2.3.28 Problems 2701 to 2800

Table 2.605: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2701	1080	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.229
2702	1282	\begin{align*} y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.229
2703	4467	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }&=9 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.229
2704	10812	\begin{align*} y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.229
2705	10972	\begin{align*} 2 \left (x +3\right ) x^{2} y^{\prime \prime }+x \left (5 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.229
2706	16032	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.229
2707	22254	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.229
2708	7841	\begin{align*} y^{\prime \prime }+2 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.230
2709	10537	\begin{align*} \left (2+4 x \right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.230
2710	10800	\begin{align*} 2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.230
2711	11126	\begin{align*} x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.230
2712	11285	\begin{align*} y^{\prime \prime }-\frac {y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.230
2713	15193	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.230
2714	15201	\begin{align*} 3 y^{\prime \prime }+8 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.230
2715	16053	\(\left [\begin {array}{cc} 0 & 1 \\ 2 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.230
2716	17532	\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +\left (t^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.230
2717	20533	\begin{align*} y^{\prime \prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.230
2718	24621	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=16 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.230
2719	380	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.231
2720	391	\begin{align*} x^{\prime \prime }+3 x^{\prime }+3 x&=8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.231
2721	1491	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.231
2722	5880	\begin{align*} f \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.231
2723	10728	\begin{align*} 2 \left (1-x \right ) x y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.231
2724	10794	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.231
2725	11315	\begin{align*} y^{\prime }+y^{2}-a x -b&=0 \\ \end{align*}	✓	✓	✓	✗	0.231
2726	17604	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=3 t^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.231
2727	18588	\begin{align*} \frac {y^{\prime }}{-\sin \left (y\right )+\frac {x}{y}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.231
2728	25083	\begin{align*} y^{\prime \prime }+9 y&=36 t \sin \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.231
2729	1079	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.232
2730	9307	\begin{align*} y^{\prime \prime \prime \prime }&=\sin \left (x \right )+24 \\ \end{align*}	✓	✓	✓	✓	0.232
2731	10348	\begin{align*} y^{\prime } x +y&=0 \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✗	✗	0.232
2732	11117	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.232
2733	11156	\begin{align*} 4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.232
2734	18221	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.232
2735	21180	\begin{align*} x^{\prime \prime \prime }+4 x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -1 \\ x^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.232
2736	412	\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.233
2737	1764	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=-6 x -4 \\ \end{align*}	✓	✓	✓	✓	0.233
2738	1768	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=4 x^{4} \\ \end{align*}	✓	✓	✓	✓	0.233
2739	5899	\begin{align*} a \,x^{2} y+2 y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
2740	7837	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.233
2741	10878	\begin{align*} t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
2742	11204	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
2743	15199	\begin{align*} y^{\prime \prime }-20 y^{\prime }+51 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -14 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.233
2744	16036	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
2745	18220	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.233
2746	24664	\begin{align*} y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y&=36 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.233
2747	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*}	✓	✓	✓	✓	0.234
2748	10687	\begin{align*} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.234
2749	10720	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.234
2750	10793	\begin{align*} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.234
2751	11124	\begin{align*} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.234
2752	11145	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.234
2753	15105	\begin{align*} y^{\left (6\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime }&=x +{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.234
2754	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*}	✓	✓	✓	✓	0.234
2755	21550	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.234
2756	22243	\begin{align*} y^{\prime }+5 y&=0 \\ y \left (1\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.234
2757	24533	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }&=12 \\ \end{align*}	✓	✓	✓	✓	0.234
2758	25060	\begin{align*} y^{\prime }-4 y&={\mathrm e}^{4 t} \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.234
2759	404	\begin{align*} y^{\prime }&=y x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.235
2760	830	\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.235
2761	2176	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y&={\mathrm e}^{-x} \left (\left (1-22 x \right ) \cos \left (2 x \right )-\left (1+6 x \right ) \sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.235
2762	10547	\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (3+2 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.235
2763	10836	\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.235
2764	15218	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.235
2765	16771	\begin{align*} t y^{\prime \prime }+y^{\prime }+t y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.235
2766	22235	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.235
2767	442	\begin{align*} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.236
2768	4489	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=40 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.236
2769	9889	\begin{align*} 8 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.236
2770	10841	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.236
2771	11113	\begin{align*} 4 y^{\prime \prime } x -y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.236
2772	11133	\begin{align*} x^{2} y^{\prime \prime }+2 x \left (2+x \right ) y^{\prime }+2 \left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.236
2773	11269	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.236
2774	15200	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.236
2775	18180	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.236
2776	18465	\begin{align*} x^{\prime \prime }+x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.236
2777	20170	\begin{align*} y^{\prime \prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.236
2778	22748	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y&=2 \,{\mathrm e}^{3 x}-4 \,{\mathrm e}^{-5 x} \\ \end{align*}	✓	✓	✓	✓	0.236
2779	25062	\begin{align*} y^{\prime }+2 y&=3 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.236
2780	851	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.237
2781	4477	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime }&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.237
2782	10608	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.237
2783	10875	\begin{align*} t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.237
2784	10975	\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.237
2785	11002	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.237
2786	11096	\begin{align*} f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \\ \end{align*}	✓	✓	✓	✗	0.237
2787	12761	\begin{align*} \left (-a^{2}+1\right ) x y^{\prime }+3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.237
2788	18313	\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.237
2789	22239	\begin{align*} y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.237
2790	23386	\begin{align*} 8 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.237
2791	25637	\begin{align*} y^{\prime \prime }+a^{2} y&=1 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.237
2792	25947	\begin{align*} y^{\prime \prime \prime }+y&=x +\sin \left (x \right )+\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.237
2793	1043	\begin{align*} y^{\prime }&=4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.238
2794	1053	\begin{align*} y^{\prime \prime }&=4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.238
2795	1097	\begin{align*} y^{\prime \prime }&=y x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.238
2796	7853	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.238
2797	10847	\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}	✓	✓	✓	✗	0.238
2798	10969	\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.238
2799	11223	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.238
2800	18369	\begin{align*} 2 y^{\prime \prime }+4 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.238