2.3.23 Problems 2201 to 2300

Table 2.619: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2201	17734	\begin{align*} \left (t +1\right )^{2} y^{\prime \prime }-2 \left (t +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.192
2202	23095	\begin{align*} x^{\prime }+2 x+y^{\prime }+y&={\mathrm e}^{-3 t} \\ 5 x+y^{\prime }+3 y&=5 \,{\mathrm e}^{-t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.192
2203	340	\begin{align*} y^{\left (5\right )}+2 y^{\prime \prime \prime }+2 y^{\prime \prime }&=3 x^{2}-1 \\ \end{align*}	✓	✓	✓	✓	0.193
2204	356	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime }&=x^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ y^{\prime \prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.193
2205	2183	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-8 y^{\prime }-8 y&={\mathrm e}^{x} \left (8 \cos \left (x \right )+16 \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.193
2206	10348	\begin{align*} x y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✗	✗	0.193
2207	10539	\begin{align*} 2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.193
2208	10828	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.193
2209	10832	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.193
2210	13183	\(\left [\begin {array}{cc} 11 & 9 \\ -16 & -13 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.193
2211	16593	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=1 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.193
2212	26576	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x}-1 \\ \end{align*}	✓	✓	✓	✓	0.193
2213	2148	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{-3 x} \left (6 x^{2}-23 x +32\right ) \\ \end{align*}	✓	✓	✓	✓	0.194
2214	2313	\begin{align*} \frac {y}{t}+y^{\prime }&=\frac {1}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	0.194
2215	4477	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime }&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.194
2216	6742	\begin{align*} 27 y-12 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2217	6752	\begin{align*} -y-2 y^{\prime }+2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2218	8637	\begin{align*} 9 y^{\prime \prime }-6 y^{\prime }+y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.194
2219	10834	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
2220	10959	\begin{align*} 2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
2221	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*}	✓	✓	✓	✗	0.194
2222	11286	\begin{align*} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
2223	16582	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2224	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*}	✓	✓	✓	✓	0.194
2225	17581	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.194
2226	23092	\begin{align*} x^{\prime }+y&=4 \\ x-y^{\prime }&=3 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.194
2227	23636	\begin{align*} y^{\prime \prime }-y&=6 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.194
2228	24617	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=6 x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.194
2229	24622	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=9 \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.194
2230	26813	\begin{align*} x^{\prime }-3 x&=3 t^{3}+3 t^{2}+2 t +1 \\ x \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.194
2231	27624	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
2232	9104	\begin{align*} 2 y-x^{3}&=x y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.195
2233	9280	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
2234	10762	\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*}	✓	✓	✓	✗	0.195
2235	10773	\begin{align*} 2 y-x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.195
2236	11000	\begin{align*} 4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.195
2237	11233	\begin{align*} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.195
2238	11240	\begin{align*} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.195
2239	15706	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=-x^{2}+1 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.195
2240	27050	\begin{align*} x^{\prime }-x+2 y^{\prime }&=0 \\ 4 x^{\prime }+3 y^{\prime }+y&=-6 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.195
2241	10557	\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*}	✓	✓	✓	✗	0.196
2242	10663	\begin{align*} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.196
2243	10830	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.196
2244	10833	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.196
2245	16581	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 x y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.196
2246	17660	\begin{align*} -y+x y^{\prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.196
2247	555	\begin{align*} t x^{\prime \prime }+\left (t -2\right ) x^{\prime }+x&=0 \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.197
2248	6740	\begin{align*} -4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2249	6761	\begin{align*} -3 y^{\prime }+11 y^{\prime \prime }-12 y^{\prime \prime \prime }+4 y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2250	8804	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=4 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.197
2251	10535	\begin{align*} \left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
2252	10886	\begin{align*} y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
2253	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*}	✓	✓	✓	✗	0.197
2254	10999	\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*}	✓	✓	✓	✗	0.197
2255	15704	\begin{align*} y^{\prime \prime }+9 y&=x +2 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.197
2256	16583	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2257	16667	\begin{align*} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.197
2258	16790	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.197
2259	21550	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.197
2260	22670	\begin{align*} y^{\left (6\right )}-4 y^{\prime \prime }+4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
2261	27021	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.197
2262	2191	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+8 y^{\prime \prime }+8 y^{\prime }+4 y&=-2 \,{\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.198
2263	2725	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=t +{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.198
2264	6658	\begin{align*} y^{\prime \prime \prime }&=a y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.198
2265	10884	\begin{align*} y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.198
2266	11099	\begin{align*} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.198
2267	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*}	✓	✓	✓	✗	0.198
2268	21892	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.198
2269	24555	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y&=3 \,{\mathrm e}^{-x}-4 x -6 \\ \end{align*}	✓	✓	✓	✓	0.198
2270	25163	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.198
2271	6788	\begin{align*} y^{\left (8\right )}&=y \\ \end{align*}	✓	✓	✓	✓	0.199
2272	7213	\begin{align*} y^{\prime \prime }+\frac {y}{4 x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.199
2273	9100	\begin{align*} y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.199
2274	10831	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.199
2275	10996	\begin{align*} 28 x^{2} \left (-3 x +1\right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.199
2276	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*}	✓	✓	✓	✗	0.199
2277	21582	\begin{align*} y^{\prime \prime \prime }+y^{\prime }+y&=\sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.199
2278	21583	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+3 y^{\prime }+9 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.199
2279	24618	\begin{align*} y^{\prime \prime \prime }+12 y^{\prime \prime }+48 y^{\prime }+64 y&=8 x \,{\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.199
2280	27043	\begin{align*} x^{\prime }+2 y^{\prime }-y&=1 \\ 2 x^{\prime }+y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.199
2281	27744	\begin{align*} x y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.199
2282	368	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=2 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.200
2283	491	\begin{align*} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.200
2284	2168	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&={\mathrm e}^{x} \left (-3 x^{2}+x +3\right ) \\ \end{align*}	✓	✓	✓	✓	0.200
2285	6757	\begin{align*} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.200
2286	7833	\begin{align*} x^{\prime \prime }+4 x^{\prime }+4 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.200
2287	8499	\begin{align*} x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.200
2288	10580	\begin{align*} 4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.200
2289	11038	\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*}	✓	✓	✓	✗	0.200
2290	11228	\begin{align*} x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.200
2291	16673	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=5 x^{5} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.200
2292	19628	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= \operatorname {yd}_{0} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.200
2293	21882	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=2 x^{2}-3 x -17 \\ \end{align*}	✓	✓	✓	✓	0.200
2294	23634	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.200
2295	25158	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.200
2296	4470	\begin{align*} y^{\prime \prime \prime \prime }+16 y&=64 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.201
2297	8165	\begin{align*} \left (-x +y\right ) y^{\prime }&=-x +y \\ \end{align*}	✓	✓	✓	✓	0.201
2298	10764	\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*}	✓	✓	✓	✗	0.201
2299	11185	\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*}	✓	✓	✓	✗	0.201
2300	11257	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.201