2.3.26 Problems 2501 to 2600

Table 2.625: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2501	11109	\begin{align*} y^{\prime \prime }+x y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.218
2502	11133	\begin{align*} x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.218
2503	11223	\begin{align*} y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.218
2504	18170	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }&=4 \\ \end{align*}	✓	✓	✓	✓	0.218
2505	24045	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{x} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.218
2506	25966	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=x^{2}-x \\ \end{align*}	✓	✓	✓	✓	0.218
2507	1680	\begin{align*} 6 x^{2} y^{2}+4 x^{3} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.219
2508	8958	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.219
2509	10721	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.219
2510	10871	\begin{align*} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.219
2511	11229	\begin{align*} 2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.219
2512	11298	\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}	✓	✓	✓	✗	0.219
2513	12347	\begin{align*} y^{\prime \prime }+f \left (x \right ) y^{\prime }+\left (\frac {f \left (x \right )^{2}}{4}+\frac {f^{\prime }\left (x \right )}{2}+a \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.219
2514	14121	\begin{align*} y^{\prime \prime \prime \prime }-y&={\mathrm e}^{x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.219
2515	18189	\begin{align*} 3 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.219
2516	23683	\begin{align*} x^{2} y^{\prime \prime }+\left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.219
2517	530	\begin{align*} x^{\prime \prime }+4 x&=0 \\ x \left (0\right ) &= 5 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.220
2518	3935	\begin{align*} y^{\prime \prime }+4 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.220
2519	4488	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=15 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.220
2520	7232	\begin{align*} 2 x y^{\prime }+y&=2 x^{{5}/{2}} \\ \end{align*}	✓	✓	✓	✓	0.220
2521	8830	\begin{align*} y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.220
2522	8937	\begin{align*} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.220
2523	8948	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.220
2524	10751	\begin{align*} y^{\prime \prime }-x y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.220
2525	10758	\begin{align*} x \left (x -1\right )^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.220
2526	11111	\begin{align*} 4 y^{\prime \prime }+x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.220
2527	15699	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=x \,{\mathrm e}^{x}-3 x^{2} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.220
2528	21578	\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+16 y^{\prime \prime }&=96 \,{\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.220
2529	10731	\begin{align*} 4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
2530	10849	\begin{align*} x^{3} y^{\prime \prime }+y^{\prime }-\frac {y}{x}&=0 \\ \end{align*}	✓	✓	✓	✗	0.221
2531	10882	\begin{align*} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.221
2532	11039	\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*}	✓	✓	✓	✗	0.221
2533	11112	\begin{align*} y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.221
2534	11275	\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}	✓	✓	✓	✗	0.221
2535	11287	\begin{align*} y^{\prime \prime }+\frac {y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
2536	12763	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+\left (a \,x^{3}-12\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.221
2537	18169	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime }&=3 \\ \end{align*}	✓	✓	✓	✓	0.221
2538	18213	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=x^{2}+x \\ \end{align*}	✓	✓	✓	✓	0.221
2539	20533	\begin{align*} y^{\prime \prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.221
2540	20705	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&={\mathrm e}^{x}+\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.221
2541	21306	\begin{align*} x^{\prime \prime \prime }+a x^{\prime \prime }+b x^{\prime }+c x&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
2542	23002	\begin{align*} y^{\prime \prime }+7 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
2543	26051	\begin{align*} {y^{\prime }}^{2}-y^{\prime }-6&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
2544	27745	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
2545	27763	\begin{align*} y^{\prime \prime }-x y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.221
2546	327	\begin{align*} 2 y^{\prime \prime }+4 y^{\prime }+7 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.222
2547	2163	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \left (x^{2}+4 x +3\right ) \\ \end{align*}	✓	✓	✓	✗	0.222
2548	2211	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=-{\mathrm e}^{-x} \left (3 x^{2}-9 x +4\right ) \\ \end{align*}	✓	✓	✓	✓	0.222
2549	9308	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=10+42 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.222
2550	10687	\begin{align*} y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.222
2551	10720	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.222
2552	18753	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.222
2553	27568	\begin{align*} x y y^{\prime \prime }-{y^{\prime }}^{2} x&=y y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.222
2554	554	\begin{align*} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+\frac {226 x}{25}&=6 \,{\mathrm e}^{-\frac {t}{5}} \cos \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.223
2555	10878	\begin{align*} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.223
2556	10914	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.223
2557	11146	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.223
2558	11156	\begin{align*} 4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.223
2559	18168	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.223
2560	18172	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.223
2561	21574	\begin{align*} y^{\left (6\right )}+8 y^{\prime \prime \prime }&=a \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	0.223
2562	21960	\begin{align*} b^{\left (7\right )}&=3 p \\ \end{align*}	✓	✓	✓	✓	0.223
2563	22664	\begin{align*} y a^{2} b^{2}+\left (a^{2}+b^{2}\right ) y^{\prime \prime }+y^{\prime \prime \prime \prime }&=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*}	✓	✓	✓	✓	0.223
2564	23652	\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=16 t \,{\mathrm e}^{-t}-15 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -9 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.223
2565	27556	\begin{align*} y^{\prime \prime \prime \prime } x&=1 \\ \end{align*}	✓	✓	✓	✓	0.223
2566	324	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=2 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.224
2567	6783	\begin{align*} y^{\prime }+2 y^{\prime \prime \prime }+y^{\left (5\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.224
2568	7229	\begin{align*} y^{\prime }+y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.224
2569	7241	\begin{align*} x^{\prime }+x-{\mathrm e}^{y}&=0 \\ \end{align*}	✓	✓	✓	✓	0.224
2570	10777	\begin{align*} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.224
2571	10972	\begin{align*} 2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.224
2572	23651	\begin{align*} y^{\prime \prime }+13 y^{\prime }+36 y&=10-72 t \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.224
2573	27044	\begin{align*} x^{\prime }+y^{\prime }-x&=\cos \left (t \right ) \\ x^{\prime }+2 y^{\prime }&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.224
2574	27055	\begin{align*} y^{\prime \prime }+8 t y^{\prime }-8 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.224
2575	27058	\begin{align*} y^{\prime \prime }+8 t y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.224
2576	371	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.225
2577	396	\begin{align*} x^{\prime \prime }+2 x^{\prime }+2 x&=2 \cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.225
2578	3621	\begin{align*} y^{\prime }-\frac {y}{x}&=2 x^{2} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.225
2579	4466	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=48 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.225
2580	9309	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=1 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.225
2581	11252	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.225
2582	11737	\begin{align*} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.225
2583	15091	\begin{align*} y^{\prime \prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.225
2584	18171	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.225
2585	18227	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=1+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.225
2586	23642	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.225
2587	27020	\begin{align*} y^{\prime \prime }+16 y&=t +1 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.225
2588	27038	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+2 y&=6 \delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.225
2589	2169	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{2 x} \left (18 x^{2}+33 x +13\right ) \\ \end{align*}	✓	✓	✓	✓	0.226
2590	6756	\begin{align*} -y^{\prime }+y^{\prime \prime }-3 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.226
2591	10841	\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*}	✓	✓	✓	✗	0.226
2592	10923	\begin{align*} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.226
2593	10969	\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.226
2594	11096	\begin{align*} f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \\ \end{align*}	✓	✓	✓	✗	0.226
2595	11145	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.226
2596	11152	\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*}	✓	✓	✓	✗	0.226
2597	12741	\begin{align*} x^{2} y^{\prime \prime \prime }-x y^{\prime \prime }+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.226
2598	15686	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&=6 x -20-120 \,{\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.226
2599	16133	\begin{align*} y^{\prime \prime }-4 y&={\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.226
2600	18749	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.226