2.3.29 Problems 2801 to 2900

Table 2.601: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2801	10538	\begin{align*} y^{\prime \prime }-3 y^{\prime } x +\left (2 x^{2}+5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.192
2802	10931	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.192
2803	11110	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.192
2804	11148	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.192
2805	11160	\begin{align*} u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.192
2806	11234	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.192
2807	13072	\begin{align*} x^{\prime }+2 x+y^{\prime }+y&={\mathrm e}^{2 t}+t \\ x^{\prime }-x+y^{\prime }+3 y&={\mathrm e}^{t}-1 \\ \end{align*}	✓	✓	✓	✗	0.192
2808	18897	\begin{align*} y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.192
2809	22093	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.192
2810	22781	\begin{align*} x^{\prime \prime \prime \prime }-x&=8 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.192
2811	23251	\begin{align*} y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.192
2812	25096	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.192
2813	25992	\begin{align*} x^{\prime }+y^{\prime }+2 x-y&=-\sin \left (t \right ) \\ x^{\prime }-3 x+y^{\prime }+2 y&=4 \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✗	0.192
2814	240	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.193
2815	849	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.193
2816	3063	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.193
2817	6726	\begin{align*} y^{\prime \prime \prime \prime }&=\cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.193
2818	7230	\begin{align*} x^{2} y^{\prime }+3 y x&=1 \\ \end{align*}	✓	✓	✓	✓	0.193
2819	10348	\begin{align*} y^{\prime } x +y&=0 \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✗	✗	0.193
2820	10666	\begin{align*} t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y&=0 \\ \end{align*}	✓	✓	✓	✗	0.193
2821	11009	\begin{align*} 16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.193
2822	22685	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.193
2823	410	\begin{align*} y^{\prime \prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.194
2824	852	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2825	2150	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&={\mathrm e}^{-2 x} \left (3 x^{2}-17 x +2\right ) \\ \end{align*}	✓	✓	✓	✓	0.194
2826	3937	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=36 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.194
2827	4253	\begin{align*} y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2828	6029	\begin{align*} \left (b x +a \right ) y+2 a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
2829	7979	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2830	10604	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
2831	10607	\begin{align*} 9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
2832	10637	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
2833	10656	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
2834	10795	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
2835	11011	\begin{align*} 36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
2836	11097	\begin{align*} z y^{\prime \prime }-2 y^{\prime }+y z&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2837	11101	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
2838	11131	\begin{align*} x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2839	12732	\begin{align*} x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 y^{\prime } x +2 y-f \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
2840	18757	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2841	18775	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2842	18887	\begin{align*} 6 y^{\prime \prime }+5 y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.194
2843	19824	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2844	20054	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.194
2845	20083	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.194
2846	26013	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.194
2847	552	\begin{align*} x^{\prime \prime }+6 x^{\prime }+18 x&=\cos \left (2 t \right ) \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.195
2848	2208	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{2 x} \left (-3 x^{2}-4 x +5\right ) \\ \end{align*}	✓	✓	✓	✓	0.195
2849	2725	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=t +{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.195
2850	3066	\begin{align*} 2 y^{\prime \prime }+2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
2851	4491	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=10 \,{\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.195
2852	6655	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=x^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.195
2853	8269	\begin{align*} {y^{\prime }}^{2}&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.195
2854	10876	\begin{align*} \left (1-t \right ) y^{\prime \prime }+y^{\prime } t -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.195
2855	10952	\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.195
2856	11293	\begin{align*} y^{\prime \prime }&=\left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y \\ \end{align*}	✓	✓	✓	✗	0.195
2857	12800	\begin{align*} 12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
2858	15220	\begin{align*} y+2 y^{\prime }&={\mathrm e}^{-\frac {t}{2}} \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.195
2859	17248	\begin{align*} 2 t +2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
2860	17366	\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
2861	18017	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.195
2862	18372	\begin{align*} y^{\prime }&=\frac {-x +y}{x +y} \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✗	✓	0.195
2863	21120	\begin{align*} x^{\prime \prime }+x^{\prime }-2 x&=0 \\ x \left (0\right ) &= a \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.195
2864	25097	\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
2865	26020	\begin{align*} y^{\prime \prime }-y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.195
2866	2167	\begin{align*} 2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime }-y&=3 \,{\mathrm e}^{-\frac {x}{2}} \left (1-6 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.196
2867	6629	\begin{align*} 4 y+2 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.196
2868	6776	\begin{align*} y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.196
2869	8639	\begin{align*} y^{\prime \prime }+10 y^{\prime }+24 y&=144 t^{2} \\ y \left (0\right ) &= {\frac {19}{12}} \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.196
2870	10966	\begin{align*} 18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.196
2871	10983	\begin{align*} 3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.196
2872	11051	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.196
2873	20540	\begin{align*} y^{\prime \prime \prime } \csc \left (x \right )^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	0.196
2874	22102	\begin{align*} y^{\prime \prime }-y^{\prime }-30 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.196
2875	23232	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.196
2876	1256	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2877	2111	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= k_{0} \\ y^{\prime }\left (1\right ) &= k_{1} \\ y^{\prime \prime }\left (1\right ) &= k_{2} \\ \end{align*}	✓	✓	✓	✓	0.197
2878	2148	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{-3 x} \left (6 x^{2}-23 x +32\right ) \\ \end{align*}	✓	✓	✓	✓	0.197
2879	2172	\begin{align*} 2 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{x} \left (11+12 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.197
2880	6925	\begin{align*} 2 y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
2881	8173	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2882	10532	\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
2883	10533	\begin{align*} x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
2884	10712	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2885	10813	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2886	11045	\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
2887	11091	\begin{align*} t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
2888	11180	\begin{align*} \left (2 x -3\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
2889	14590	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2890	15331	\begin{align*} y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2891	18298	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime \prime }-12 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2892	20697	\begin{align*} 2 y^{\prime \prime }+9 y^{\prime }-18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2893	23349	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.197
2894	25099	\begin{align*} y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2895	400	\begin{align*} y^{\prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.198
2896	4121	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.198
2897	6223	\begin{align*} -2 y+\left (1-x \right )^{2} x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.198
2898	8127	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.198
2899	10623	\begin{align*} 9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.198
2900	10730	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}&=0 \\ \end{align*}	✓	✓	✓	✗	0.198