2.3.79 Problems 7801 to 7900

Table 2.689: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7801	578	\begin{align*} x^{\prime }&=-2 y \\ y^{\prime }&=2 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.392
7802	971	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=6 x_{1}-5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.392
7803	1859	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x +\frac {y}{4}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.392
7804	1895	\begin{align*} \left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.392
7805	2388	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.392
7806	3742	\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=24 \,{\mathrm e}^{x} \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.392
7807	6510	\begin{align*} 4 y^{\prime } y-4 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.392
7808	7994	\begin{align*} y^{\prime \prime }-y&=4 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.392
7809	8052	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.392
7810	9246	\begin{align*} 4 y+y^{\prime \prime }&=3 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.392
7811	9265	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{1+{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✗	0.392
7812	9577	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.392
7813	10356	\begin{align*} \cos \left (x \right ) y^{\prime }+\frac {y}{x}&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✗	✗	0.392
7814	15000	\begin{align*} x^{\prime }&=8 x+14 y \\ y^{\prime }&=7 x+y \\ \end{align*}	✓	✓	✓	✓	0.392
7815	15743	\(\left [\begin {array}{ccc} 3 & 1 & -1 \\ 1 & 3 & -1 \\ 3 & 3 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.392
7816	16634	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=6 \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.392
7817	18857	\begin{align*} y^{\prime \prime }+y+\frac {y^{3}}{5}&=\cos \left (t w \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	0.392
7818	21913	\begin{align*} y^{\prime \prime }+n^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= k \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.392
7819	22639	\begin{align*} y^{\prime \prime }-\left (m_{1} +m_{2} \right ) y^{\prime }+m_{1} m_{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.392
7820	23074	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.392
7821	23498	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.392
7822	23601	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.392
7823	25601	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{i t} \\ \end{align*}	✓	✓	✓	✓	0.392
7824	1317	\begin{align*} 4 y^{\prime \prime }+12 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.393
7825	5774	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=8 x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.393
7826	9592	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.393
7827	9858	\begin{align*} \left (x^{2}-2 x +2\right ) y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }+6 y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.393
7828	15028	\begin{align*} {y^{\prime }}^{2}+x^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	0.393
7829	15879	\begin{align*} v^{\prime }&=-v^{2}-2 v-2 \\ \end{align*}	✓	✓	✓	✓	0.393
7830	17232	\begin{align*} y^{2}-2 \sin \left (2 t \right )+\left (1+2 t y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	0.393
7831	17821	\begin{align*} x^{\prime }&=6 \\ y^{\prime }&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.393
7832	18703	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.393
7833	18738	\begin{align*} t^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.393
7834	18813	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{4}+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.393
7835	21214	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=3 x+y \\ \end{align*}	✓	✓	✓	✓	0.393
7836	22419	\begin{align*} \left (x^{2}+x \right ) y^{\prime }+2 x +1+2 \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.393
7837	23528	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\ \end{align*}	✓	✓	✓	✓	0.393
7838	24038	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.393
7839	25762	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=-12 x +8 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -11 \\ \end{align*}	✓	✓	✓	✓	0.393
7840	151	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.394
7841	596	\begin{align*} x^{\prime }+2 y^{\prime }&=4 x+5 y \\ 2 x^{\prime }-y^{\prime }&=3 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.394
7842	1739	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.394
7843	1897	\begin{align*} \left (x +4\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.394
7844	3628	\begin{align*} y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right . \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.394
7845	5661	\begin{align*} y^{2} {y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.394
7846	6153	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=\sqrt {x} \\ \end{align*}	✓	✓	✓	✓	0.394
7847	8736	\begin{align*} 2 x \left (x -y^{2}\right ) y^{\prime }+y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.394
7848	8793	\begin{align*} s^{\prime \prime }+2 s^{\prime }+s&=0 \\ s \left (0\right ) &= 4 \\ s^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.394
7849	9352	\begin{align*} y^{\prime }-y&=2 \\ \end{align*}	✓	✓	✓	✓	0.394
7850	10846	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.394
7851	12515	\begin{align*} x \left (x +1\right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.394
7852	14979	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.394
7853	15051	\begin{align*} y&=x^{2}+2 y^{\prime } x +\frac {{y^{\prime }}^{2}}{2} \\ \end{align*}	✓	✓	✗	✓	0.394
7854	15075	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.394
7855	15573	\begin{align*} y^{\prime }&=x \sin \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.394
7856	16277	\begin{align*} y^{\prime }-3 y&=6 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.394
7857	18389	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x^{2}-\frac {1}{9}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.394
7858	18390	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.394
7859	18410	\begin{align*} x^{\prime }&=-9 y \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.394
7860	21032	\begin{align*} {\mathrm e}^{x^{\prime }}&=x \\ x \left (t_{0} \right ) &= a \\ \end{align*}	✓	✓	✓	✓	0.394
7861	22881	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\left (1-3 x \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.394
7862	25266	\begin{align*} y^{\prime \prime }-4 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.394
7863	4	\begin{align*} y^{\prime }&=\frac {1}{x^{2}} \\ y \left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.395
7864	579	\begin{align*} x^{\prime }&=10 y \\ y^{\prime }&=-10 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.395
7865	856	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.395
7866	1514	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=\delta \left (-1+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.395
7867	1905	\begin{align*} y^{\prime \prime }+3 y^{\prime } x +\left (2 x^{2}+4\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.395
7868	2242	\begin{align*} y_{1}^{\prime }&=2 y_{1}-4 y_{2} \\ y_{2}^{\prime }&=-y_{1}-y_{2} \\ \end{align*}	✓	✓	✓	✓	0.395
7869	2419	\begin{align*} y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y&=0 \\ y \left (-1\right ) &= 0 \\ y^{\prime }\left (-1\right ) &= 1 \\ \end{align*} Series expansion around \(t=-1\).	✓	✓	✓	✓	0.395
7870	3508	\begin{align*} z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}&=0 \\ \end{align*} Series expansion around \(z=0\).	✓	✓	✓	✓	0.395
7871	4186	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}+\left (1+\frac {1}{x^{2}}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.395
7872	5720	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.395
7873	6285	\begin{align*} a y-x^{5} y^{\prime }+x^{6} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.395
7874	6586	\begin{align*} a x -2 y^{\prime } y^{\prime \prime }+x {y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✓	✓	✗	✗	0.395
7875	8107	\begin{align*} 2 y^{\prime \prime } x -y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.395
7876	8272	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.395
7877	8938	\begin{align*} y^{\prime \prime \prime \prime }-y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.395
7878	9666	\begin{align*} x^{\prime }&=-x+\frac {y}{4} \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.395
7879	9733	\begin{align*} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.395
7880	10136	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.395
7881	10387	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x^{3}+x^{2}+x +1 \\ \end{align*}	✓	✓	✓	✓	0.395
7882	13777	\begin{align*} x^{2} y^{\prime \prime }-\left (a \,x^{3}+\frac {5}{16}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.395
7883	14540	\begin{align*} \left (2+x \right ) y^{\prime }+y&=\left \{\begin {array}{cc} 2 x & 0\le x \le 2 \\ 4 & 2<x \end {array}\right . \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	0.395
7884	15464	\begin{align*} x^{\prime }&=x-5 y \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.395
7885	15752	\begin{align*} y_{1}^{\prime }&=2 y_{1}-3 y_{2} \\ y_{2}^{\prime }&=y_{1}-2 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.395
7886	16090	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=2 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.395
7887	18452	\begin{align*} x^{\prime }&=6 x+y \\ y^{\prime }&=4 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.395
7888	20132	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.395
7889	20455	\begin{align*} 4 {y^{\prime }}^{2}&=9 x \\ \end{align*}	✓	✓	✓	✓	0.395
7890	24727	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )^{4} \\ \end{align*}	✓	✓	✓	✓	0.395
7891	25372	\begin{align*} y_{1}^{\prime }&=2 y_{1}-y_{2} \\ y_{2}^{\prime }&=3 y_{1}-2 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.395
7892	25737	\begin{align*} y^{\prime }&=2 y-4 \\ \end{align*}	✓	✓	✓	✓	0.395
7893	3179	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.396
7894	3861	\begin{align*} x_{1}^{\prime }&=4 x_{1} \\ x_{2}^{\prime }&=x_{1}+4 x_{2} \\ x_{3}^{\prime }&=x_{2}+4 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.396
7895	7105	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.396
7896	9583	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.396
7897	14401	\begin{align*} x^{\prime }&=-5 x+3 y \\ y^{\prime }&=2 x-10 y \\ \end{align*}	✓	✓	✓	✓	0.396
7898	14935	\begin{align*} x^{\prime \prime }+x^{\prime }-2 x&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.396
7899	16117	\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=-\cos \left (5 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.396
7900	17424	\begin{align*} y^{\prime \prime }+y&=8 \,{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.396