2.3.28 Problems 2701 to 2800

Table 2.587: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2701	10999	\begin{align*} 3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.162
2702	11150	\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.162
2703	11186	\begin{align*} 2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.162
2704	13182	\(\left [\begin {array}{cc} 5 & 1 \\ -9 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.162
2705	16765	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{4 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.162
2706	17658	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.162
2707	18258	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }&=4 x +3 \sin \left (x \right )+\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.162
2708	22813	\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=100 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 20 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.162
2709	23243	\begin{align*} y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y&=2 x^{2}+3 \\ \end{align*}	✓	✓	✓	✗	0.162
2710	24802	\begin{align*} {y^{\prime }}^{2}+x^{3} y^{\prime }-2 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.162
2711	2110	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.163
2712	2513	\begin{align*} 2 t y^{3}+3 t^{2} y^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.163
2713	7259	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.163
2714	9617	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.163
2715	10495	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.163
2716	10995	\begin{align*} 6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.163
2717	14773	\begin{align*} x^{\prime }+y^{\prime }-x-3 y&={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }+x&={\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✗	0.163
2718	15702	\begin{align*} y^{\prime }-y&=2 \,{\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.163
2719	18080	\begin{align*} x y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.163
2720	18907	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.163
2721	19189	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.163
2722	19445	\begin{align*} y^{\prime \prime } x +3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.163
2723	20018	\begin{align*} {y^{\prime }}^{2}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.163
2724	22628	\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.163
2725	23664	\begin{align*} y^{\prime \prime }+7 y^{\prime }+6 y&=250 \,{\mathrm e}^{t} \cos \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -7 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.163
2726	24009	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.163
2727	25066	\begin{align*} y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.163
2728	1518	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.164
2729	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*}	✓	✓	✓	✓	0.164
2730	2149	\begin{align*} 4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y&=-{\mathrm e}^{x} \left (6 x^{2}+45 x +4\right ) \\ \end{align*}	✓	✓	✓	✓	0.164
2731	6367	\begin{align*} y^{\prime \prime }&=f \left (x , \frac {y^{\prime }}{y}\right ) y \\ \end{align*}	✗	✗	✗	✗	0.164
2732	7459	\begin{align*} \cos \left (\theta \right ) r^{\prime }-r \sin \left (\theta \right )+{\mathrm e}^{\theta }&=0 \\ \end{align*}	✓	✓	✓	✓	0.164
2733	8631	\begin{align*} y^{\prime \prime }+\frac {y}{25}&=\frac {t^{2}}{50} \\ y \left (0\right ) &= -25 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.164
2734	9653	\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=\delta \left (t \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.164
2735	9824	\begin{align*} x^{2} {y^{\prime }}^{2}&=\left (x -y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.164
2736	10476	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.164
2737	15708	\begin{align*} y^{\prime }-2 y&=6 \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.164
2738	15712	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.164
2739	16398	\begin{align*} x y^{\prime \prime \prime }+2 y^{\prime \prime }&=6 x \\ \end{align*}	✓	✓	✓	✓	0.164
2740	18888	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{t} t^{2}+7 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.164
2741	20612	\begin{align*} y^{\prime \prime }-a x y^{\prime }+a^{2} \left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.164
2742	25069	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=4 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.164
2743	25071	\begin{align*} y^{\prime \prime }+4 y&=8 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.164
2744	25072	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=9 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.164
2745	350	\begin{align*} y-2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=x^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.165
2746	6850	\begin{align*} x +y^{\prime } y+\frac {x y^{\prime }}{y^{2}+x^{2}}-\frac {y}{y^{2}+x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.165
2747	7364	\begin{align*} y^{\prime } x&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.165
2748	10350	\begin{align*} y^{\prime } x +y&=1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.165
2749	10489	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.165
2750	12859	\begin{align*} y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n}&=0 \\ \end{align*}	✗	✗	✗	✗	0.165
2751	14949	\begin{align*} x^{\prime \prime \prime \prime }-4 x^{\prime \prime \prime }+8 x^{\prime \prime }-8 x^{\prime }+4 x&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.165
2752	15212	\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=9 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.165
2753	18179	\begin{align*} y^{\prime \prime \prime \prime }-2 n^{2} y^{\prime \prime }+n^{4} y&=\cos \left (n x +\alpha \right ) \\ \end{align*}	✓	✓	✓	✓	0.165
2754	18372	\begin{align*} y^{\prime }&=\frac {y-x}{x +y} \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✗	✓	0.165
2755	20380	\begin{align*} {y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\ \end{align*}	✓	✓	✓	✓	0.165
2756	22614	\begin{align*} 3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+y&=\sin \left (x \right )+{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✗	0.165
2757	22999	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.165
2758	24058	\begin{align*} y^{\prime \prime }+y&=x^{2} \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi ^{2}}{4} \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 2 \pi \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.165
2759	25075	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=4 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.165
2760	4554	\begin{align*} x^{\prime }-2 x-y&=2 \,{\mathrm e}^{t} \\ x-y^{\prime }+2 y&=3 \,{\mathrm e}^{4 t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= x_{0} \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	0.166
2761	9359	\begin{align*} y^{\prime } x&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.166
2762	10014	\begin{align*} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.166
2763	11013	\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.166
2764	11298	\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}	✓	✓	✓	✗	0.166
2765	14182	\begin{align*} 6 y+18 y^{\prime } x +9 x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.166
2766	16132	\begin{align*} y^{\prime \prime }+4 y&=8 \\ y \left (0\right ) &= 11 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.166
2767	16802	\begin{align*} y^{\prime }&=\delta \left (t -2\right )-\delta \left (t -4\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.166
2768	22232	\begin{align*} y^{\prime \prime }-3 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.166
2769	22814	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=12 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.166
2770	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*}	✓	✓	✓	✓	0.166
2771	23841	\begin{align*} y^{2} y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.166
2772	25680	\begin{align*} 2 y^{\prime \prime }+9 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.166
2773	558	\begin{align*} t x^{\prime \prime }+2 \left (-1+t \right ) x^{\prime }-2 x&=0 \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.167
2774	1487	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.167
2775	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*}	✓	✓	✓	✓	0.167
2776	2152	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y&={\mathrm e}^{x} \left (15 x^{2}+34 x +14\right ) \\ \end{align*}	✓	✓	✓	✓	0.167
2777	3201	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-2 x} \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.167
2778	3690	\begin{align*} \frac {1}{x}-\frac {y}{y^{2}+x^{2}}+\frac {x y^{\prime }}{y^{2}+x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.167
2779	4471	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }-y&=44 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.167
2780	5366	\begin{align*} {y^{\prime }}^{2}&=y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.167
2781	6503	\begin{align*} x y y^{\prime \prime }&=b^{2} x y^{3}+a y y^{\prime }+x {y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.167
2782	6682	\begin{align*} 6 y^{\prime }+6 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.167
2783	6930	\begin{align*} 2 x +y \cos \left (x \right )+\left (2 y+\sin \left (x \right )-\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.167
2784	10150	\begin{align*} x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.167
2785	10713	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.167
2786	10764	\begin{align*} 4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.167
2787	11083	\begin{align*} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.167
2788	11285	\begin{align*} y^{\prime \prime }-\frac {y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.167
2789	12535	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.167
2790	12890	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+x \,{\mathrm e}^{y}&=0 \\ \end{align*}	✗	✗	✗	✗	0.167
2791	14816	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.167
2792	15400	\begin{align*} x y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.167
2793	16458	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.167
2794	16762	\begin{align*} y^{\prime \prime }+4 y&=20 \,{\mathrm e}^{4 t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.167
2795	17588	\begin{align*} y^{\prime \prime \prime \prime }-10 y^{\prime \prime \prime }+38 y^{\prime \prime }-64 y^{\prime }+40 y&=153 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.167
2796	18917	\begin{align*} y_{1}^{\prime }&=5 y_{1}-y_{2}+{\mathrm e}^{-t} \\ y_{2}^{\prime }&=y_{1}+3 y_{2}+2 \,{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= -3 \\ y_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.167
2797	20030	\begin{align*} y&=y^{\prime } x -{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.167
2798	25238	\begin{align*} t y^{\prime \prime }+\left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.167
2799	4552	\begin{align*} x^{\prime }-2 x+y&=5 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x+y^{\prime }-2 y&=10 \,{\mathrm e}^{t} \sin \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.168
2800	7268	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.168