2.3.29 Problems 2801 to 2900

Table 2.631: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2801	7230	\begin{align*} x^{2} y^{\prime }+3 y x&=1 \\ \end{align*}	✓	✓	✓	✓	0.241
2802	10536	\begin{align*} y^{\prime \prime }+3 x y^{\prime }+\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.241
2803	10594	\begin{align*} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.241
2804	10675	\begin{align*} 4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.241
2805	10862	\begin{align*} 3 y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.241
2806	11176	\begin{align*} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.241
2807	18176	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.241
2808	18214	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.241
2809	26243	\begin{align*} \sin \left (y^{\prime }\right )&=x \\ \end{align*}	✓	✓	✓	✓	0.241
2810	27015	\begin{align*} y^{\prime }+2 y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.241
2811	10635	\begin{align*} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.242
2812	10659	\begin{align*} y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✗	0.242
2813	10785	\begin{align*} x^{4} y^{\prime \prime }+\lambda y&=0 \\ \end{align*}	✓	✓	✓	✓	0.242
2814	10925	\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.242
2815	10967	\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.242
2816	16194	\begin{align*} y^{\prime }&=\left \{\begin {array}{cc} 0 & x <0 \\ 1 & 0\le x \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.242
2817	21939	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=3 x +x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.242
2818	23003	\begin{align*} 3 x^{\prime \prime }+19 x^{\prime }-14 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.242
2819	23420	\begin{align*} 6 y-2 x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.242
2820	27057	\begin{align*} y^{\prime \prime }+2 t y^{\prime }-4 y&=6 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.242
2821	551	\begin{align*} x^{\prime \prime }+4 x^{\prime }+13 x&=t \,{\mathrm e}^{-t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.243
2822	4371	\begin{align*} \left (x +1\right ) y^{\prime }-y&=x \left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.243
2823	10619	\begin{align*} 16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.243
2824	10665	\begin{align*} t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.243
2825	10709	\begin{align*} x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.243
2826	10763	\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.243
2827	10935	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.243
2828	11055	\begin{align*} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.243
2829	11221	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.243
2830	12724	\begin{align*} y^{\prime \prime \prime }-\sin \left (x \right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }+y \sin \left (x \right )-\ln \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.243
2831	12798	\begin{align*} 6 y^{\prime \prime }+6 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.243
2832	12800	\begin{align*} 12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.243
2833	14569	\begin{align*} \left (x^{2}-x +1\right ) y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.243
2834	18276	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=-2 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.243
2835	18752	\begin{align*} x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.243
2836	19814	\begin{align*} \left (x^{2}-2 y x \right ) y^{\prime }+x^{2}-3 y x +2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.243
2837	23418	\begin{align*} x \left (1-2 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+4 x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (4 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✗	✗	0.243
2838	23649	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=\cos \left (t \right )+57 \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.243
2839	24010	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.243
2840	25337	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{t}+\frac {\left (1-t \right ) y}{t^{3}}&=0 \\ \end{align*} Series expansion around \(t=0\).	✗	✗	✓	✗	0.243
2841	25896	\begin{align*} 2 x y y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.243
2842	3940	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=30 \,{\mathrm e}^{-3 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.244
2843	10331	\begin{align*} x^{\prime }+y^{\prime }-x&=y+t +\sin \left (t \right )+\cos \left (t \right ) \\ x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✗	0.244
2844	10595	\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.244
2845	10630	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.244
2846	10669	\begin{align*} t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.244
2847	10770	\begin{align*} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.244
2848	10989	\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.244
2849	11150	\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.244
2850	11209	\begin{align*} 2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.244
2851	14567	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.244
2852	15708	\begin{align*} y^{\prime }-2 y&=6 \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.244
2853	16775	\begin{align*} y^{\prime \prime }-8 y^{\prime }+17 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.244
2854	16799	\begin{align*} y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.244
2855	27111	\(\left [\begin {array}{cc} 5 & 3 \\ 1 & 3 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.244
2856	3939	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=4 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.245
2857	10629	\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.245
2858	10761	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (x y^{\prime }-y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.245
2859	10876	\begin{align*} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.245
2860	11080	\begin{align*} y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.245
2861	11118	\begin{align*} x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.245
2862	11197	\begin{align*} x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.245
2863	11199	\begin{align*} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.245
2864	13201	\begin{align*} y^{\prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.245
2865	18174	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime }&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.245
2866	20540	\begin{align*} y^{\prime \prime \prime } \csc \left (x \right )^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	0.245
2867	23239	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.245
2868	23416	\begin{align*} x \left (1-3 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+9 x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (3+9 x \right ) y&=0 \\ \end{align*}	✓	✓	✗	✗	0.245
2869	27018	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.245
2870	424	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.246
2871	847	\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.246
2872	3612	\begin{align*} y^{\prime }+2 y x&=2 x^{3} \\ \end{align*}	✓	✓	✓	✓	0.246
2873	4494	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=32 \,{\mathrm e}^{2 x}+16 x^{3} \\ \end{align*}	✓	✓	✓	✓	0.246
2874	7231	\begin{align*} y^{\prime }+2 y x -x \,{\mathrm e}^{-x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.246
2875	10548	\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (5+x \right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.246
2876	10729	\begin{align*} 2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.246
2877	10735	\begin{align*} u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.246
2878	10855	\begin{align*} \left (x +1\right ) y^{\prime \prime }-\left (x +2\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.246
2879	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*}	✓	✓	✓	✗	0.246
2880	11016	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.246
2881	11129	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.246
2882	11155	\begin{align*} x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}&=0 \\ \end{align*}	✓	✓	✓	✗	0.246
2883	14102	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.246
2884	16672	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=3 x \,{\mathrm e}^{x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.246
2885	18278	\begin{align*} y^{\prime \prime \prime }-y&=2 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.246
2886	19634	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.246
2887	26100	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.246
2888	27559	\begin{align*} y^{\prime \prime \prime \prime } x +y^{\prime \prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.246
2889	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.	✓	✓	✓	✓	0.247
2890	2106	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\ y \left (-1\right ) &= -4 \\ y^{\prime }\left (-1\right ) &= -14 \\ y^{\prime \prime }\left (-1\right ) &= -20 \\ \end{align*}	✓	✓	✓	✓	0.247
2891	7214	\begin{align*} x y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.247
2892	7234	\begin{align*} y^{\prime }+\frac {y}{\sqrt {x^{2}+1}}&=\frac {1}{x +\sqrt {x^{2}+1}} \\ \end{align*}	✓	✓	✓	✗	0.247
2893	9392	\begin{align*} x^{4} y^{\prime \prime }+y \sin \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.247
2894	10700	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.247
2895	10982	\begin{align*} 4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.247
2896	11050	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.247
2897	11193	\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.247
2898	11265	\begin{align*} x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.247
2899	17674	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-12 x^{2} y^{\prime \prime }-12 x y^{\prime }+48 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.247
2900	19641	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.247