{\prime \prime }+n^{2} y&={\mathrm e}^{x} x^{4} \\ \end{align*}	✓	✓	✓	✓	0.585
7908	20517	\begin{align*} y^{\prime \prime }+{\mathrm e}^{x} \left (y^{\prime }+y\right )&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	0.585
7909	24644	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.585
7910	24653	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.585
7911	25175	\begin{align*} y_{1}^{\prime }-y_{1}&=-2 y_{2} \\ y_{2}^{\prime }-y_{2}&=2 y_{1} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 2 \\ y_{2} \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.585
7912	1033	\begin{align*} x_{1}^{\prime }&=5 x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ x_{3}^{\prime }&=-3 x_{1}+2 x_{2}+x_{3} \\ \end{align*}	✓	✓	✓	✓	0.586
7913	1806	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {4}{1+{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✗	0.586
7914	2402	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 t} t \\ \end{align*}	✓	✓	✓	✓	0.586
7915	3159	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	0.586
7916	3911	\begin{align*} x_{1}^{\prime }&=-2 x_{1}-x_{3} \\ x_{2}^{\prime }&=-x_{2} \\ x_{3}^{\prime }&=x_{1} \\ \end{align*}	✓	✓	✓	✓	0.586
7917	11677	\begin{align*} {y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.586
7918	11768	\begin{align*} x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.586
7919	15746	\(\left [\begin {array}{cccc} 1 & 3 & 5 & 7 \\ 2 & 6 & 10 & 14 \\ 3 & 9 & 15 & 21 \\ 6 & 18 & 30 & 42 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.586
7920	19112	\begin{align*} x {y^{\prime }}^{3}&=y^{\prime }+1 \\ \end{align*}	✓	✓	✓	✓	0.586
7921	20927	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=-3 x \\ \end{align*}	✓	✓	✓	✓	0.586
7922	21527	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.586
7923	21666	\begin{align*} y^{\prime \prime }&=y^{2} {\mathrm e}^{x}-{y^{\prime }}^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.586
7924	22131	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.586
7925	24630	\begin{align*} y^{\prime \prime }-4 y&=16 \,{\mathrm e}^{-2 x} x +8 x +4 \\ \end{align*}	✓	✓	✓	✓	0.586
7926	25549	\begin{align*} y^{\prime \prime }+y&=10 \,{\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	0.586
7927	25586	\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.586
7928	25591	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.586
7929	26624	\begin{align*} \left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.586
7930	26755	\begin{align*} x^{\prime }&=x-13 y \\ y^{\prime }&=\frac {x}{4}-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.586
7931	8196	\begin{align*} {y^{\prime }}^{2}-2 y^{\prime }+4 y&=4 x -1 \\ \end{align*}	✓	✓	✓	✗	0.587
7932	16676	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=5 \sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.587
7933	19778	\begin{align*} v^{\prime \prime }+\frac {2 v^{\prime }}{r}&=0 \\ \end{align*}	✓	✓	✓	✓	0.587
7934	19780	\begin{align*} y^{\prime \prime }-{y^{\prime }}^{2}-y {y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	0.587
7935	19841	\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.587
7936	20117	\begin{align*} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y&=x^{4}+2 x -5 \\ \end{align*}	✓	✓	✗	✗	0.587
7937	22183	\begin{align*} 2 y-x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.587
7938	605	\begin{align*} x^{\prime }&=y+z \\ y^{\prime }&=x+z \\ z^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.588
7939	888	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=x +1 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.588
7940	1919	\begin{align*} \left (4 x^{2}-4 x +1\right ) y^{\prime \prime }-\left (8-16 x \right ) y^{\prime }+8 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.588
7941	3718	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=5 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.588
7942	6767	\begin{align*} 6 y^{\prime \prime }+6 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.588
7943	8852	\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=4 x_{1}-2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.588
7944	9064	\begin{align*} \left (x +1\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.588
7945	9459	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=3 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.588
7946	9599	\begin{align*} -y+y^{\prime }&=1 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.588
7947	10162	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=8 \sqrt {x}\, \left (1+\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.588
7948	14583	\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.588
7949	15886	\begin{align*} y^{\prime }&=y^{2}-4 y+2 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	0.588
7950	17138	\begin{align*} -y+y^{\prime }&=10 \\ \end{align*}	✓	✓	✓	✓	0.588
7951	17771	\begin{align*} y^{\prime \prime }+y&=\csc \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.588
7952	20180	\begin{align*} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.588
7953	21136	\begin{align*} x^{\prime \prime }-x&={\mathrm e}^{2 t} t \\ \end{align*}	✓	✓	✓	✓	0.588
7954	21585	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.588
7955	23462	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=x^{2} {\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.588
7956	24431	\begin{align*} y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=0 \\ \end{align*}	✓	✓	✓	✓	0.588
7957	24552	\begin{align*} y^{\prime \prime }-y&=8 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.588
7958	24651	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.588
7959	24812	\begin{align*} y^{\prime } \left (x y^{\prime }-y+k \right )+a&=0 \\ \end{align*}	✓	✓	✓	✗	0.588
7960	25267	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.588
7961	1909	\begin{align*} \left (x +4\right ) y^{\prime \prime }-\left (2 x +4\right ) y^{\prime }+\left (6+x \right ) y&=0 \\ y \left (-3\right ) &= 2 \\ y^{\prime }\left (-3\right ) &= -2 \\ \end{align*} Series expansion around \(x=-3\).	✓	✓	✓	✓	0.589
7962	1911	\begin{align*} \left (2 x +3\right ) y^{\prime \prime }+3 y^{\prime }-y x&=0 \\ y \left (-1\right ) &= 2 \\ y^{\prime }\left (-1\right ) &= -3 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✓	0.589
7963	6690	\begin{align*} y^{\prime }+8 x y^{\prime \prime }+4 x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.589
7964	7097	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \left (2 x -3\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.589
7965	7205	\begin{align*} u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.589
7966	9266	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.589
7967	9502	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.589
7968	9765	\begin{align*} x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }&=0 \\ y \left (2\right ) &= 5 \\ y^{\prime }\left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.589
7969	10133	\begin{align*} y^{\prime \prime }+c y^{\prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	0.589
7970	10198	\begin{align*} -y+y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.589
7971	15414	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.589
7972	16080	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=-3 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.589
7973	16120	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.589
7974	16855	\begin{align*} y^{\prime }-y \tan \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.589
7975	18259	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=x \,{\mathrm e}^{2 x}+\sin \left (x \right )+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.589
7976	19589	\begin{align*} n^{2} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.589
7977	22291	\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.589
7978	25364	\begin{align*} y_{1}^{\prime }&=5 y_{1}-2 y_{2} \\ y_{2}^{\prime }&=4 y_{1}-y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.589
7979	2297	\begin{align*} y+y^{\prime }&=\frac {1}{t^{2}+1} \\ y \left (2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.590
7980	4128	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.590
7981	19878	\begin{align*} V^{\prime \prime }+\frac {2 V^{\prime }}{r}&=0 \\ \end{align*}	✓	✓	✓	✓	0.590
7982	24652	\begin{align*} y^{\prime \prime }+9 y&=\cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.590
7983	24690	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.590
7984	24750	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{\sqrt {1+{\mathrm e}^{-2 x}}} \\ \end{align*}	✓	✓	✓	✓	0.590
7985	25587	\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{c t} \\ \end{align*}	✓	✓	✓	✓	0.590
7986	919	\begin{align*} x^{\prime \prime }+6 x^{\prime }+13 x&=10 \sin \left (5 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.591
7987	1904	\begin{align*} \left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y&=0 \\ y \left (-1\right ) &= 1 \\ y^{\prime }\left (-1\right ) &= 0 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✗	0.591
7988	3160	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\sin \left ({\mathrm e}^{-x}\right ) \\ \end{align*}	✓	✓	✓	✓	0.591
7989	3428	\begin{align*} y^{\prime }&=\sin \left (t \right )^{2} \\ y \left (\frac {\pi }{6}\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.591
7990	7101	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.591
7991	7300	\begin{align*} y^{\prime \prime }+y&=8 x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.591
7992	9320	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.591
7993	9454	\begin{align*} y^{\prime \prime }+y^{\prime }+2 y&=t \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.591
7994	9616	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=t^{3} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.591
7995	16586	\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=8 x^{2}-3 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.591
7996	16621	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.591
7997	19261	\begin{align*} y^{\prime }&=\ln \left (x \right ) \\ y \left ({\mathrm e}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.591
7998	20393	\begin{align*} \left (y^{\prime }+y+x \right ) \left (x y^{\prime }+x +y\right ) \left (y^{\prime }+2 x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.591
7999	24659	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=15 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.591
8000	25982	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.591