2.3.25 Problems 2401 to 2500

Table 2.599: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2401	14366	\begin{align*} x^{\prime \prime }+3 x^{\prime }+2 x&={\mathrm e}^{-4 t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.205
2402	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.	✓	✓	✓	✓	0.205
2403	17572	\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 16 \\ 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 \\ y^{\left (5\right )}\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.205
2404	20610	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.205
2405	24530	\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime }&=11 \\ \end{align*}	✓	✓	✓	✓	0.205
2406	25633	\begin{align*} y^{\prime \prime }-y^{\prime }&=1 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.205
2407	25955	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y&=-2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.205
2408	523	\begin{align*} 2 x^{2} y^{\prime \prime }-3 y^{\prime } x -2 \left (-x^{5}+14\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.206
2409	10574	\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.206
2410	10773	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.206
2411	10781	\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.206
2412	10996	\begin{align*} 28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.206
2413	16779	\begin{align*} y^{\prime \prime }&={\mathrm e}^{t} \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.206
2414	20579	\begin{align*} y^{\left (5\right )}-n^{2} y^{\prime \prime \prime }&={\mathrm e}^{a x} \\ \end{align*}	✓	✓	✓	✓	0.206
2415	4474	\begin{align*} y^{\prime \prime \prime \prime }-y&=4 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.207
2416	6657	\begin{align*} -a^{3} y+3 a^{2} y^{\prime }-3 a y^{\prime \prime }+y^{\prime \prime \prime }&={\mathrm e}^{a x} \\ \end{align*}	✓	✓	✓	✓	0.207
2417	9308	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=10+42 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.207
2418	10577	\begin{align*} 8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.207
2419	10804	\begin{align*} y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.207
2420	10826	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.207
2421	11255	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.207
2422	11257	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.207
2423	11260	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.207
2424	16789	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.207
2425	16793	\begin{align*} y^{\prime }&=\operatorname {Heaviside}\left (t -3\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.207
2426	17576	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+30 y^{\prime \prime }-56 y^{\prime }+49 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ y^{\prime \prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.207
2427	17658	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.207
2428	20164	\begin{align*} y^{\prime \prime \prime }&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.207
2429	21552	\begin{align*} y^{\prime \prime \prime \prime }&=5 x \\ \end{align*}	✓	✓	✓	✓	0.207
2430	22250	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=3 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.207
2431	22262	\begin{align*} w^{\prime }-w-2 y&=1 \\ y^{\prime }-4 w-3 y&=-1 \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 2 \\ w \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.207
2432	25635	\begin{align*} y^{\prime \prime }+y&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.207
2433	3708	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.208
2434	6697	\begin{align*} -8 y+3 y^{\prime } x +x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.208
2435	9104	\begin{align*} 2 y-x^{3}&=y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	0.208
2436	9312	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.208
2437	10997	\begin{align*} 8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.208
2438	11109	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.208
2439	11171	\begin{align*} y^{\prime \prime } x -2 \left (x +1\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.208
2440	11259	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.208
2441	11262	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.208
2442	14637	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=3 \,{\mathrm e}^{x} x^{2}-7 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.208
2443	14814	\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.208
2444	14844	\begin{align*} x^{\prime \prime }+\left (1+t \right ) x&=0 \\ \end{align*}	✓	✓	✓	✓	0.208
2445	16670	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=30 x \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.208
2446	17659	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.208
2447	18170	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }&=4 \\ \end{align*}	✓	✓	✓	✓	0.208
2448	18188	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }&=-6 \\ \end{align*}	✓	✓	✓	✓	0.208
2449	20072	\begin{align*} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=\cos \left (x m \right ) \\ \end{align*}	✓	✓	✓	✓	0.208
2450	24531	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }&=12 \\ \end{align*}	✓	✓	✓	✓	0.208
2451	1312	\begin{align*} 2 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.209
2452	8948	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.209
2453	9100	\begin{align*} y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.209
2454	9101	\begin{align*} y^{\prime }+y x&=x \\ \end{align*}	✓	✓	✓	✓	0.209
2455	10977	\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.209
2456	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*}	✓	✓	✓	✗	0.209
2457	11041	\begin{align*} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (3+2 x \right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.209
2458	11228	\begin{align*} y^{\prime \prime } x +\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.209
2459	11254	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.209
2460	11258	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.209
2461	17626	\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }-46 y^{\prime } x +100 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.209
2462	273	\begin{align*} y^{\prime \prime }+y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.210
2463	411	\begin{align*} y^{\prime \prime }&=4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.210
2464	3610	\begin{align*} y^{\prime }+\frac {2 y}{x}&=5 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.210
2465	6601	\begin{align*} y^{\prime \prime \prime }&=\cos \left (x \right )+1 \\ \end{align*}	✓	✓	✓	✓	0.210
2466	6637	\begin{align*} -3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&={\mathrm e}^{-x}+3 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.210
2467	6693	\begin{align*} -y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.210
2468	10896	\begin{align*} x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.210
2469	11253	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.210
2470	11297	\begin{align*} y^{\prime \prime }&=-\frac {y}{4 x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.210
2471	15104	\begin{align*} y^{\left (6\right )}-y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.210
2472	16773	\begin{align*} y^{\prime \prime }+9 y&=27 t^{3} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.210
2473	16785	\begin{align*} y^{\prime \prime }+4 y&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.210
2474	18190	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=1 \\ \end{align*}	✓	✓	✓	✓	0.210
2475	20866	\begin{align*} -y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.210
2476	23388	\begin{align*} x^{4} y^{\prime \prime \prime \prime }-5 x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.210
2477	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.	✓	✓	✓	✓	0.211
2478	7169	\begin{align*} x^{4} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.211
2479	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*}	✓	✓	✓	✗	0.211
2480	8531	\begin{align*} x^{4} y^{\prime \prime }+\lambda y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.211
2481	10880	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.211
2482	11099	\begin{align*} y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.211
2483	11105	\begin{align*} y^{\prime \prime }+y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.211
2484	11192	\begin{align*} \left (-x +3\right ) y-x \left (4-x \right ) y^{\prime }+2 \left (2-x \right ) x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.211
2485	15188	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.211
2486	17628	\begin{align*} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.211
2487	18750	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.211
2488	21197	\begin{align*} x^{\prime \prime \prime \prime }+3 x^{\prime \prime \prime }+2 x^{\prime \prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.211
2489	21316	\begin{align*} x^{\prime }&=-x+y+y^{2} \\ y^{\prime }&=-2 y-x^{2} \\ \end{align*}	✗	✗	✗	✗	0.211
2490	21960	\begin{align*} b^{\left (7\right )}&=3 p \\ \end{align*}	✓	✓	✓	✓	0.211
2491	23391	\begin{align*} x^{5} y^{\left (5\right )}-2 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.211
2492	278	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.212
2493	410	\begin{align*} y^{\prime \prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.212
2494	2671	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.212
2495	10899	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.212
2496	10959	\begin{align*} 2 y^{\prime \prime }+5 y^{\prime } x +\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.212
2497	11036	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.212
2498	11233	\begin{align*} y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.212
2499	11240	\begin{align*} y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.212
2500	17625	\begin{align*} x^{3} y^{\prime \prime \prime }+22 x^{2} y^{\prime \prime }+124 y^{\prime } x +140 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.212