2.3.89 Problems 8801 to 8900

Table 2.727: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
8801	5776	\begin{align*} 3 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.647
8802	6931	\begin{align*} x \sqrt {x^{2}+y^{2}}-\frac {x^{2} y y^{\prime }}{y-\sqrt {x^{2}+y^{2}}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.647
8803	14334	\begin{align*} x^{\prime \prime }+x&=\frac {1}{1+t} \\ \end{align*}	✓	✓	✓	✓	0.647
8804	16907	\begin{align*} 4 x^{2} y^{\prime \prime }+8 x^{2} y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.647
8805	18212	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\left (x^{2}+x \right ) {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.647
8806	18821	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.647
8807	19696	\begin{align*} x^{\prime \prime }-x&=t^{2} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.647
8808	21647	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.647
8809	23625	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=z-x \\ z^{\prime }&=x+3 y+z \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ z \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.647
8810	24007	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 x}}{x} \\ \end{align*}	✓	✓	✓	✓	0.647
8811	619	\begin{align*} x_{1}^{\prime }&=-8 x_{1}-11 x_{2}-2 x_{3} \\ x_{2}^{\prime }&=6 x_{1}+9 x_{2}+2 x_{3} \\ x_{3}^{\prime }&=-6 x_{1}-6 x_{2}+x_{3} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 5 \\ x_{2} \left (0\right ) &= -7 \\ x_{3} \left (0\right ) &= 11 \\ \end{align*}	✓	✓	✓	✓	0.648
8812	1345	\begin{align*} t^{2} y^{\prime \prime }-2 y&=3 t^{2}-1 \\ \end{align*}	✓	✓	✓	✓	0.648
8813	3159	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	0.648
8814	5607	\begin{align*} {y^{\prime }}^{3}&=b x +a \\ \end{align*}	✓	✓	✓	✓	0.648
8815	6584	\begin{align*} y^{\prime }-y^{\prime \prime } x +{y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.648
8816	7297	\begin{align*} y^{\prime \prime }+y&=2 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.648
8817	14338	\begin{align*} x^{\prime \prime }-x&=\frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}} \\ \end{align*}	✓	✓	✓	✓	0.648
8818	14382	\begin{align*} x^{\prime }&=-2 x-3 y \\ y^{\prime }&=-x+4 y \\ \end{align*}	✓	✓	✓	✓	0.648
8819	14426	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=-8 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.648
8820	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*}	✓	✓	✓	✓	0.648
8821	15008	\begin{align*} x^{\prime }&=7 x-5 y \\ y^{\prime }&=10 x-3 y \\ \end{align*}	✓	✓	✓	✓	0.648
8822	15075	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.648
8823	16626	\begin{align*} y^{\prime \prime }+9 y&=39 x \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.648
8824	16912	\begin{align*} 4 y^{\prime \prime }+\frac {\left (4 x -3\right ) y}{\left (x -1\right )^{2}}&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.648
8825	17402	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.648
8826	19218	\begin{align*} x^{\prime }&=y+z-x \\ y^{\prime }&=x-y+z \\ z^{\prime }&=x+y-z \\ \end{align*}	✓	✓	✓	✓	0.648
8827	21649	\begin{align*} y^{\prime \prime }-y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.648
8828	21740	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=4 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.648
8829	22778	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x}+{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.648
8830	24630	\begin{align*} y^{\prime \prime }-4 y&=16 \,{\mathrm e}^{-2 x} x +8 x +4 \\ \end{align*}	✓	✓	✓	✓	0.648
8831	25567	\begin{align*} y^{\prime \prime }+y&=\sin \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.648
8832	25660	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.648
8833	1292	\begin{align*} y^{\prime \prime }+2 a y^{\prime }+\left (a^{2}+1\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.649
8834	3863	\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{2} \\ x_{2}^{\prime }&=-x_{1}+5 x_{2} \\ x_{3}^{\prime }&=4 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.649
8835	4153	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{8}&=\frac {\sin \left (x \right )}{8}-\frac {\cos \left (x \right )}{4} \\ \end{align*}	✓	✓	✓	✓	0.649
8836	7574	\begin{align*} y^{\prime \prime }+6 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.649
8837	8147	\begin{align*} \cos \left (x \right ) y^{\prime \prime }-\sin \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.649
8838	15328	\begin{align*} {y^{\prime }}^{2}-y^{\prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.649
8839	16390	\begin{align*} y y^{\prime \prime }&=-{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.649
8840	19051	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }&=-3 x_{1}+2 x_{2}+4 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.649
8841	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*}	✓	✓	✓	✓	0.649
8842	1393	\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+4 y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.650
8843	1434	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }&=4 x_{1}+x_{2}-{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.650
8844	8509	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+5 \left (x +1\right ) y^{\prime }+\left (x^{2}-x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.650
8845	9995	\begin{align*} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.650
8846	15997	\begin{align*} x^{\prime }&=-2 x-2 y \\ y^{\prime }&=-2 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.650
8847	23509	\begin{align*} y^{\prime \prime }-y&=x \,{\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.650
8848	3882	\begin{align*} x_{1}^{\prime }&=3 x_{1} \\ x_{2}^{\prime }&=3 x_{2}-x_{3} \\ x_{3}^{\prime }&=x_{2}+x_{3} \\ \end{align*}	✓	✓	✓	✓	0.651
8849	7496	\begin{align*} y^{3}-x y^{2}+2 x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.651
8850	7796	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=4 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.651
8851	8553	\begin{align*} y^{\prime \prime } x +y^{\prime }-7 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.651
8852	12895	\begin{align*} y^{\prime \prime } x +a \left (-y+y^{\prime } x \right )^{2}-b&=0 \\ \end{align*}	✗	✓	✓	✗	0.651
8853	17426	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=2 \,{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.651
8854	18902	\begin{align*} y^{\prime \prime }+4 y^{\prime }+29 y&={\mathrm e}^{-2 t} \sin \left (5 t \right ) \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.651
8855	20166	\begin{align*} y^{\prime \prime \prime }+\cos \left (x \right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✗	0.651
8856	20765	\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3+7 x \right ) y^{\prime }-3 y&=x^{2} \\ \end{align*}	✓	✓	✓	✗	0.651
8857	21140	\begin{align*} x^{\prime \prime }+4 x&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.651
8858	21933	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 x}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.651
8859	24652	\begin{align*} y^{\prime \prime }+9 y&=\cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.651
8860	24667	\begin{align*} y^{\prime \prime }+16 y&=24 \sin \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.651
8861	24932	\begin{align*} y^{\prime }&={\mathrm e}^{2 t}-1 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.651
8862	26112	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.651
8863	1845	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -3 y x&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.652
8864	1990	\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.652
8865	2467	\begin{align*} t y^{\prime \prime }+y^{\prime }-4 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.652
8866	2703	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=5 x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.652
8867	3862	\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=3 x_{2}+2 x_{3} \\ x_{3}^{\prime }&=2 x_{1}-2 x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	0.652
8868	10294	\begin{align*} f \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.652
8869	15268	\begin{align*} x^{\prime }+5 x-2 y&=0 \\ 2 x+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.652
8870	15996	\begin{align*} x^{\prime }&=-2 x-2 y \\ y^{\prime }&=-2 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.652
8871	18728	\begin{align*} y^{\prime \prime }+3 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.652
8872	19868	\begin{align*} x^{2} y^{\prime \prime }&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.652
8873	21711	\begin{align*} y^{\prime }+2 y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.652
8874	23582	\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1 \\ x_{2}^{\prime }&=x_{1}+t \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= -{\frac {1}{2}} \\ x_{2} \left (0\right ) &= -{\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	0.652
8875	24002	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }-2 y&=\cosh \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	0.652
8876	24019	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \sec \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.652
8877	24677	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.652
8878	489	\begin{align*} \left (5 x^{3}+2 x^{2}\right ) y^{\prime \prime }+\left (-x^{2}+3 x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.653
8879	3997	\begin{align*} y^{\prime \prime }+2 y^{\prime }+4 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.653
8880	6947	\begin{align*} x -2 y x +{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.653
8881	8271	\begin{align*} y^{\prime \prime }+y&=2 \cos \left (x \right )-2 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.653
8882	8594	\begin{align*} 4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.653
8883	14185	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.653
8884	17795	\begin{align*} t \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right )+y y^{\prime }&=1 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	0.653
8885	19110	\begin{align*} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.653
8886	19167	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.653
8887	20349	\begin{align*} y^{\prime \prime }+9 y&=\cos \left (2 x \right )+\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.653
8888	22923	\begin{align*} x^{\prime }+2 y&=4 \,{\mathrm e}^{2 t} \\ x+y^{\prime }-y&=2 \,{\mathrm e}^{2 t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 7 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.653
8889	23291	\begin{align*} \left (x^{3}-1\right ) y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y x&=0 \\ y \left (-1\right ) &= 0 \\ y^{\prime }\left (-1\right ) &= 2 \\ y^{\prime \prime }\left (-1\right ) &= 2 \\ \end{align*}	✗	✗	✗	✗	0.653
8890	23554	\begin{align*} x^{\prime \prime }+2 x^{\prime }+x&=-\frac {{\mathrm e}^{-t}}{\left (1+t \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	0.653
8891	24536	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.653
8892	24668	\begin{align*} y^{\prime \prime }+16 y&=48 \cos \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.653
8893	25570	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{i \omega t} \\ \end{align*}	✓	✓	✓	✓	0.653
8894	11	\begin{align*} x^{\prime \prime }&=50 \\ x \left (0\right ) &= 20 \\ x^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	0.654
8895	3725	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=-10 \sin \left (x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.654
8896	13155	\(\left [\begin {array}{ccc} 1 & 0 & 0 \\ -6 & 8 & 2 \\ 12 & -15 & -3 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.654
8897	17027	\begin{align*} y^{\prime }&=\frac {2 x^{2}-x +1}{\left (x -1\right ) \left (x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	0.654
8898	17428	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=t^{2} \\ \end{align*}	✓	✓	✓	✓	0.654
8899	19606	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.654
8900	19663	\begin{align*} x^{\prime }&=\cos \left (t \right ) \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.654