2.3.27 Problems 2601 to 2700

Table 2.627: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2601	22178	\begin{align*} x^{3} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.226
2602	23654	\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=3 \,{\mathrm e}^{-2 t}-6 \,{\mathrm e}^{-5 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.226
2603	25322	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.226
2604	323	\begin{align*} y^{\prime \prime }-y^{\prime }+2 y&=3 x +4 \\ \end{align*}	✓	✓	✓	✓	0.227
2605	534	\begin{align*} x^{\prime \prime }+x&=\sin \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.227
2606	10753	\begin{align*} 2 y-x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.227
2607	10818	\begin{align*} u^{\prime \prime }+\frac {u}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.227
2608	10934	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.227
2609	11002	\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*}	✓	✓	✓	✗	0.227
2610	11014	\begin{align*} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.227
2611	14104	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=x \\ \end{align*}	✓	✓	✓	✓	0.227
2612	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*}	✓	✓	✓	✓	0.227
2613	18188	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }&=-6 \\ \end{align*}	✓	✓	✓	✓	0.227
2614	22619	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.227
2615	23007	\begin{align*} 20 y^{\prime \prime }-3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.227
2616	23643	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=24 \cosh \left (t \right ) \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.227
2617	25068	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.227
2618	25979	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.227
2619	823	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.228
2620	10692	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.228
2621	10699	\begin{align*} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.228
2622	14566	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.228
2623	16809	\begin{align*} y^{\prime \prime }+3 y^{\prime }&=\delta \left (t \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.228
2624	23010	\begin{align*} 12 x^{\prime \prime }-25 x^{\prime }+12 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.228
2625	27059	\begin{align*} y^{\prime \prime }-4 t y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.228
2626	1097	\begin{align*} y^{\prime \prime }&=y x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.229
2627	10745	\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.229
2628	10793	\begin{align*} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.229
2629	10875	\begin{align*} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.229
2630	11095	\begin{align*} 4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.229
2631	11106	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.229
2632	11315	\begin{align*} y^{\prime }+y^{2}-a x -b&=0 \\ \end{align*}	✓	✓	✓	✗	0.229
2633	12732	\begin{align*} x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-f \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.229
2634	14343	\begin{align*} t^{2} x^{\prime \prime }+x^{\prime } t +\left (t^{2}-\frac {1}{4}\right ) x&=0 \\ \end{align*}	✓	✓	✓	✓	0.229
2635	23650	\begin{align*} y^{\prime \prime }-3 y^{\prime }-4 y&=25 t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.229
2636	26714	\begin{align*} y^{\prime }&=x^{2}+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.229
2637	27566	\begin{align*} x y^{\prime \prime }&=2 y y^{\prime }-y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.229
2638	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.	✓	✓	✓	✓	0.230
2639	2108	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.230
2640	9101	\begin{align*} y^{\prime }+y x&=x \\ \end{align*}	✓	✓	✓	✓	0.230
2641	10698	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.230
2642	10799	\begin{align*} x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.230
2643	10812	\begin{align*} y-\left (x +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.230
2644	10824	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.230
2645	11092	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.230
2646	11124	\begin{align*} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.230
2647	11126	\begin{align*} x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.230
2648	11289	\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.230
2649	13050	\begin{align*} 2 y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.230
2650	15099	\begin{align*} x^{3} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.230
2651	23008	\begin{align*} 35 y^{\prime \prime }-29 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.230
2652	25064	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.230
2653	25957	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.230
2654	3341	\begin{align*} y^{\prime }&=\sqrt {y x +1} \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.231
2655	7717	\begin{align*} x y^{\prime }-y&=x^{3}+3 x^{2}-2 x \\ \end{align*}	✓	✓	✓	✓	0.231
2656	7824	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.231
2657	10547	\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.231
2658	10856	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.231
2659	10879	\begin{align*} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.231
2660	12745	\begin{align*} x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime }-\ln \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.231
2661	14341	\begin{align*} x^{\prime \prime }-2 a x^{\prime }+a^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	0.231
2662	14568	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.231
2663	15262	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=5 \\ \end{align*}	✓	✓	✓	✓	0.231
2664	15683	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y&=2 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.231
2665	16772	\begin{align*} y^{\prime \prime }-9 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 9 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.231
2666	16796	\begin{align*} y^{\prime \prime }&=\operatorname {Heaviside}\left (t -2\right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.231
2667	23657	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=3 t^{3}-9 t^{2}-5 t +1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.231
2668	1483	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.232
2669	2174	\begin{align*} y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y&={\mathrm e}^{2 x} \left (-5 x^{2}-8 x +3\right ) \\ \end{align*}	✓	✓	✓	✓	0.232
2670	10697	\begin{align*} x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.232
2671	10768	\begin{align*} x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.232
2672	10885	\begin{align*} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.232
2673	10975	\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.232
2674	11037	\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*}	✓	✓	✓	✗	0.232
2675	11087	\begin{align*} t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.232
2676	11103	\begin{align*} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.232
2677	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
2678	11123	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.232
2679	11174	\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.232
2680	11235	\begin{align*} 4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.232
2681	23653	\begin{align*} y^{\prime \prime }-10 y^{\prime }+21 y&=21 t^{2}+t +13 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.232
2682	27737	\begin{align*} y^{\prime \prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.232
2683	4164	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
2684	6787	\begin{align*} y+2 y^{\prime \prime \prime }+y^{\left (6\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
2685	9106	\begin{align*} x y^{\prime }-3 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.233
2686	9312	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
2687	10667	\begin{align*} t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
2688	10672	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
2689	11113	\begin{align*} 4 x y^{\prime \prime }-x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
2690	11134	\begin{align*} x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
2691	11136	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
2692	11187	\begin{align*} x y^{\prime \prime }+x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
2693	11241	\begin{align*} y-\left (x +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
2694	11244	\begin{align*} 2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
2695	14097	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.233
2696	14342	\begin{align*} x^{\prime \prime }-\frac {\left (t +2\right ) x^{\prime }}{t}+\frac {\left (t +2\right ) x}{t^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
2697	16195	\begin{align*} y^{\prime }&=\left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.233
2698	18173	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.233
2699	18464	\begin{align*} x^{\prime \prime }+x^{\prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.233
2700	22146	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=1+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.233