2.3.89 Problems 8801 to 8900

Table 2.709: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
8801	5641	\begin{align*} 2 {y^{\prime }}^{3}+y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✗	✗	0.443
8802	8193	\begin{align*} {y^{\prime }}^{2}&=4 y \\ \end{align*}	✓	✓	✓	✓	0.443
8803	8336	\begin{align*} y^{\prime }&=y^{2}-y-6 \\ \end{align*}	✓	✓	✓	✓	0.443
8804	8761	\begin{align*} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+{\mathrm e}^{x} y&=0 \\ \end{align*}	✗	✗	✗	✗	0.443
8805	9354	\begin{align*} y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.443
8806	9642	\begin{align*} y^{\prime \prime }+y&=\delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.443
8807	12998	\begin{align*} \left (x +y^{2}\right ) y^{\prime \prime }-2 \left (x -y^{2}\right ) {y^{\prime }}^{3}+y^{\prime } \left (1+4 y^{\prime } y\right )&=0 \\ \end{align*}	✗	✓	✗	✗	0.443
8808	20080	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.443
8809	22061	\begin{align*} y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.443
8810	24735	\begin{align*} y^{\prime \prime }-y&=\frac {2}{\sqrt {1-{\mathrm e}^{-2 x}}} \\ \end{align*}	✓	✓	✓	✓	0.443
8811	25140	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.443
8812	25283	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=f \left (t \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.443
8813	495	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (1-x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.444
8814	1392	\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+4 y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.444
8815	1874	\begin{align*} \left (3 x^{2}-6 x +5\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+12 y&=0 \\ y \left (1\right ) &= -1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.444
8816	2601	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=2 \cos \left (t \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.444
8817	4046	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.444
8818	5439	\begin{align*} 3 {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.444
8819	5574	\begin{align*} y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 a x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.444
8820	5723	\begin{align*} y^{\prime \prime }+y&=4 x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.444
8821	5805	\begin{align*} b^{2} y+2 a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.444
8822	6823	\begin{align*} y&=x {y^{\prime }}^{2}+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.444
8823	7303	\begin{align*} y^{\prime \prime }-y&=\sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.444
8824	9045	\begin{align*} y_{1}^{\prime }&=y_{2} \\ y_{2}^{\prime }&=6 y_{1}+y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.444
8825	9187	\begin{align*} \left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.444
8826	9372	\begin{align*} y^{\prime \prime }+2 y^{\prime } x -y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.444
8827	10061	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=y \\ z^{\prime }&=z \\ \end{align*}	✓	✓	✓	✓	0.444
8828	15986	\begin{align*} x^{\prime }&=-4 x-2 y \\ y^{\prime }&=-x-3 y \\ \end{align*}	✓	✓	✓	✓	0.444
8829	16104	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=4+{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.444
8830	18121	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=y^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.444
8831	18702	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.444
8832	22883	\begin{align*} u^{\prime }&=2 v-1 \\ v^{\prime }&=1+2 u \\ \end{align*}	✓	✓	✓	✓	0.444
8833	25704	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.444
8834	639	\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+4 x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2}+4 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.445
8835	973	\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.445
8836	1871	\begin{align*} \left (3 x^{2}+6 x +5\right ) y^{\prime \prime }+9 \left (x +1\right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✓	0.445
8837	2391	\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.445
8838	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.	✓	✓	✓	✓	0.445
8839	3178	\begin{align*} y^{\prime \prime }+3 y^{\prime }-2 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.445
8840	4047	\begin{align*} y^{\prime \prime } x +y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.445
8841	8994	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.445
8842	10339	\begin{align*} t y^{\prime }+y&=\sin \left (t \right ) \\ y \left (1\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✗	✓	✓	0.445
8843	12976	\begin{align*} f \left (x \right )+a y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.445
8844	16051	\begin{align*} x^{\prime }&=z-y \\ y^{\prime }&=z-x \\ z^{\prime }&=z \\ \end{align*}	✓	✓	✓	✓	0.445
8845	16441	\begin{align*} \left (1+y\right ) y^{\prime \prime }&={y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.445
8846	17402	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.445
8847	17426	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=2 \,{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.445
8848	17755	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=3 \,{\mathrm e}^{-2 t} \\ \end{align*}	✓	✓	✓	✓	0.445
8849	18160	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&={\mathrm e}^{-3 x} \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.445
8850	18729	\begin{align*} y^{\prime \prime }-y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.445
8851	18868	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{t}}{t^{2}+1} \\ \end{align*}	✓	✓	✓	✗	0.445
8852	20187	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+n^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.445
8853	22750	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=2 x^{2} {\mathrm e}^{-2 x}+3 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.445
8854	22868	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.445
8855	23090	\begin{align*} 16 y+8 y^{\prime }+y^{\prime \prime }&=x \left (12-{\mathrm e}^{-4 x}\right ) \\ \end{align*}	✓	✓	✓	✓	0.445
8856	25117	\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&={\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	0.445
8857	25166	\begin{align*} y_{1}^{\prime }-6 y_{1}&=-4 y_{2} \\ y_{2}^{\prime }&=2 y_{1} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 2 \\ y_{2} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.445
8858	260	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=2 x \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.446
8859	2428	\begin{align*} y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{t}&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.446
8860	5728	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{x} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.446
8861	9375	\begin{align*} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.446
8862	12294	\begin{align*} y^{\prime \prime }-c \,x^{a} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.446
8863	17692	\begin{align*} \left (2 x^{2}+2\right ) y^{\prime \prime }+2 y^{\prime } x -3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.446
8864	20101	\begin{align*} \left (2 x -1\right )^{3} y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.446
8865	22866	\begin{align*} \left (1-x \right ) y^{\prime \prime }+\left (2-4 x \right ) y^{\prime }-y&=4 x^{2} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.446
8866	24834	\begin{align*} 4 y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.446
8867	25399	\begin{align*} y^{\prime }&=2-y \\ \end{align*}	✓	✓	✓	✓	0.446
8868	25434	\begin{align*} y^{\prime }-a \left (t \right ) y&=\delta \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.446
8869	617	\begin{align*} x_{1}^{\prime }&=x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 10 \\ x_{2} \left (0\right ) &= 12 \\ x_{3} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.447
8870	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*}	✓	✓	✓	✓	0.447
8871	915	\begin{align*} 2 x^{\prime \prime }+2 x^{\prime }+x&=3 \sin \left (10 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.447
8872	1894	\begin{align*} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.447
8873	2240	\begin{align*} y_{1}^{\prime }&=-\frac {4 y_{1}}{5}+\frac {3 y_{2}}{5} \\ y_{2}^{\prime }&=-\frac {2 y_{1}}{5}-\frac {11 y_{2}}{5} \\ \end{align*}	✓	✓	✓	✓	0.447
8874	2717	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\tan \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.447
8875	3159	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	0.447
8876	3427	\begin{align*} y^{\prime }&={\mathrm e}^{2 t} t \\ y \left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.447
8877	3744	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=4 \,{\mathrm e}^{3 x} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.447
8878	6036	\begin{align*} -\left (3 x +2\right ) y+x \left (-x +2\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.447
8879	6463	\begin{align*} -y^{\prime }+{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.447
8880	6613	\begin{align*} 4 y-2 y^{\prime }+y^{\prime \prime \prime }&={\mathrm e}^{x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.447
8881	7101	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.447
8882	7667	\begin{align*} x^{\prime \prime }+42 x^{\prime }+x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.447
8883	7888	\begin{align*} x +y+1-\left (3-x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.447
8884	8133	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.447
8885	8946	\begin{align*} y^{\prime \prime }+i y^{\prime }+2 y&=2 \cosh \left (2 x \right )+{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.447
8886	9565	\begin{align*} 16 x^{2} y^{\prime \prime }+16 y^{\prime } x +\left (16 x^{2}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.447
8887	10138	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.447
8888	16042	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=-2 y \\ z^{\prime }&=-z \\ \end{align*}	✓	✓	✓	✓	0.447
8889	16752	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=x \,{\mathrm e}^{\frac {3 x}{2}} \\ \end{align*}	✓	✓	✓	✓	0.447
8890	16941	\begin{align*} x^{\prime }&=3 x+2 y \\ y^{\prime }&=-2 x+3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= a_{1} \\ y \left (0\right ) &= a_{2} \\ \end{align*}	✓	✓	✓	✓	0.447
8891	18022	\begin{align*} y^{\prime }+y^{2}-2 y \sin \left (x \right )+\sin \left (x \right )^{2}-\cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.447
8892	18204	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=\sin \left (2 x \right ) {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.447
8893	18399	\begin{align*} y^{\prime \prime }-4 y&=\cos \left (\pi x \right ) \\ \end{align*}	✓	✓	✓	✓	0.447
8894	19393	\begin{align*} \left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime \prime }&=2 y x -{\mathrm e}^{y}-x \\ \end{align*}	✗	✗	✗	✗	0.447
8895	22175	\begin{align*} \left (x -2\right ) y^{\prime \prime }+3 \left (x^{2}-3 x +2\right ) y^{\prime }+\left (x -2\right )^{2} x y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.447
8896	23595	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-3 x+6 y \\ \end{align*}	✓	✓	✓	✓	0.447
8897	24757	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\sec \left ({\mathrm e}^{-x}\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.447
8898	24823	\begin{align*} {y^{\prime }}^{3}-y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.447
8899	3429	\begin{align*} y^{\prime }&=8 \,{\mathrm e}^{4 t}+t \\ y \left (0\right ) &= 12 \\ \end{align*}	✓	✓	✓	✓	0.448
8900	4042	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (1-x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.448