2.3.25 Problems 2401 to 2500

Table 2.593: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2401	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*}	✓	✓	✓	✗	0.171
2402	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*}	✓	✓	✓	✗	0.171
2403	11129	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.171
2404	11177	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.171
2405	15210	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= 8 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.171
2406	20053	\begin{align*} y^{\prime \prime \prime }+8 y&=x^{4}+2 x +1 \\ \end{align*}	✓	✓	✓	✓	0.171
2407	20090	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.171
2408	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.	✓	✓	✓	✓	0.171
2409	521	\begin{align*} 4 x^{2} y^{\prime \prime }-12 y^{\prime } x +\left (15+16 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
2410	2207	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y&=-{\mathrm e}^{3 x} \left (17 x^{2}+67 x +9\right ) \\ \end{align*}	✓	✓	✓	✓	0.172
2411	3202	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime }&=x^{2} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.172
2412	4164	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
2413	8629	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= {\frac {81}{10}} \\ y^{\prime }\left (0\right ) &= {\frac {39}{10}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.172
2414	9101	\begin{align*} y^{\prime }+y x&=x \\ \end{align*}	✓	✓	✓	✓	0.172
2415	9129	\begin{align*} y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
2416	10639	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.172
2417	10641	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (4 x +1\right ) y^{\prime }-\left (49+27 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.172
2418	10885	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.172
2419	11126	\begin{align*} x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
2420	11169	\begin{align*} \left (-x +2\right ) x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.172
2421	16813	\begin{align*} y^{\prime \prime }+y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.172
2422	18240	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }&={\mathrm e}^{x}+3 \sin \left (2 x \right )+1 \\ \end{align*}	✓	✓	✓	✓	0.172
2423	19548	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
2424	20330	\begin{align*} 2 x^{\prime \prime }+5 x^{\prime }-12 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
2425	22146	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x}+1 \\ \end{align*}	✓	✓	✓	✓	0.172
2426	23341	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
2427	6705	\begin{align*} 8 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.173
2428	7060	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.173
2429	8623	\begin{align*} y^{\prime }+2 y&=0 \\ y \left (0\right ) &= {\frac {3}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.173
2430	10599	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.173
2431	10686	\begin{align*} 4 y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.173
2432	10879	\begin{align*} \left (1-t \right ) y^{\prime \prime }+y^{\prime } t -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.173
2433	11272	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.173
2434	15012	\begin{align*} x^{\prime }&=13 x \\ y^{\prime }&=13 y \\ \end{align*}	✓	✓	✓	✓	0.173
2435	15219	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=t +2 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.173
2436	19560	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.173
2437	19582	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.173
2438	21415	\begin{align*} y^{2}+y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.173
2439	24011	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\ \end{align*}	✓	✓	✓	✓	0.173
2440	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.	✓	✓	✓	✓	0.173
2441	414	\begin{align*} y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.174
2442	518	\begin{align*} 36 x^{2} y^{\prime \prime }+60 y^{\prime } x +\left (9 x^{3}-5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
2443	2295	\begin{align*} y^{\prime }-2 t y&=t \\ \end{align*}	✓	✓	✓	✓	0.174
2444	6617	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=-3 \,{\mathrm e}^{2 x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.174
2445	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*}	✓	✓	✓	✓	0.174
2446	10638	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.174
2447	10645	\begin{align*} x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.174
2448	10718	\begin{align*} x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
2449	10757	\begin{align*} y^{\prime \prime } x +y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.174
2450	10982	\begin{align*} 4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.174
2451	11030	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.174
2452	11173	\begin{align*} x \left (x +1\right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.174
2453	11182	\begin{align*} y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.174
2454	11197	\begin{align*} x \left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.174
2455	11198	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.174
2456	11267	\begin{align*} y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.174
2457	15413	\begin{align*} y^{\prime \prime }+12 y&=7 y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.174
2458	15694	\begin{align*} y^{\prime }-y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.174
2459	16661	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=10 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.174
2460	19545	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=10+42 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.174
2461	19576	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=12 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.174
2462	24027	\begin{align*} y^{\left (6\right )}+y^{\prime \prime \prime \prime }-y&=4 x^{5}-6 x^{2}+2 \\ \end{align*}	✓	✓	✓	✓	0.174
2463	310	\begin{align*} y^{\prime \prime }-i y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2464	517	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +\left (8+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2465	2153	\begin{align*} 4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y&=-{\mathrm e}^{-2 x} \left (1-15 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.175
2466	3589	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2467	3641	\begin{align*} y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2468	6695	\begin{align*} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2469	7186	\begin{align*} y^{\prime \prime }+\frac {a y}{x^{{3}/{2}}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.175
2470	7329	\begin{align*} 3 y^{\prime \prime } x -2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2471	10668	\begin{align*} t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2472	10765	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2473	10853	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2474	10857	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2475	10958	\begin{align*} y^{\prime \prime }-3 y^{\prime } x +\left (2 x^{2}+5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2476	10989	\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2477	11021	\begin{align*} 4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2478	11044	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2479	11053	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2480	11055	\begin{align*} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2481	11077	\begin{align*} \left (2 t +1\right ) y^{\prime \prime }-4 \left (1+t \right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2482	11196	\begin{align*} x \left (2+x \right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2483	11207	\begin{align*} x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2484	14093	\begin{align*} -y-2 y^{\prime }+2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2485	16466	\begin{align*} y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y&={\mathrm e}^{3 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.175
2486	16577	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2487	18028	\begin{align*} {y^{\prime }}^{2}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2488	21892	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.175
2489	26009	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.175
2490	26043	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2491	1742	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.176
2492	2576	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.176
2493	7916	\begin{align*} -y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.176
2494	8624	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 11 \\ y^{\prime }\left (0\right ) &= 28 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.176
2495	10837	\begin{align*} x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.176
2496	11128	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.176
2497	11154	\begin{align*} 2 \left (1-x \right ) x y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.176
2498	15206	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+13 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.176
2499	16579	\begin{align*} -8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.176
2500	16665	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=30 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.176