2.3.70 Problems 6901 to 7000

Table 2.671: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
6901	21291	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.353
6902	22138	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x^{2}-1 \\ \end{align*}	✓	✓	✓	✓	0.353
6903	24026	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.353
6904	24091	\begin{align*} y^{\prime \prime } x +y^{\prime }-x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.353
6905	24434	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.353
6906	24474	\begin{align*} y^{\prime \prime }-4 y^{\prime }+7 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.353
6907	24794	\begin{align*} 3 x^{4} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.353
6908	25328	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }+2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.353
6909	1287	\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.354
6910	1818	\begin{align*} y^{\prime \prime } x -\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y&=6 \,{\mathrm e}^{x} x^{3} \\ \end{align*}	✓	✓	✓	✗	0.354
6911	1925	\begin{align*} y^{\prime \prime }-2 y^{\prime } x -\left (3 x^{2}+2\right ) y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.354
6912	1926	\begin{align*} y^{\prime \prime }+3 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.354
6913	2838	\begin{align*} y^{\prime \prime }-2 y^{\prime }+\left (1+\lambda \right ) y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.354
6914	3433	\begin{align*} y^{\prime }&=y-1 \\ \end{align*}	✓	✓	✓	✓	0.354
6915	3802	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=2 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.354
6916	3898	\begin{align*} x_{1}^{\prime }&=3 x_{1}+13 x_{2} \\ x_{2}^{\prime }&=-x_{1}-3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.354
6917	6456	\begin{align*} {y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.354
6918	6536	\begin{align*} \left (1+y^{2}\right ) y^{\prime \prime }&=3 y {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.354
6919	12853	\begin{align*} y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.354
6920	14380	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.354
6921	16088	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.354
6922	16953	\begin{align*} x^{\prime }&=-x+2 y \\ y^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.354
6923	18649	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=3 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.354
6924	18700	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=8 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.354
6925	22056	\begin{align*} 3 y^{2} x^{2}+\left (2 x^{3} y+y^{4} x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.354
6926	24761	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\sin \left ({\mathrm e}^{-x}\right ) \\ \end{align*}	✓	✓	✓	✓	0.354
6927	24814	\begin{align*} y&=x^{6} {y^{\prime }}^{3}-y^{\prime } x \\ \end{align*}	✓	✓	✗	✗	0.354
6928	24889	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.354
6929	25122	\begin{align*} y^{\prime \prime }+y&=2 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.354
6930	25532	\begin{align*} y^{\prime }&=a y \\ \end{align*}	✓	✓	✓	✓	0.354
6931	25678	\begin{align*} 3 y^{\prime }&=4 y \\ \end{align*}	✓	✓	✓	✓	0.354
6932	261	\begin{align*} y^{\prime \prime }+2 y&=6 x +4 \\ \end{align*}	✓	✓	✓	✓	0.355
6933	323	\begin{align*} y^{\prime \prime }-y^{\prime }+2 y&=3 x +4 \\ \end{align*}	✓	✓	✓	✓	0.355
6934	352	\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*}	✓	✓	✓	✓	0.355
6935	1087	\begin{align*} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \\ y \left (-3\right ) &= 1 \\ y^{\prime }\left (-3\right ) &= 0 \\ \end{align*} Series expansion around \(x=-3\).	✓	✓	✓	✓	0.355
6936	1418	\begin{align*} x_{1}^{\prime }&=-\frac {3 x_{1}}{2}+x_{2} \\ x_{2}^{\prime }&=-\frac {x_{1}}{4}-\frac {x_{2}}{2} \\ \end{align*}	✓	✓	✓	✓	0.355
6937	1419	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=-\frac {5 x_{1}}{2}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.355
6938	1846	\begin{align*} \left (-x +2\right ) y^{\prime \prime }+2 y&=0 \\ y \left (0\right ) &= a_{0} \\ y^{\prime }\left (0\right ) &= a_{1} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.355
6939	1923	\begin{align*} y^{\prime \prime }-3 y^{\prime } x +\left (2 x^{2}+5\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.355
6940	3719	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=3 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.355
6941	3849	\begin{align*} x_{1}^{\prime }&=-x_{1}+4 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 3 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.355
6942	5825	\begin{align*} -\left (-x^{2}-x +1\right ) y-\left (2 x +1\right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.355
6943	8904	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.355
6944	8944	\begin{align*} y^{\prime \prime }+9 y&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.355
6945	9806	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=x^{2}+2 x +1 \\ \end{align*}	✓	✓	✓	✓	0.355
6946	10384	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.355
6947	14285	\begin{align*} \frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2}&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.355
6948	14917	\begin{align*} x^{\prime \prime }-3 x^{\prime }+2 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.355
6949	15125	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.355
6950	15265	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=3 x-4 y \\ \end{align*}	✓	✓	✓	✓	0.355
6951	15267	\begin{align*} x^{\prime }-x+2 y&=0 \\ y^{\prime }+y-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.355
6952	15442	\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.355
6953	16034	\begin{align*} x^{\prime }&=-3 x-y \\ y^{\prime }&=4 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.355
6954	17701	\begin{align*} 6 y-2 y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.355
6955	18660	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=3 x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.355
6956	18819	\begin{align*} y^{\prime \prime }+9 y&=t^{2} {\mathrm e}^{3 t}+6 \\ \end{align*}	✓	✓	✓	✓	0.355
6957	20625	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.355
6958	23073	\begin{align*} 2 y^{\prime \prime }-4 y^{\prime }-y&=7 \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.355
6959	24259	\begin{align*} \left (x +a \right ) y^{\prime }&=b x \\ \end{align*}	✓	✓	✓	✓	0.355
6960	24565	\begin{align*} x^{\prime \prime }+4 x^{\prime }+5 x&=10 \\ x \left (0\right ) &= 4 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.355
6961	24568	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=x \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.355
6962	224	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 13 \\ \end{align*}	✓	✓	✓	✓	0.356
6963	342	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.356
6964	626	\begin{align*} x_{1}^{\prime }&=9 x_{1}+5 x_{2} \\ x_{2}^{\prime }&=-6 x_{1}-2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.356
6965	844	\begin{align*} y^{\prime \prime }+2 y&=6 x +4 \\ \end{align*}	✓	✓	✓	✓	0.356
6966	963	\begin{align*} x_{1}^{\prime }&=6 x_{1} \\ x_{2}^{\prime }&=-3 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.356
6967	1074	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.356
6968	3113	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.356
6969	3189	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=x^{2}-8 \\ \end{align*}	✓	✓	✓	✓	0.356
6970	4561	\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2} \\ x_{2}^{\prime }&=-4 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.356
6971	5526	\begin{align*} 4 x^{2} {y^{\prime }}^{2}-4 x y^{\prime } y&=8 x^{3}-y^{2} \\ \end{align*}	✓	✓	✓	✓	0.356
6972	8013	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{x}+x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.356
6973	8192	\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y&=10 \\ \end{align*}	✓	✓	✓	✓	0.356
6974	9005	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.356
6975	9169	\begin{align*} y x -1+\left (x^{2}-y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.356
6976	9174	\begin{align*} x +3 y^{2}+2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	0.356
6977	10064	\begin{align*} \frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}}&=-x \\ \end{align*}	✓	✓	✓	✗	0.356
6978	10771	\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.356
6979	10930	\begin{align*} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.356
6980	14398	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=3 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.356
6981	15010	\begin{align*} x^{\prime }&=-6 x+2 y \\ y^{\prime }&=-2 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.356
6982	16622	\begin{align*} y^{\prime \prime }+9 y&=54 x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.356
6983	16840	\begin{align*} y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=-2\).	✓	✓	✓	✓	0.356
6984	16992	\begin{align*} y^{\prime }&=\sin \left (x \right )^{3} \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.356
6985	18117	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2}+y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.356
6986	18704	\begin{align*} x^{\prime }&=2 x-4 y \\ y^{\prime }&=2 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.356
6987	20016	\begin{align*} y&=2 y^{\prime } x +y^{2} {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.356
6988	20620	\begin{align*} x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.356
6989	20889	\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.356
6990	22201	\begin{align*} y^{\prime \prime }-2 y x&=x^{2} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✗	0.356
6991	23758	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.356
6992	24635	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=48 \,{\mathrm e}^{-x} \cos \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.356
6993	24703	\begin{align*} y^{\prime \prime }+16 y&=8 x +8 \sin \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.356
6994	24807	\begin{align*} x^{8} {y^{\prime }}^{2}+3 y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.356
6995	8	\begin{align*} y^{\prime }&=\cos \left (2 x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.357
6996	8813	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.357
6997	9458	\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=3 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 5 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.357
6998	15151	\begin{align*} \left (x -3\right ) y^{\prime \prime }+y \ln \left (x \right )&=x^{2} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✗	✗	✗	✗	0.357
6999	15227	\begin{align*} -2 y+y^{\prime }&=4 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )\right ) \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.357
7000	15988	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-x+4 y \\ \end{align*}	✓	✓	✓	✓	0.357