2.3.81 Problems 8001 to 8100

Table 2.735: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
8001	26965	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=8 \sin \left (4 x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.591
8002	1807	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=3 \,{\mathrm e}^{x} \sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.592
8003	2583	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 t} t \\ \end{align*}	✓	✓	✓	✓	0.592
8004	5377	\begin{align*} {y^{\prime }}^{2}+2 y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.592
8005	7100	\begin{align*} y^{\prime \prime }+y&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.592
8006	7601	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.592
8007	8001	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=\frac {1}{1+{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✗	0.592
8008	8036	\begin{align*} x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+\left (x^{2}+3 x +3\right ) y&=\left (-x^{2}+6\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	0.592
8009	8906	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.592
8010	9175	\begin{align*} y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.592
8011	9473	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=4 x+y \\ \end{align*}	✓	✓	✓	✓	0.592
8012	10142	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ y^{\prime }\left (1\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.592
8013	14818	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=t \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.592
8014	15473	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.592
8015	16099	\begin{align*} y^{\prime \prime }+4 y&=-3 t^{2}+2 t +3 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.592
8016	16103	\begin{align*} y^{\prime \prime }+4 y&=t -\frac {1}{20} t^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.592
8017	16587	\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=8 x^{2}-3 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.592
8018	19218	\begin{align*} x^{\prime }&=y+z-x \\ y^{\prime }&=x-y+z \\ z^{\prime }&=x+y-z \\ \end{align*}	✓	✓	✓	✓	0.592
8019	20415	\begin{align*} y&=x y^{\prime }+y^{\prime }-{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.592
8020	21901	\begin{align*} \left (2 x -1\right ) y^{\prime \prime }-3 y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.592
8021	23681	\begin{align*} n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.592
8022	24595	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=6 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.592
8023	25958	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.592
8024	1415	\begin{align*} x_{1}^{\prime }&=-\frac {x_{1}}{2}-\frac {x_{2}}{8} \\ x_{2}^{\prime }&=2 x_{1}-\frac {x_{2}}{2} \\ \end{align*}	✓	✓	✓	✓	0.593
8025	3717	\begin{align*} 4 y+y^{\prime \prime }&=8 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.593
8026	3806	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=5 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.593
8027	8560	\begin{align*} \left (x -1\right ) y^{\prime \prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.593
8028	9073	\begin{align*} y^{\prime }&=2 \sin \left (x \right ) \cos \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.593
8029	9258	\begin{align*} y^{\prime \prime }-3 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.593
8030	9521	\begin{align*} y^{\prime \prime }-y x&=1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.593
8031	12888	\begin{align*} x y^{\prime \prime }+2 y^{\prime }-x y^{n}&=0 \\ \end{align*}	✗	✗	✗	✗	0.593
8032	14716	\begin{align*} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.593
8033	15001	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=-5 x-3 y \\ \end{align*}	✓	✓	✓	✓	0.593
8034	15418	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.593
8035	16347	\begin{align*} \left (x^{2}-4\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.593
8036	16658	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=3 x^{2} {\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.593
8037	17407	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.593
8038	19606	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.593
8039	23987	\begin{align*} y^{\prime \prime }-9 y&={\mathrm e}^{x}+3 \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.593
8040	24678	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=x^{2}+3 x +3 \\ \end{align*}	✓	✓	✓	✓	0.593
8041	24723	\begin{align*} y^{\prime \prime }+y&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.593
8042	25566	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=5 \cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.593
8043	5886	\begin{align*} x y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.594
8044	9340	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x^{2}+2 x +2 \\ \end{align*}	✓	✓	✓	✓	0.594
8045	10248	\begin{align*} y^{\prime \prime }+y&=\frac {1}{x} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.594
8046	14077	\begin{align*} {y^{\prime }}^{2} x^{2}-2 \left (y x +2 y^{\prime }\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.594
8047	14175	\begin{align*} \left (x y^{\prime }-y\right )^{2}+x^{2} y y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.594
8048	14636	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.594
8049	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.	✓	✓	✓	✓	0.594
8050	15415	\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.594
8051	16093	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.594
8052	20606	\begin{align*} \left (x +1\right ) y^{\prime \prime }-2 \left (x +3\right ) y^{\prime }+\left (5+x \right ) y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	0.594
8053	25590	\begin{align*} y^{\prime \prime }+y&=t +{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.594
8054	26971	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=9 \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.594
8055	351	\begin{align*} 4 y+y^{\prime \prime }&=2 x \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.595
8056	1028	\begin{align*} x_{1}^{\prime }&=-x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ x_{3}^{\prime }&=x_{1}+2 x_{2}+x_{3} \\ x_{4}^{\prime }&=x_{2}+x_{4} \\ \end{align*}	✓	✓	✓	✓	0.595
8057	1842	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+\left (2-x \right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.595
8058	2743	\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2} \\ x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.595
8059	3213	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=x^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.595
8060	4004	\begin{align*} y^{\prime \prime }+x y^{\prime }-4 y&=6 \,{\mathrm e}^{x} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.595
8061	5494	\begin{align*} {y^{\prime }}^{2} x^{2}&=a^{2} \\ \end{align*}	✓	✓	✓	✓	0.595
8062	5499	\begin{align*} {y^{\prime }}^{2} x^{2}-x y^{\prime }+y \left (1-y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.595
8063	7776	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=3 \sin \left (x \right ) \\ y \left (0\right ) &= -{\frac {9}{10}} \\ y^{\prime }\left (0\right ) &= -{\frac {7}{10}} \\ \end{align*}	✓	✓	✓	✓	0.595
8064	8944	\begin{align*} y^{\prime \prime }+9 y&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.595
8065	10360	\begin{align*} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.595
8066	13152	\(\left [\begin {array}{ccc} 2 & -2 & 0 \\ 2 & -2 & -1 \\ -2 & 2 & 3 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.595
8067	14286	\begin{align*} x^{\prime \prime }+4 x^{\prime }+3 x&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.595
8068	15009	\begin{align*} x^{\prime }&=5 x-4 y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.595
8069	15010	\begin{align*} x^{\prime }&=-6 x+2 y \\ y^{\prime }&=-2 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.595
8070	16168	\begin{align*} x&=\left (x^{2}-9\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.595
8071	16701	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=12 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.595
8072	17403	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.595
8073	21539	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=x^{2}+2 x \\ \end{align*}	✓	✓	✓	✓	0.595
8074	22635	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.595
8075	25371	\begin{align*} y_{1}^{\prime }&=-y_{1}+2 y_{2} \\ y_{2}^{\prime }&=-2 y_{1}-y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.595
8076	25385	\begin{align*} y_{1}^{\prime }&=-2 y_{1}+y_{2} \\ y_{2}^{\prime }&=-4 y_{1}+3 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.595
8077	25597	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=t^{2} \\ \end{align*}	✓	✓	✓	✓	0.595
8078	26581	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\cos \left (x \right ) {\mathrm e}^{-x}+x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.595
8079	26597	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.595
8080	26732	\begin{align*} x^{\prime }&=y+z \\ y^{\prime }&=x+z \\ z^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.595
8081	900	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.596
8082	1899	\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y&=0 \\ y \left (-1\right ) &= 1 \\ y^{\prime }\left (-1\right ) &= -1 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✓	0.596
8083	5552	\begin{align*} y {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.596
8084	7112	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.596
8085	9612	\begin{align*} -y+y^{\prime }&=1+{\mathrm e}^{t} t \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.596
8086	10037	\begin{align*} t^{2} y^{\prime \prime }-2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.596
8087	10212	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.596
8088	12667	\begin{align*} y^{\prime \prime }&=-\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {\left (-2 x^{2}+1\right ) y}{4 x^{6}} \\ \end{align*}	✓	✓	✓	✗	0.596
8089	16619	\begin{align*} y^{\prime \prime }+9 y&=x^{3} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.596
8090	16884	\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-5 \left (x -1\right ) y^{\prime }+9 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.596
8091	21514	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.596
8092	22676	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.596
8093	23086	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=x^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.596
8094	24605	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.596
8095	26761	\begin{align*} x^{\prime }&=3 x+7 y \\ y^{\prime }&=2 x+5 y \\ \end{align*}	✓	✓	✓	✓	0.596
8096	27128	\(\left [\begin {array}{ccc} 0 & 0 & 0 \\ 1 & 1 & -2 \\ 0 & -2 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.596
8097	632	\begin{align*} x_{1}^{\prime }&=x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.597
8098	1016	\begin{align*} x_{1}^{\prime }&=-19 x_{1}+12 x_{2}+84 x_{3} \\ x_{2}^{\prime }&=5 x_{2} \\ x_{3}^{\prime }&=-8 x_{1}+4 x_{2}+33 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.597
8099	1453	\begin{align*} x_{1}^{\prime }&=2 x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=\frac {9 x_{1}}{5}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.597
8100	1935	\begin{align*} y^{\prime \prime }+\left (3 x^{2}+12 x +13\right ) y^{\prime }+\left (5+2 x \right ) y&=0 \\ y \left (-2\right ) &= 2 \\ y^{\prime }\left (-2\right ) &= -3 \\ \end{align*} Series expansion around \(x=-2\).	✓	✓	✓	✓	0.597