2.3.14 Problems 1301 to 1400

Table 2.559: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1301	7327	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.097
1302	9103	\begin{align*} y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.097
1303	10843	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.097
1304	10877	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.097
1305	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*}	✓	✓	✓	✗	0.097
1306	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*}	✓	✓	✓	✗	0.097
1307	11250	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.097
1308	15702	\begin{align*} y^{\prime }-y&=2 \,{\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.097
1309	19547	\begin{align*} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.097
1310	22161	\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*}	✓	✓	✓	✓	0.097
1311	22670	\begin{align*} y^{\left (6\right )}-4 y^{\prime \prime }+4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.097
1312	23145	\begin{align*} y y^{\prime }&=x^{3} y^{2}+x y^{2} \\ \end{align*}	✓	✓	✓	✓	0.097
1313	24454	\begin{align*} 27 y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+8 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.097
1314	321	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.098
1315	8532	\begin{align*} x^{3} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.098
1316	10653	\begin{align*} y^{\prime \prime }-4 y^{\prime } t +\left (4 t^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.098
1317	10713	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.098
1318	10916	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.098
1319	11271	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.098
1320	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*}	✓	✓	✓	✗	0.098
1321	14097	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.098
1322	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*}	✓	✓	✓	✓	0.098
1323	16551	\begin{align*} y^{\left (6\right )}+16 y^{\prime \prime \prime }+64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.098
1324	17545	\begin{align*} 3 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.098
1325	18163	\begin{align*} y^{\prime \prime \prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.098
1326	18751	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.098
1327	19186	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.098
1328	19569	\begin{align*} y^{\prime \prime \prime }-8 y&=16 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.098
1329	24429	\begin{align*} 4 y^{\prime \prime \prime \prime }-45 y^{\prime \prime }-70 y^{\prime }-24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.098
1330	24485	\begin{align*} 2 y^{\prime \prime \prime }-y^{\prime \prime }+36 y^{\prime }-18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.098
1331	341	\begin{align*} y^{\prime \prime \prime }-y&={\mathrm e}^{x}+7 \\ \end{align*}	✓	✓	✓	✓	0.099
1332	961	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1333	1730	\begin{align*} y^{4} x^{4}+x^{5} y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1334	2575	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.099
1335	3086	\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1336	9292	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1337	10873	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1338	10890	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1339	10901	\begin{align*} y^{\prime \prime } x +\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.099
1340	10902	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1341	11219	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1342	12813	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a \right ) x^{3} y^{\prime \prime \prime }+\left (4 x^{2 c} b^{2} c^{2}+6 \left (-1+a \right )^{2}-2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )+1\right ) x^{2} y^{\prime \prime }+\left (4 \left (3 c -2 a +1\right ) b^{2} c^{2} x^{2 c}+\left (2 a -1\right ) \left (2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )-2 a \left (-1+a \right )-1\right )\right ) x y^{\prime }+\left (4 \left (a -c \right ) \left (a -2 c \right ) b^{2} c^{2} x^{2 c}+\left (c \mu +c \nu +a \right ) \left (c \mu +c \nu -a \right ) \left (c \mu -c \nu +a \right ) \left (c \mu -c \nu -a \right )\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.099
1343	15708	\begin{align*} y^{\prime }-2 y&=6 \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.099
1344	17208	\begin{align*} y^{2}+2 t y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1345	17547	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1346	18366	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ y \left (0\right ) &= -1 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.099
1347	18749	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.099
1348	20053	\begin{align*} y^{\prime \prime \prime }+8 y&=x^{4}+2 x +1 \\ \end{align*}	✓	✓	✓	✓	0.099
1349	24425	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1350	24444	\begin{align*} 4 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }-2 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1351	24496	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1352	24500	\begin{align*} 18 y^{\prime \prime \prime }-33 y^{\prime \prime }+20 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1353	24518	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.099
1354	25065	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.099
1355	10540	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.100
1356	11273	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1357	12806	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }+\left (4 n^{2}-1\right ) x y^{\prime }-4 x^{4} y&=0 \\ \end{align*}	✗	✓	✓	✗	0.100
1358	14709	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 y^{\prime } x -8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1359	16547	\begin{align*} y^{\left (6\right )}-2 y^{\prime \prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1360	17544	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1361	17573	\begin{align*} y^{\prime \prime \prime }+9 y^{\prime \prime }+16 y^{\prime }-26 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1362	18188	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }&=-6 \\ \end{align*}	✓	✓	✓	✓	0.100
1363	18972	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1364	19582	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.100
1365	19624	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.100
1366	20090	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.100
1367	24414	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-15 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1368	24417	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1369	24481	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1370	24495	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1371	25344	\begin{align*} t^{2} y^{\prime \prime }+5 y^{\prime } t +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.100
1372	1319	\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1373	2136	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= -2 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.101
1374	3153	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime }&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.101
1375	8008	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=x^{2}+4 x +8 \\ \end{align*}	✓	✓	✓	✓	0.101
1376	10782	\begin{align*} y^{\prime \prime } x +2 y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1377	10783	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1378	10842	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1379	11246	\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.101
1380	14102	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.101
1381	14614	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -8 \\ y^{\prime \prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.101
1382	14710	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-6 y^{\prime } x +18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1383	17745	\begin{align*} 2 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1384	18189	\begin{align*} 3 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.101
1385	18464	\begin{align*} x^{\prime \prime }+x^{\prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.101
1386	19565	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=9 x^{2}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	0.101
1387	20083	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.101
1388	22049	\begin{align*} 2 y x +y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1389	24422	\begin{align*} 10 y^{\prime \prime \prime }+y^{\prime \prime }-7 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1390	24451	\begin{align*} 4 y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }-3 y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1391	24453	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-6 y^{\prime \prime }-28 y^{\prime }-24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1392	24457	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }-6 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.101
1393	313	\begin{align*} y^{\prime \prime \prime \prime }&=y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+2 y \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 15 \\ \end{align*}	✓	✓	✓	✓	0.102
1394	2452	\begin{align*} t^{3} y^{\prime \prime }-y^{\prime } t -\left (t^{2}+\frac {5}{4}\right ) y&=0 \\ \end{align*} Series expansion around \(t=0\).	✗	✗	✓	✗	0.102
1395	3156	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.102
1396	4253	\begin{align*} y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1397	8015	\begin{align*} y^{\prime \prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.102
1398	10801	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+4 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.102
1399	10874	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.102
1400	11216	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.102