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	5406	\begin{align*} {y^{\prime }}^{2}+\left (b x +a \right ) y^{\prime }+c&=b y \\ \end{align*}	✓	✓	✓	✓	0.490
8002	7852	\begin{align*} y^{\prime \prime }-y&=4-x \\ \end{align*}	✓	✓	✓	✓	0.490
8003	7905	\begin{align*} y+x \left (x^{2} y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.490
8004	9666	\begin{align*} x^{\prime }&=-x+\frac {y}{4} \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.490
8005	10182	\begin{align*} 2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.490
8006	14066	\begin{align*} y&=2 y^{\prime } x +y^{2} {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.490
8007	14639	\begin{align*} 4 y+y^{\prime \prime }&=12 x^{2}-16 x \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.490
8008	15433	\begin{align*} y^{\prime \prime }+9 y&=6 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.490
8009	16005	\begin{align*} x^{\prime }&=4 x-2 y \\ y^{\prime }&=x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.490
8010	16363	\begin{align*} \left (2+x \right ) y^{\prime }-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.490
8011	17351	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.490
8012	18444	\begin{align*} x^{\prime }&=x+y+{\mathrm e}^{t} \\ y^{\prime }&=x+y-{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.490
8013	18702	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.490
8014	20925	\begin{align*} x^{\prime }&=3 x \\ y^{\prime }&=-2 y \\ \end{align*}	✓	✓	✓	✓	0.490
8015	21143	\begin{align*} x^{\prime \prime }+x&=t \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.490
8016	21300	\begin{align*} x^{\prime \prime }+2 h x^{\prime }+k^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	0.490
8017	22152	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{5}} \\ \end{align*}	✓	✓	✓	✓	0.490
8018	23306	\begin{align*} y^{\prime \prime }-y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.490
8019	23471	\begin{align*} y^{\prime \prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.490
8020	24716	\begin{align*} y^{\prime \prime }-y&=\sin \left (2 x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.490
8021	25246	\begin{align*} t y^{\prime \prime }+2 y^{\prime }+9 t y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.490
8022	2649	\begin{align*} t^{2} y^{\prime \prime }-y^{\prime } t -\left (t^{2}+\frac {5}{4}\right ) y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.491
8023	3920	\begin{align*} x_{1}^{\prime }&=-6 x_{2} \\ x_{2}^{\prime }&=x_{1}-5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.491
8024	4107	\begin{align*} y^{\prime }&=x +\frac {1}{x} \\ y \left (-2\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.491
8025	5726	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.491
8026	7101	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.491
8027	8003	\begin{align*} y^{\prime \prime }-y&=\frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	0.491
8028	8820	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.491
8029	8854	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}-8 \\ x_{2}^{\prime }&=x_{1}+x_{2}+3 \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.491
8030	9664	\begin{align*} x^{\prime }&=3 x-4 y \\ y^{\prime }&=4 x-7 y \\ \end{align*}	✓	✓	✓	✓	0.491
8031	9672	\begin{align*} x^{\prime }&=-4 x+2 y \\ y^{\prime }&=-\frac {5 x}{2}+2 y \\ \end{align*}	✓	✓	✓	✓	0.491
8032	9857	\begin{align*} y^{\prime \prime }+\left (x -2\right ) y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.491
8033	10846	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.491
8034	12952	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}-4 y^{2} \left (x +2 y\right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.491
8035	14602	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.491
8036	15164	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.491
8037	16948	\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=8 x+y \\ \end{align*}	✓	✓	✓	✓	0.491
8038	19508	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	0.491
8039	25333	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-6 y^{\prime } t -4 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.491
8040	26763	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.491
8041	346	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right ) \\ \end{align*}	✓	✓	✓	✓	0.492
8042	3833	\begin{align*} x_{1}^{\prime }&=-x_{1}+2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.492
8043	5404	\begin{align*} {y^{\prime }}^{2}-a x y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	0.492
8044	8022	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 x}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.492
8045	14688	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\frac {{\mathrm e}^{-x}}{x} \\ \end{align*}	✓	✓	✓	✓	0.492
8046	16502	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.492
8047	18448	\begin{align*} x^{\prime }+y^{\prime }+y&={\mathrm e}^{-t} \\ 2 x^{\prime }+y^{\prime }+2 y&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.492
8048	23653	\begin{align*} y^{\prime \prime }-10 y^{\prime }+21 y&=21 t^{2}+t +13 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.492
8049	487	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-4 x^{2}+3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.493
8050	493	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.493
8051	875	\begin{align*} y^{\prime \prime }-4 y&=\sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.493
8052	1928	\begin{align*} 3 y^{\prime \prime }+2 y^{\prime } x +\left (-x^{2}+4\right ) y&=0 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.493
8053	3932	\begin{align*} -y+y^{\prime }&=5 \sin \left (2 t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.493
8054	3933	\begin{align*} y+y^{\prime }&=5 \,{\mathrm e}^{t} \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.493
8055	7281	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.493
8056	8497	\begin{align*} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.493
8057	8594	\begin{align*} 4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.493
8058	10813	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.493
8059	13853	\begin{align*} x^{2} \left (a x +b \right ) y^{\prime \prime }-2 x \left (a x +2 b \right ) y^{\prime }+2 \left (a x +3 b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.493
8060	14556	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{x} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	0.493
8061	17028	\begin{align*} y^{\prime }&=\frac {x^{2}}{\sqrt {x^{2}-1}} \\ \end{align*}	✓	✓	✓	✓	0.493
8062	18203	\begin{align*} y^{\prime \prime }-2 m y^{\prime }+m^{2} y&=\sin \left (x n \right ) \\ \end{align*}	✓	✓	✓	✓	0.493
8063	20342	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.493
8064	22221	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.493
8065	23321	\begin{align*} y^{\prime \prime }+3 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.493
8066	23602	\begin{align*} x^{\prime }&=-4 x+y \\ y^{\prime }&=-x-2 y \\ \end{align*}	✓	✓	✓	✓	0.493
8067	23785	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.493
8068	25578	\begin{align*} r^{\prime \prime }+\frac {5 r^{\prime }}{2}+r&=1 \\ r \left (0\right ) &= 0 \\ r^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.493
8069	25601	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{i t} \\ \end{align*}	✓	✓	✓	✓	0.493
8070	26930	\begin{align*} y^{\prime \prime }+36 y&=x -1 \\ \end{align*}	✓	✓	✓	✓	0.493
8071	26949	\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \\ y \left (2\right ) &= 2 \\ y^{\prime }\left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.493
8072	866	\begin{align*} 4 x^{\prime \prime }+20 x^{\prime }+169 x&=0 \\ x \left (0\right ) &= 4 \\ x^{\prime }\left (0\right ) &= 16 \\ \end{align*}	✓	✓	✓	✓	0.494
8073	885	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.494
8074	1406	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-5 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.494
8075	1807	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=3 \,{\mathrm e}^{x} \sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.494
8076	1927	\begin{align*} 2 y^{\prime \prime }+5 y^{\prime } x +\left (2 x^{2}+4\right ) y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.494
8077	2766	\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2}-t^{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2}+2 t \\ \end{align*}	✓	✓	✓	✓	0.494
8078	6390	\begin{align*} a \,{\mathrm e}^{-1+y}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.494
8079	7366	\begin{align*} y^{\prime \prime }&=-4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.494
8080	8649	\begin{align*} y^{\prime \prime }+y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.494
8081	9253	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=6 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.494
8082	9370	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.494
8083	13755	\begin{align*} y^{\prime \prime } x +\left (a \,x^{n}+b \right ) y^{\prime }+x^{n -1} a n y&=0 \\ \end{align*}	✓	✓	✓	✗	0.494
8084	14607	\begin{align*} y^{\prime \prime }+6 y^{\prime }+58 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.494
8085	15985	\begin{align*} x^{\prime }&=3 x \\ y^{\prime }&=-2 y \\ \end{align*}	✓	✓	✓	✓	0.494
8086	16496	\begin{align*} y^{\prime \prime }-8 y^{\prime }+15 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 19 \\ \end{align*}	✓	✓	✓	✓	0.494
8087	17733	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.494
8088	18663	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=4 x-y \\ \end{align*}	✓	✓	✓	✓	0.494
8089	18833	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=3 \,{\mathrm e}^{2 t} t \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.494
8090	19562	\begin{align*} y^{\prime \prime }+y^{\prime }-y&=-x^{4}+3 x \\ \end{align*}	✓	✓	✓	✓	0.494
8091	21564	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}&=2 \\ \end{align*}	✓	✓	✓	✓	0.494
8092	23663	\begin{align*} y^{\prime \prime }-y&=2 t^{2}+2 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.494
8093	23702	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.494
8094	24740	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=15 \sqrt {1+{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✓	0.494
8095	25991	\begin{align*} y^{\prime }&=4 y-z \\ z^{\prime }&=2 y+z \\ \end{align*}	✓	✓	✓	✓	0.494
8096	26966	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=2 x^{2}+5 \\ \end{align*}	✓	✓	✓	✓	0.494
8097	27659	\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=5 x \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{4 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.494
8098	7113	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\cos \left ({\mathrm e}^{-x}\right ) \\ \end{align*}	✓	✓	✓	✓	0.495
8099	7496	\begin{align*} y^{3}-x y^{2}+2 x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.495
8100	7784	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.495