2.3.69 Problems 6801 to 6900

Table 2.711: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
6801	16615	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-200 \\ \end{align*}	✓	✓	✓	✓	0.428
6802	17380	\begin{align*} y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.428
6803	19034	\begin{align*} x_{1}^{\prime }&=2 x_{1}-x_{2} \\ x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.428
6804	21499	\begin{align*} y^{\prime \prime }-\frac {6 y^{\prime }}{5}+\frac {9 y}{25}&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.428
6805	22920	\begin{align*} 2 x-y^{\prime }-5 y&=0 \\ x^{\prime }+x+2 y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= -10 \\ \end{align*}	✓	✓	✓	✓	0.428
6806	23042	\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.428
6807	23766	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.428
6808	23769	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.428
6809	24284	\begin{align*} y^{\prime }+a y&=b \\ \end{align*}	✓	✓	✓	✓	0.428
6810	25588	\begin{align*} y^{\prime \prime }-y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.428
6811	26836	\begin{align*} x^{\prime \prime }+4 x&=4 \cos \left (2 t \right )-\frac {\sin \left (2 t \right )}{2} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= {\frac {1}{8}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.428
6812	27089	\(\left [\begin {array}{cc} -2 & 0 \\ 1 & 4 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.428
6813	127	\begin{align*} y^{\prime } x +6 y&=3 x y^{{4}/{3}} \\ \end{align*}	✓	✓	✓	✓	0.429
6814	351	\begin{align*} 4 y+y^{\prime \prime }&=2 x \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.429
6815	513	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.429
6816	894	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=2 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.429
6817	972	\begin{align*} x_{1}^{\prime }&=x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.429
6818	1447	\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.429
6819	2043	\begin{align*} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (-x^{2}+14\right ) y^{\prime }+2 \left (x^{2}+9\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.429
6820	2051	\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.429
6821	5742	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.429
6822	7302	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{x}+6 x -5 \\ \end{align*}	✓	✓	✓	✓	0.429
6823	11167	\begin{align*} y^{\prime \prime }+q y^{\prime }&=\frac {2 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	0.429
6824	16982	\begin{align*} y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\ \end{align*}	✓	✓	✓	✓	0.429
6825	17739	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.429
6826	18668	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=-5 x-y \\ \end{align*}	✓	✓	✓	✓	0.429
6827	18793	\begin{align*} y^{\prime \prime }+6 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.429
6828	23067	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.429
6829	25587	\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{c t} \\ \end{align*}	✓	✓	✓	✓	0.429
6830	27576	\begin{align*} x^{2} \left ({y^{\prime }}^{2}-2 y y^{\prime \prime }\right )&=y^{2} \\ \end{align*}	✗	✓	✓	✗	0.429
6831	967	\begin{align*} x_{1}^{\prime }&=3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=3 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*}	✓	✓	✓	✓	0.430
6832	3423	\begin{align*} y^{\prime }&=\frac {t}{\sqrt {t}+1} \\ \end{align*}	✓	✓	✓	✓	0.430
6833	4606	\begin{align*} y^{\prime \prime } x +y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.430
6834	8132	\begin{align*} x^{2} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.430
6835	8164	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.430
6836	8553	\begin{align*} y^{\prime \prime } x +y^{\prime }-7 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.430
6837	9250	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.430
6838	14098	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{{\mathrm e}^{x}} \\ \end{align*}	✓	✓	✓	✓	0.430
6839	14791	\begin{align*} x^{\prime }&=5 x-2 y \\ y^{\prime }&=4 x-y \\ \end{align*}	✓	✓	✓	✓	0.430
6840	14853	\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=3 x+y \\ \end{align*}	✓	✓	✓	✓	0.430
6841	15500	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.430
6842	16670	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=30 x \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.430
6843	17777	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.430
6844	18204	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.430
6845	19415	\begin{align*} {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.430
6846	19662	\begin{align*} x^{\prime }&=\frac {1}{\sqrt {t^{2}+1}} \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.430
6847	20030	\begin{align*} y&=y^{\prime } x -{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.430
6848	21297	\begin{align*} x^{\prime }&=-x+4 y \\ y^{\prime }&=3 x-5 y \\ \end{align*}	✓	✓	✓	✗	0.430
6849	21747	\begin{align*} 2 x^{\prime }-3 y^{\prime }&=2 \,{\mathrm e}^{2 t} \\ x^{\prime }-2 y^{\prime }&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.430
6850	899	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.431
6851	2042	\begin{align*} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-9 x^{2}+5\right ) y^{\prime }+\left (-3 x^{2}+4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.431
6852	2696	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t}+3 \delta \left (t -3\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.431
6853	5398	\begin{align*} {y^{\prime }}^{2}-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.431
6854	7761	\begin{align*} 3 y^{\prime \prime }-2 y^{\prime }-y&=2 x -3 \\ \end{align*}	✓	✓	✓	✓	0.431
6855	7812	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.431
6856	10223	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.431
6857	10456	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.431
6858	11165	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.431
6859	12514	\begin{align*} \left (-a^{2}+x^{2}\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.431
6860	13702	\begin{align*} y^{\prime \prime }+\left (a \,x^{3}+2 b \right ) y^{\prime }+\left (a \,x^{3} b -a \,x^{2}+b^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.431
6861	14208	\begin{align*} \sqrt {t}\, x^{\prime }&=\cos \left (\sqrt {t}\right ) \\ \end{align*}	✓	✓	✓	✓	0.431
6862	14331	\begin{align*} x^{\prime \prime }-x&={\mathrm e}^{t} t \\ \end{align*}	✓	✓	✓	✓	0.431
6863	14383	\begin{align*} x^{\prime }&=-3 y \\ y^{\prime }&=-2 x+y \\ \end{align*}	✓	✓	✓	✓	0.431
6864	14794	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=7 x+4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 6 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.431
6865	15697	\begin{align*} y^{\prime \prime }-9 y&=2 \sin \left (3 x \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.431
6866	16672	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=3 x \,{\mathrm e}^{x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.431
6867	18248	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (\frac {x}{2}\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.431
6868	20147	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.431
6869	21698	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.431
6870	22891	\begin{align*} x^{\prime }-2 y^{\prime }&={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }&=\sqrt {t} \\ \end{align*}	✓	✓	✓	✓	0.431
6871	23804	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.431
6872	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*}	✓	✓	✓	✓	0.431
6873	24662	\begin{align*} 4 y^{\prime \prime }-y&={\mathrm e}^{\frac {x}{2}}+12 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.431
6874	24709	\begin{align*} y^{\prime \prime }+25 y&=\sin \left (5 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.431
6875	25589	\begin{align*} y^{\prime \prime }+y&=\cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.431
6876	25604	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&={\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.431
6877	27657	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\sin \left (x \right )+\cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.431
6878	486	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.432
6879	974	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=9 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.432
6880	1093	\begin{align*} y^{\prime \prime }+{\mathrm e}^{-x} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.432
6881	1525	\begin{align*} y^{\prime }&=-x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.432
6882	1786	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=4 x^{4} \\ y \left (-1\right ) &= 7 \\ y^{\prime }\left (-1\right ) &= -8 \\ \end{align*}	✓	✓	✓	✓	0.432
6883	6664	\begin{align*} \sin \left (x \right ) y-2 \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	0.432
6884	7297	\begin{align*} y^{\prime \prime }+y&=2 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.432
6885	12633	\begin{align*} y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}-1}+\frac {a^{2} y}{\left (x^{2}-1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	0.432
6886	14332	\begin{align*} x^{\prime \prime }-x&=\frac {1}{t} \\ \end{align*}	✓	✓	✓	✓	0.432
6887	14861	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=3 x-y \\ \end{align*}	✓	✓	✓	✓	0.432
6888	16188	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x^{2}} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.432
6889	17732	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.432
6890	18117	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2}+y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.432
6891	18266	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=\left (12 x -7\right ) {\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.432
6892	18373	\begin{align*} y^{\prime }&=\sin \left (x \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.432
6893	18703	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.432
6894	20881	\begin{align*} y^{\prime }&=y \\ y \left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.432
6895	21623	\begin{align*} y^{\prime }&=2 y-5 z \\ z^{\prime }&=4 y-2 z \\ \end{align*}	✓	✓	✓	✓	0.432
6896	27017	\begin{align*} y^{\prime \prime }+y&=1 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.432
6897	2050	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.433
6898	5776	\begin{align*} 3 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.433
6899	10566	\begin{align*} 2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.433
6900	10714	\begin{align*} 2 y^{\prime \prime } x +5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.433