2.3.24 Problems 2301 to 2400

Table 2.621: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2301	14111	\begin{align*} y^{\prime \prime \prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.201
2302	17248	\begin{align*} 2 t +2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.201
2303	17629	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.201
2304	19787	\begin{align*} x^{3} v^{\prime \prime \prime }+2 x^{2} v^{\prime \prime }+v&=0 \\ \end{align*}	✓	✓	✓	✓	0.201
2305	21504	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ y^{\prime \prime }\left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.201
2306	21589	\begin{align*} y^{\prime \prime \prime \prime }-y&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.201
2307	26002	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=2 \,{\mathrm e}^{-t} \cos \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.201
2308	27054	\begin{align*} y^{\prime \prime }-16 t y^{\prime }+32 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.201
2309	535	\begin{align*} x^{\prime \prime }+4 x&=\cos \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.202
2310	4489	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=40 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.202
2311	10755	\begin{align*} x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.202
2312	11258	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.202
2313	11260	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.202
2314	14612	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.202
2315	14774	\begin{align*} x^{\prime }+y^{\prime }-x-2 y&=2 \,{\mathrm e}^{t} \\ x^{\prime }+y^{\prime }-3 x-4 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✗	0.202
2316	23638	\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=2 \,{\mathrm e}^{-5 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.202
2317	322	\begin{align*} y^{\prime \prime }+16 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.203
2318	2109	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.203
2319	2315	\begin{align*} \frac {y}{t}+y^{\prime }&=\cos \left (t \right )+\frac {\sin \left (t \right )}{t} \\ \end{align*}	✓	✓	✓	✓	0.203
2320	3610	\begin{align*} y^{\prime }+\frac {2 y}{x}&=5 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.203
2321	6739	\begin{align*} -8 y-2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.203
2322	10494	\begin{align*} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.203
2323	10579	\begin{align*} 3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.203
2324	10826	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.203
2325	10827	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.203
2326	10880	\begin{align*} y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.203
2327	11040	\begin{align*} x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (-3 x +4\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.203
2328	12298	\begin{align*} a \,{\mathrm e}^{b x} y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.203
2329	17586	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-24 y^{\prime }+36 y&=108 t \\ \end{align*}	✓	✓	✓	✓	0.203
2330	18164	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.203
2331	18216	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=x^{2}+x \\ \end{align*}	✓	✓	✓	✓	0.203
2332	25610	\begin{align*} y^{\prime \prime \prime \prime }-y&=t^{3} {\mathrm e}^{5 t} \\ \end{align*}	✓	✓	✓	✓	0.203
2333	536	\begin{align*} x^{\prime \prime }+x&=\cos \left (3 t \right ) \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.204
2334	2147	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=-{\mathrm e}^{x} \left (-24 x^{2}+76 x +4\right ) \\ \end{align*}	✓	✓	✓	✓	0.204
2335	2159	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }-7 y^{\prime }+6 y&=-3 \,{\mathrm e}^{-x} \left (-8 x^{2}+8 x +12\right ) \\ \end{align*}	✓	✓	✓	✓	0.204
2336	8814	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=2 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.204
2337	10618	\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.204
2338	10620	\begin{align*} x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (-3 x +4\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.204
2339	10775	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.204
2340	10938	\begin{align*} y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.204
2341	11104	\begin{align*} y^{\prime \prime }+2 x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.204
2342	11253	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.204
2343	11256	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.204
2344	15697	\begin{align*} y^{\prime \prime }-9 y&=2 \sin \left (3 x \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.204
2345	16148	\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.204
2346	18187	\begin{align*} 5 y^{\prime \prime \prime }-7 y^{\prime \prime }&=3 \\ \end{align*}	✓	✓	✓	✓	0.204
2347	19768	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.204
2348	23386	\begin{align*} 8 y-8 x y^{\prime }+4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.204
2349	24034	\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&={\mathrm e}^{2 x} \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.204
2350	24620	\begin{align*} y^{\prime \prime \prime }-12 y^{\prime \prime }+48 y^{\prime }-64 y&=15 x^{2} {\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.204
2351	26839	\begin{align*} x^{\prime \prime }-4 x^{\prime }+5 x&=2 \,{\mathrm e}^{2 t} \left (\sin \left (t \right )+\cos \left (t \right )\right ) \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.204
2352	539	\begin{align*} x^{\prime \prime }+3 x^{\prime }+2 x&=t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.205
2353	6741	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.205
2354	11254	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.205
2355	11255	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.205
2356	11262	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.205
2357	12738	\begin{align*} \left (2 x -1\right ) y^{\prime \prime \prime }+\left (x +4\right ) y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.205
2358	16803	\begin{align*} y^{\prime \prime }&=\delta \left (-3+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.205
2359	21534	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=4 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.205
2360	26850	\begin{align*} x^{\prime }+y^{\prime }&=y+{\mathrm e}^{t} \\ 2 x^{\prime }+y^{\prime }+2 y&=\cos \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.205
2361	10621	\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*}	✓	✓	✓	✗	0.206
2362	11183	\begin{align*} 2 y-x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.206
2363	12290	\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.206
2364	20901	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=\infty \).	✗	✗	✓	✓	0.206
2365	21282	\begin{align*} x^{\prime \prime }-2 x^{\prime }+x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.206
2366	23996	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+2 y^{\prime }-y&=x^{4}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	0.206
2367	357	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&=1+x \,{\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.207
2368	560	\begin{align*} t x^{\prime \prime }+\left (4 t -2\right ) x^{\prime }+\left (13 t -4\right ) x&=0 \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.207
2369	3334	\begin{align*} y^{\prime }&=\sqrt {1-y} \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.207
2370	3730	\begin{align*} y^{\prime \prime \prime \prime }+104 y^{\prime \prime \prime }+2740 y^{\prime \prime }&=5 \cos \left (3 x \right ) {\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.207
2371	10728	\begin{align*} 2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.207
2372	15701	\begin{align*} y^{\prime }&={\mathrm e}^{x} \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.207
2373	16580	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 x y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.207
2374	18746	\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.207
2375	19996	\begin{align*} {y^{\prime }}^{2}-9 y^{\prime }+18&=0 \\ \end{align*}	✓	✓	✓	✓	0.207
2376	21535	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=2 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.207
2377	23640	\begin{align*} y^{\prime \prime }-9 y^{\prime }+18 y&=54 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.207
2378	24619	\begin{align*} y^{\prime \prime \prime }+9 y^{\prime \prime }+27 y^{\prime }+27 y&=15 x^{2} {\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.207
2379	26602	\begin{align*} y^{\prime \prime \prime \prime }-y&=8 \,{\mathrm e}^{x} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.207
2380	325	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=3 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.208
2381	382	\begin{align*} y^{\prime \prime }+y&=2 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.208
2382	6744	\begin{align*} a^{4} y+2 a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.208
2383	7242	\begin{align*} x^{\prime }&=\frac {3 y^{{2}/{3}}-x}{3 y} \\ \end{align*}	✓	✓	✓	✓	0.208
2384	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*}	✓	✓	✓	✗	0.208
2385	11194	\begin{align*} 4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.208
2386	11261	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.208
2387	12754	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime \prime }+8 x y^{\prime \prime }+10 y^{\prime }-3+\frac {1}{x^{2}}-2 \ln \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.208
2388	16776	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=t^{2} {\mathrm e}^{3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.208
2389	27746	\begin{align*} x y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.208
2390	2110	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.209
2391	2166	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }-4 y&=-{\mathrm e}^{2 x} \left (15 x^{2}+28 x +4\right ) \\ \end{align*}	✓	✓	✓	✓	0.209
2392	2184	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }-4 y&={\mathrm e}^{x} \left (2 \cos \left (2 x \right )-\sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.209
2393	4468	\begin{align*} y^{\left (5\right )}+4 y^{\prime \prime \prime }&=7+x \\ \end{align*}	✓	✓	✓	✓	0.209
2394	11181	\begin{align*} y^{\prime \prime }-x y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.209
2395	12746	\begin{align*} 6 y^{\prime }+6 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.209
2396	18748	\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.209
2397	21203	\begin{align*} t^{3} x^{\prime \prime \prime }+4 t^{2} x^{\prime \prime }+3 x^{\prime } t +x&=0 \\ \end{align*}	✓	✓	✓	✓	0.209
2398	23644	\begin{align*} y^{\prime \prime }+10 y^{\prime }+26 y&=37 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.209
2399	27019	\begin{align*} y^{\prime \prime }+9 y&=t^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.209
2400	367	\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=3 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.210