2.3.25 Problems 2401 to 2500

Table 2.623: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2401	545	\begin{align*} x^{\prime \prime \prime }+x^{\prime \prime }-6 x^{\prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ x^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.210
2402	572	\begin{align*} x^{\prime \prime }+4 x&=f \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.210
2403	6758	\begin{align*} 16 y-16 y^{\prime }+12 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.210
2404	8978	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.210
2405	10804	\begin{align*} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.210
2406	11302	\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.210
2407	12793	\begin{align*} y^{\prime \prime \prime \prime } x +5 y^{\prime \prime \prime }-24&=0 \\ \end{align*}	✓	✓	✓	✓	0.210
2408	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*}	✓	✓	✓	✓	0.210
2409	17659	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.210
2410	20170	\begin{align*} y^{\prime \prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.210
2411	20667	\begin{align*} x y^{\prime \prime } \left (x \cos \left (x \right )-2 \sin \left (x \right )\right )+\left (x^{2}+2\right ) y^{\prime } \sin \left (x \right )-2 y \left (x \sin \left (x \right )+\cos \left (x \right )\right )&=0 \\ \end{align*}	✓	✓	✗	✗	0.210
2412	21533	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.210
2413	23648	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=27 t \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.210
2414	24663	\begin{align*} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }-8 y^{\prime \prime }&=48 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.210
2415	26699	\begin{align*} y^{\prime \prime \prime \prime }-\lambda ^{4} y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.210
2416	26838	\begin{align*} x^{\prime \prime }-2 x^{\prime }+10 x&=\cos \left (3 t \right ) \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= {\frac {18}{37}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.210
2417	261	\begin{align*} y^{\prime \prime }+2 y&=6 x +4 \\ \end{align*}	✓	✓	✓	✓	0.211
2418	3618	\begin{align*} x^{\prime } t +2 x&=4 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.211
2419	9560	\begin{align*} x^{3} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.211
2420	10794	\begin{align*} y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.211
2421	11042	\begin{align*} x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.211
2422	11202	\begin{align*} 2 y-x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.211
2423	11285	\begin{align*} y^{\prime \prime }-\frac {y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.211
2424	17627	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.211
2425	17658	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.211
2426	17761	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }+20 y^{\prime }+25 y&=t^{2} \\ \end{align*}	✓	✓	✓	✓	0.211
2427	18311	\begin{align*} x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.211
2428	18751	\begin{align*} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.211
2429	25974	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }&={\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.211
2430	26698	\begin{align*} y^{\prime \prime \prime \prime }-\lambda ^{4} y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.211
2431	27612	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.211
2432	10956	\begin{align*} y^{\prime \prime }+3 x y^{\prime }+\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.212
2433	11204	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.212
2434	17631	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.212
2435	18747	\begin{align*} t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.212
2436	21287	\begin{align*} x^{\prime }-x&=k \delta \left (t \right ) \\ x \left (0\right ) &= a \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.212
2437	23637	\begin{align*} y^{\prime \prime }-4 y&=-3 \,{\mathrm e}^{t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.212
2438	350	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=x^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.213
2439	2209	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=-2 \,{\mathrm e}^{-x} \left (6 x^{2}-18 x +7\right ) \\ \end{align*}	✓	✓	✓	✓	0.213
2440	3937	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=36 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.213
2441	8957	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.213
2442	10847	\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}	✓	✓	✓	✗	0.213
2443	10955	\begin{align*} \left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.213
2444	11041	\begin{align*} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.213
2445	15698	\begin{align*} y^{\prime \prime }+9 y&=2 \sin \left (3 x \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.213
2446	17625	\begin{align*} x^{3} y^{\prime \prime \prime }+22 x^{2} y^{\prime \prime }+124 x y^{\prime }+140 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.213
2447	17626	\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }-46 x y^{\prime }+100 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.213
2448	17630	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.213
2449	21576	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=a \sin \left (b x \right ) \\ \end{align*}	✓	✓	✓	✓	0.213
2450	25186	\begin{align*} y^{\prime \prime }-2 y&=y t \\ \end{align*}	✓	✓	✓	✓	0.213
2451	370	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.214
2452	388	\begin{align*} x^{\prime \prime }+4 x^{\prime }+4 x&=10 \cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.214
2453	558	\begin{align*} t x^{\prime \prime }+2 \left (t -1\right ) x^{\prime }-2 x&=0 \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.214
2454	2216	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=-{\mathrm e}^{-x} \left (4-8 x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.214
2455	2295	\begin{align*} y^{\prime }-2 y t&=t \\ \end{align*}	✓	✓	✓	✓	0.214
2456	2680	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{t} t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.214
2457	3934	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.214
2458	10622	\begin{align*} x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.214
2459	11105	\begin{align*} y^{\prime \prime }+x y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.214
2460	11188	\begin{align*} x \left (x -1\right )^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.214
2461	17208	\begin{align*} y^{2}+2 t y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.214
2462	17628	\begin{align*} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.214
2463	17673	\begin{align*} x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 x y^{\prime }+125 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.214
2464	21200	\begin{align*} x^{\prime \prime \prime }-x^{\prime }&=t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.214
2465	21201	\begin{align*} x^{\prime \prime \prime \prime }+x^{\prime \prime \prime }&=t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.214
2466	21888	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=x^{3}+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.214
2467	23663	\begin{align*} y^{\prime \prime }-y&=2 t^{2}+2 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.214
2468	27617	\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.214
2469	366	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.215
2470	557	\begin{align*} t x^{\prime \prime }-\left (4 t +1\right ) x^{\prime }+2 \left (2 t +1\right ) x&=0 \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.215
2471	1486	\begin{align*} y^{\prime \prime }-2 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.215
2472	2215	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{x} \left (1-6 x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 7 \\ y^{\prime \prime }\left (0\right ) &= 9 \\ \end{align*}	✓	✓	✓	✓	0.215
2473	2217	\begin{align*} 4 y^{\prime \prime \prime }-3 y^{\prime }-y&={\mathrm e}^{-\frac {x}{2}} \left (2-3 x \right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 15 \\ y^{\prime \prime }\left (0\right ) &= -17 \\ \end{align*}	✓	✓	✓	✓	0.215
2474	4491	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=10 \,{\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.215
2475	9310	\begin{align*} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.215
2476	11153	\begin{align*} 2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.215
2477	23005	\begin{align*} y^{\prime \prime }-9 y^{\prime }+18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.215
2478	25956	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&=16 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.215
2479	27741	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.215
2480	544	\begin{align*} x^{\prime \prime }+4 x^{\prime }+8 x&={\mathrm e}^{-t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.216
2481	8924	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }-y^{\prime }+y&=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 \\ y^{\prime \prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.216
2482	10864	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.216
2483	22029	\begin{align*} y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.216
2484	24017	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{x} \sin \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.216
2485	1730	\begin{align*} x^{4} y^{4}+x^{5} y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.217
2486	6595	\begin{align*} \left (y^{2}-{y^{\prime }}^{2} x^{2}+x^{2} y y^{\prime \prime }\right )^{2}&=4 x y \left (x y^{\prime }-y\right )^{3} \\ \end{align*}	✗	✗	✓	✗	0.217
2487	6638	\begin{align*} 10 y+3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.217
2488	6754	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.217
2489	6782	\begin{align*} 2 y^{\prime }-2 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\left (5\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.217
2490	12829	\begin{align*} x \left (a y^{\prime }+b y^{\prime \prime }+c y^{\prime \prime \prime }+e y^{\prime \prime \prime \prime }\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.217
2491	17608	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.217
2492	18461	\begin{align*} x^{\prime \prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.217
2493	21890	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.217
2494	26246	\begin{align*} {\mathrm e}^{y^{\prime }}&=x \\ \end{align*}	✓	✓	✓	✓	0.217
2495	26534	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=\sin \left (2 x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.217
2496	375	\begin{align*} y^{\prime \prime }-4 y&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.218
2497	2170	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{2 x} \left (12 x^{2}+26 x +15\right ) \\ \end{align*}	✓	✓	✓	✓	0.218
2498	3614	\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {4}{\left (x^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	0.218
2499	6753	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.218
2500	10866	\begin{align*} y^{\prime \prime }+x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.218