2.3.13 Problems 1201 to 1300

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

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1201	249	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.109
1202	1322	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.109
1203	3156	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.109
1204	6662	\begin{align*} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.109
1205	6678	\begin{align*} a \,x^{2} y-6 y^{\prime }+x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.109
1206	6795	\begin{align*} y^{3} y^{\prime }-y^{\prime } y^{\prime \prime }+y y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.109
1207	6799	\begin{align*} 15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.109
1208	6800	\begin{align*} 40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.109
1209	7326	\begin{align*} \left (2-x \right ) x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.109
1210	10851	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.109
1211	10874	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.109
1212	10919	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.109
1213	11263	\begin{align*} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.109
1214	11273	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.109
1215	11277	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.109
1216	14422	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.109
1217	16420	\begin{align*} y^{\prime \prime \prime }&=y^{\prime \prime } \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= 5 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.109
1218	17421	\begin{align*} {y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2}&=0 \\ \end{align*}	✗	✓	✗	✗	0.109
1219	20052	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.109
1220	20355	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2&=0 \\ \end{align*}	✓	✓	✓	✓	0.109
1221	22116	\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.109
1222	26524	\begin{align*} y^{\prime \prime \prime \prime }-y&=1 \\ \end{align*}	✓	✓	✓	✓	0.109
1223	4451	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.110
1224	10819	\begin{align*} u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u&=0 \\ \end{align*}	✓	✓	✓	✗	0.110
1225	10843	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.110
1226	10893	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.110
1227	11164	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.110
1228	14579	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.110
1229	15498	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+12 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.110
1230	16539	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 13 \\ y^{\prime \prime }\left (0\right ) &= 86 \\ \end{align*}	✓	✓	✓	✓	0.110
1231	20770	\begin{align*} y^{\prime \prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.110
1232	23264	\begin{align*} y^{\prime \prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.110
1233	23519	\begin{align*} e i u^{\prime \prime \prime \prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.110
1234	24466	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }&=0 \\ y \left (0\right ) &= -3 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 12 \\ \end{align*}	✓	✓	✓	✓	0.110
1235	311	\begin{align*} y^{\prime \prime }&=\left (-2+2 i \sqrt {3}\right ) y \\ \end{align*}	✓	✓	✓	✓	0.111
1236	2134	\begin{align*} 2 y^{\prime \prime \prime }-11 y^{\prime \prime }+12 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= 13 \\ \end{align*}	✓	✓	✓	✓	0.111
1237	4453	\begin{align*} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.111
1238	6620	\begin{align*} y+2 x y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.111
1239	6791	\begin{align*} -y y^{\prime }+{y^{\prime }}^{2}+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.111
1240	10917	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.111
1241	10920	\begin{align*} x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.111
1242	11140	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.111
1243	14091	\begin{align*} 4 y^{\prime \prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.111
1244	15691	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ y^{\prime \prime \prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.111
1245	25916	\begin{align*} y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.111
1246	246	\begin{align*} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.112
1247	264	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.112
1248	266	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.112
1249	492	\begin{align*} x^{3} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.112
1250	955	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+100 y^{\prime }-500 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 10 \\ y^{\prime \prime }\left (0\right ) &= 250 \\ \end{align*}	✓	✓	✓	✓	0.112
1251	1326	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.112
1252	6621	\begin{align*} a y+2 a x y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.112
1253	6687	\begin{align*} -2 y x +y^{\prime } \left (x^{2}+2\right )-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.112
1254	7330	\begin{align*} x^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.112
1255	11247	\begin{align*} u^{\prime \prime }+2 u^{\prime }+u&=0 \\ \end{align*}	✓	✓	✓	✓	0.112
1256	11250	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.112
1257	12792	\begin{align*} 4 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+11 y^{\prime \prime }-3 y^{\prime }-4 \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.112
1258	14564	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.112
1259	21312	\begin{align*} x^{\prime \prime \prime \prime }+8 x^{\prime \prime \prime }+23 x^{\prime \prime }+2 x^{\prime }+12 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.112
1260	23992	\begin{align*} y^{\prime \prime \prime }-y&=1 \\ \end{align*}	✓	✓	✓	✓	0.112
1261	25542	\begin{align*} y^{\left (8\right )}&=y \\ \end{align*}	✓	✓	✓	✓	0.112
1262	25689	\begin{align*} y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }+158 y^{\prime \prime }-580 y^{\prime }+841 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.112
1263	267	\begin{align*} \left (x +1\right ) y^{\prime \prime }-\left (x +2\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.113
1264	1321	\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.113
1265	6607	\begin{align*} a y+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.113
1266	6798	\begin{align*} 2 {y^{\prime }}^{3}+3 y^{\prime \prime }+6 y y^{\prime } y^{\prime \prime }+\left (x +y^{2}\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.113
1267	7616	\begin{align*} 3 y^{\prime \prime \prime }+18 y^{\prime \prime }+13 y^{\prime }-19 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.113
1268	10842	\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.113
1269	10906	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.113
1270	10922	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.113
1271	10924	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.113
1272	11219	\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.113
1273	11270	\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.113
1274	14578	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.113
1275	17560	\begin{align*} y^{\left (6\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.113
1276	18138	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.113
1277	3511	\begin{align*} y^{\prime \prime }+\frac {y}{z^{3}}&=0 \\ \end{align*} Series expansion around \(z=0\).	✗	✗	✓	✗	0.114
1278	7331	\begin{align*} x \left (x +1\right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.114
1279	9300	\begin{align*} a^{4} y+2 a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.114
1280	10817	\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.114
1281	11230	\begin{align*} x y^{\prime \prime }+2 y^{\prime }+4 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.114
1282	11246	\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.114
1283	11301	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.114
1284	12535	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.114
1285	19450	\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.114
1286	23521	\begin{align*} e i u^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.114
1287	25919	\begin{align*} y^{\prime \prime \prime \prime }-10 y^{\prime \prime \prime }+24 y^{\prime \prime }+10 y^{\prime }-25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.114
1288	25929	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.114
1289	962	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1290	4149	\begin{align*} y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1291	6622	\begin{align*} f^{\prime }\left (x \right ) y+2 f \left (x \right ) y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.115
1292	9305	\begin{align*} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+48 y^{\prime \prime }+16 y^{\prime }-96 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1293	10739	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1294	10888	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1295	11100	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1296	11232	\begin{align*} x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1297	11278	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.115
1298	12818	\begin{align*} y^{\prime \prime \prime \prime } \sin \left (x \right )^{4}+2 y^{\prime \prime \prime } \sin \left (x \right )^{3} \cos \left (x \right )+y^{\prime \prime } \sin \left (x \right )^{2} \left (\sin \left (x \right )^{2}-3\right )+y^{\prime } \sin \left (x \right ) \cos \left (x \right ) \left (2 \sin \left (x \right )^{2}+3\right )+\left (a^{4} \sin \left (x \right )^{4}-3\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.115
1299	14590	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1300	17568	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= 4 \\ y^{\prime \prime \prime }\left (0\right ) &= -24 \\ \end{align*}	✓	✓	✓	✓	0.115