2.3.23 Problems 2201 to 2300

Table 2.589: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2201	18002	\begin{align*} x&={y^{\prime }}^{2}-2 y^{\prime }+2 \\ \end{align*}	✓	✓	✓	✓	0.161
2202	18315	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=5 x^{4} \\ \end{align*}	✓	✓	✓	✓	0.161
2203	18622	\begin{align*} 5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.161
2204	18745	\begin{align*} a y^{\prime \prime }+b y^{\prime }+\frac {b^{2} y}{4 a}&=0 \\ \end{align*}	✓	✓	✓	✓	0.161
2205	20332	\begin{align*} 9 x^{\prime \prime }+18 x^{\prime }-16 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.161
2206	20922	\begin{align*} x^{\prime }&=-4 x-y+{\mathrm e}^{-t} \\ y^{\prime }&=x-2 y+2 \,{\mathrm e}^{-3 t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.161
2207	22151	\begin{align*} y^{\prime \prime \prime \prime }&=5 x \\ \end{align*}	✓	✓	✓	✓	0.161
2208	24010	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.161
2209	1781	\begin{align*} 4 x^{2} \sin \left (x \right ) y^{\prime \prime }-4 x \left (\sin \left (x \right )+\cos \left (x \right ) x \right ) y^{\prime }+\left (2 \cos \left (x \right ) x +3 \sin \left (x \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.162
2210	6669	\begin{align*} 18 \,{\mathrm e}^{x}-3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.162
2211	8958	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.162
2212	10593	\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*}	✓	✓	✓	✗	0.162
2213	10601	\begin{align*} 4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.162
2214	10681	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.162
2215	10731	\begin{align*} 4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.162
2216	11118	\begin{align*} x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.162
2217	11123	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.162
2218	11237	\begin{align*} 3 t \left (1+t \right ) y^{\prime \prime }+y^{\prime } t -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.162
2219	11287	\begin{align*} y^{\prime \prime }+\frac {y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.162
2220	15205	\begin{align*} y^{\prime \prime \prime }+8 y^{\prime \prime }+16 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -8 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.162
2221	16663	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=32 x \\ \end{align*}	✓	✓	✓	✓	0.162
2222	20170	\begin{align*} y^{\prime \prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.162
2223	21290	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-x-4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	0.162
2224	21550	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.162
2225	24617	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=6 x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.162
2226	24618	\begin{align*} y^{\prime \prime \prime }+12 y^{\prime \prime }+48 y^{\prime }+64 y&=8 x \,{\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.162
2227	25930	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.162
2228	3059	\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.163
2229	8626	\begin{align*} y^{\prime \prime }-\frac {y}{4}&=0 \\ y \left (0\right ) &= 12 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.163
2230	9104	\begin{align*} 2 y-x^{3}&=y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	0.163
2231	10661	\begin{align*} 2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.163
2232	10703	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.163
2233	10770	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.163
2234	10878	\begin{align*} t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.163
2235	11095	\begin{align*} 4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.163
2236	11275	\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}	✓	✓	✓	✗	0.163
2237	18985	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.163
2238	19838	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x \\ \end{align*}	✓	✓	✓	✓	0.163
2239	21306	\begin{align*} x^{\prime \prime \prime }+a x^{\prime \prime }+b x^{\prime }+c x&=0 \\ \end{align*}	✓	✓	✓	✓	0.163
2240	22132	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=2 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.163
2241	350	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=x^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.164
2242	1305	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.164
2243	1462	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y&=t \\ \end{align*}	✓	✓	✓	✓	0.164
2244	2714	\begin{align*} y^{\prime \prime \prime \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 ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.164
2245	6024	\begin{align*} \left (b +c \,x^{2 k}\right ) y+a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.164
2246	6693	\begin{align*} -y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.164
2247	8183	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.164
2248	8830	\begin{align*} y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.164
2249	9310	\begin{align*} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.164
2250	10624	\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*}	✓	✓	✓	✗	0.164
2251	10629	\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.164
2252	10630	\begin{align*} x^{2} y^{\prime \prime }+x \left (2+x \right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.164
2253	10892	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (3+2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.164
2254	10914	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (3+2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.164
2255	11015	\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.164
2256	11085	\begin{align*} t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.164
2257	11089	\begin{align*} t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.164
2258	11090	\begin{align*} t y^{\prime \prime }+y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.164
2259	11103	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.164
2260	14096	\begin{align*} y^{\prime }-y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.164
2261	15212	\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=9 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.164
2262	15223	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=4 \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.164
2263	20612	\begin{align*} y^{\prime \prime }-a x y^{\prime }+a^{2} \left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.164
2264	20761	\begin{align*} \left (x^{2}+x +1\right ) y^{\prime \prime \prime }+\left (3+6 x \right ) y^{\prime \prime }+6 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.164
2265	24664	\begin{align*} y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y&=36 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.164
2266	25158	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.164
2267	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.	✓	✓	✓	✓	0.165
2268	2572	\begin{align*} y^{\prime \prime }-\frac {2 \left (1+t \right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1}&=0 \\ \end{align*}	✓	✓	✓	✗	0.165
2269	3616	\begin{align*} y^{\prime }+\frac {y}{x \ln \left (x \right )}&=9 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.165
2270	3799	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime }&=\sin \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.165
2271	10704	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.165
2272	10707	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.165
2273	10841	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.165
2274	10849	\begin{align*} x^{3} y^{\prime \prime }+y^{\prime }-\frac {y}{x}&=0 \\ \end{align*}	✓	✓	✓	✗	0.165
2275	10967	\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (3+2 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.165
2276	10973	\begin{align*} x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.165
2277	11096	\begin{align*} f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \\ \end{align*}	✓	✓	✓	✗	0.165
2278	11132	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.165
2279	11206	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.165
2280	14422	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.165
2281	14423	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.165
2282	19845	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.165
2283	22029	\begin{align*} y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.165
2284	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*}	✓	✓	✓	✓	0.165
2285	1252	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.166
2286	3341	\begin{align*} y^{\prime }&=\sqrt {y x +1} \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.166
2287	4467	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }&=9 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.166
2288	8184	\begin{align*} 2 y^{\prime \prime }+7 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.166
2289	10582	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.166
2290	11187	\begin{align*} y^{\prime \prime } x +y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.166
2291	11191	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+y^{\prime } x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.166
2292	15314	\begin{align*} y^{\prime \prime } x +y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.166
2293	18131	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.166
2294	18297	\begin{align*} x^{2} y^{\prime \prime \prime }&=2 y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.166
2295	19558	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime }+y&=2 x^{3}-3 x^{2}+4 x +5 \\ \end{align*}	✓	✓	✓	✓	0.166
2296	19834	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.166
2297	20331	\begin{align*} y^{\prime \prime }+3 y^{\prime }-54 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.166
2298	24012	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\ \end{align*}	✓	✓	✓	✓	0.166
2299	534	\begin{align*} x^{\prime \prime }+x&=\sin \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.167
2300	2206	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&={\mathrm e}^{2 x} \left (10+3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.167