2.3.28 Problems 2701 to 2800

Table 2.629: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2701	23630	\begin{align*} y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.233
2702	1080	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.234
2703	2726	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y&=t^{3} {\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.234
2704	3609	\begin{align*} y^{\prime }+y&=4 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.234
2705	10242	\begin{align*} y^{\prime }+y&=\frac {1}{x} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.234
2706	10537	\begin{align*} \left (4 x +2\right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.234
2707	10676	\begin{align*} f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \\ \end{align*}	✓	✓	✓	✗	0.234
2708	10688	\begin{align*} 4 x y^{\prime \prime }-x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.234
2709	10889	\begin{align*} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.234
2710	10958	\begin{align*} y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.234
2711	16151	\begin{align*} y^{\prime \prime }+16 y&=t \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.234
2712	25690	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 x y^{\prime }-78 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.234
2713	330	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=1+x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.235
2714	361	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }-2 y&=8 x^{5} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.235
2715	1079	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.235
2716	1196	\begin{align*} 2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.235
2717	1323	\begin{align*} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.235
2718	3616	\begin{align*} y^{\prime }+\frac {y}{x \ln \left (x \right )}&=9 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.235
2719	10661	\begin{align*} 2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.235
2720	10702	\begin{align*} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.235
2721	10765	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.235
2722	10892	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.235
2723	11081	\begin{align*} 2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.235
2724	18220	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.235
2725	22053	\begin{align*} x y^{2}+x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.235
2726	23641	\begin{align*} y^{\prime \prime }-9 y&=20 \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 18 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.235
2727	23660	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=3 \,{\mathrm e}^{2 t} t -4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.235
2728	7140	\begin{align*} y y^{\prime }-2 {y^{\prime }}^{2} x +x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.236
2729	10681	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.236
2730	10859	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.236
2731	10861	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.236
2732	11028	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.236
2733	11175	\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.236
2734	16795	\begin{align*} y^{\prime \prime }&=\operatorname {Heaviside}\left (t -2\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.236
2735	19582	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.236
2736	22510	\begin{align*} \left (y^{2}+2 y x \right ) \left (x^{2}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.236
2737	398	\begin{align*} x^{\prime \prime }+6 x^{\prime }+45 x&=50 \cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.237
2738	3241	\begin{align*} 5 y^{\prime }-3 x^{\prime }-5 y&=5 t \\ 3 x^{\prime }-5 y^{\prime }-2 x&=0 \\ \end{align*}	✓	✓	✓	✗	0.237
2739	3936	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.237
2740	10617	\begin{align*} 9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (4 x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.237
2741	10670	\begin{align*} t y^{\prime \prime }+t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.237
2742	10680	\begin{align*} y^{\prime \prime }+x y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.237
2743	10707	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.237
2744	10727	\begin{align*} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4}&=0 \\ \end{align*}	✓	✓	✓	✗	0.237
2745	11049	\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*}	✓	✓	✓	✗	0.237
2746	11084	\begin{align*} 2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.237
2747	11127	\begin{align*} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.237
2748	11206	\begin{align*} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.237
2749	14348	\begin{align*} x^{\prime \prime \prime }+x^{\prime \prime }&=2 \,{\mathrm e}^{t}+3 t^{2} \\ \end{align*}	✓	✓	✓	✓	0.237
2750	14951	\begin{align*} t^{2} y^{\prime \prime }-\left (t^{2}+2 t \right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.237
2751	15715	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ y^{\prime \prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.237
2752	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*}	✓	✓	✓	✓	0.237
2753	19625	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=2 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.237
2754	22478	\begin{align*} y^{\prime \prime \prime \prime }&=\frac {x}{3} \\ \end{align*}	✓	✓	✓	✓	0.237
2755	23587	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-y \\ \end{align*}	✓	✓	✓	✓	0.237
2756	26015	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.237
2757	26417	\begin{align*} x y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.237
2758	399	\begin{align*} x^{\prime \prime }+10 x^{\prime }+650 x&=100 \cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.238
2759	8201	\begin{align*} y^{\prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.238
2760	10582	\begin{align*} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.238
2761	10704	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.238
2762	10815	\begin{align*} 2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.238
2763	10883	\begin{align*} 2 y^{\prime \prime }+x y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.238
2764	11237	\begin{align*} 3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.238
2765	16778	\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.	✓	✓	✓	✓	0.238
2766	17199	\begin{align*} y \cos \left (y t \right )+t \cos \left (y t \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.238
2767	23805	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.238
2768	23824	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.238
2769	23825	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-y \\ \end{align*}	✓	✓	✓	✓	0.238
2770	26048	\begin{align*} x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }-3 y x&=1 \\ \end{align*}	✓	✓	✓	✗	0.238
2771	10538	\begin{align*} y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.239
2772	10664	\begin{align*} 2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.239
2773	10868	\begin{align*} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.239
2774	10957	\begin{align*} \left (4 x +2\right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.239
2775	11015	\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*}	✓	✓	✓	✗	0.239
2776	11085	\begin{align*} t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.239
2777	11114	\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.239
2778	11122	\begin{align*} x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.239
2779	11132	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.239
2780	11177	\begin{align*} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.239
2781	11269	\begin{align*} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.239
2782	16852	\begin{align*} y^{\prime \prime }-y^{2}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.239
2783	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*}	✓	✓	✓	✓	0.239
2784	23765	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.239
2785	23806	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-y \\ \end{align*}	✓	✓	✓	✓	0.239
2786	4472	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+5 y^{\prime }+5 y&=5 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.240
2787	9311	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.240
2788	10686	\begin{align*} 4 y^{\prime \prime }+x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.240
2789	10747	\begin{align*} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.240
2790	10973	\begin{align*} x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (-3 x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.240
2791	11090	\begin{align*} t y^{\prime \prime }+t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.240
2792	11222	\begin{align*} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.240
2793	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*}	✓	✓	✓	✗	0.240
2794	16804	\begin{align*} y^{\prime \prime }&=\delta \left (t -1\right )-\delta \left (-4+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.240
2795	18279	\begin{align*} y^{\prime \prime \prime \prime }-y&=8 \,{\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= 4 \\ y^{\prime \prime \prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.240
2796	26814	\begin{align*} x^{\prime }-x&=\cos \left (t \right )-\sin \left (t \right ) \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.240
2797	339	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime }+4 y&={\mathrm e}^{x}-x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.241
2798	397	\begin{align*} x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.241
2799	848	\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.241
2800	1052	\begin{align*} y^{\prime \prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.241