2.3.14 Problems 1301 to 1400

Table 2.601: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1301	18982	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }-4 y^{\prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1302	19446	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1303	20078	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.115
1304	20104	\begin{align*} -8 y+7 x y^{\prime }-3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1305	20106	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1306	20356	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.115
1307	21231	\begin{align*} x^{\prime \prime \prime }-2 x^{\prime \prime }+3 x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1308	21502	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.115
1309	23480	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.115
1310	23486	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.115
1311	26482	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.115
1312	26520	\begin{align*} y^{\prime \prime \prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.115
1313	26826	\begin{align*} x^{\prime \prime }+6 x^{\prime }&=t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= -{\frac {1}{36}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.115
1314	253	\begin{align*} y^{\prime \prime \prime }+9 y^{\prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.116
1315	859	\begin{align*} y^{\prime \prime }&=\left (-2+2 i \sqrt {3}\right ) y \\ \end{align*}	✓	✓	✓	✓	0.116
1316	11102	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.116
1317	14587	\begin{align*} 4 y^{\prime \prime \prime }+4 y^{\prime \prime }-7 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.116
1318	21202	\begin{align*} x^{\prime \prime \prime \prime }-3 x^{\prime \prime \prime }+2 x^{\prime }-5 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.116
1319	26521	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.116
1320	958	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.117
1321	960	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.117
1322	2135	\begin{align*} 8 y^{\prime \prime \prime }-4 y^{\prime \prime }-2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -3 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.117
1323	6793	\begin{align*} y^{2}-\left (1-2 y x \right ) y^{\prime }+x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=f \left (x \right ) \\ \end{align*}	✗	✗	✗	✗	0.117
1324	10854	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.117
1325	10911	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.117
1326	14093	\begin{align*} -y-2 y^{\prime }+2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.117
1327	14586	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.117
1328	15069	\begin{align*} y^{\prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.117
1329	17548	\begin{align*} 5 y^{\prime \prime \prime }-15 y^{\prime }+11 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.117
1330	17561	\begin{align*} y^{\left (6\right )}+12 y^{\prime \prime \prime \prime }+48 y^{\prime \prime }+64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.117
1331	22117	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.117
1332	24036	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.117
1333	959	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.118
1334	3117	\begin{align*} y^{\prime \prime \prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.118
1335	3194	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&={\mathrm e}^{2 x} \left (x -3\right ) \\ \end{align*}	✓	✓	✓	✓	0.118
1336	6674	\begin{align*} y-x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime }&=-x^{2}+1 \\ \end{align*}	✗	✓	✓	✗	0.118
1337	6680	\begin{align*} 3 y x +y^{\prime } \left (x^{2}+2\right )+4 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=f \left (x \right ) \\ \end{align*}	✗	✓	✓	✗	0.118
1338	6713	\begin{align*} -8 y+3 \left (x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right )^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.118
1339	10870	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.118
1340	10895	\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*}	✓	✓	✓	✗	0.118
1341	10918	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.118
1342	20359	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.118
1343	21881	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+42 y^{\prime \prime }-104 y^{\prime }+169 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.118
1344	24438	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -7 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.118
1345	24461	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 9 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.118
1346	25153	\begin{align*} y^{\left (6\right )}+27 y^{\prime \prime \prime \prime }+243 y^{\prime \prime }+729 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.118
1347	268	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.119
1348	935	\begin{align*} 5 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.119
1349	2138	\begin{align*} 4 y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.119
1350	6619	\begin{align*} y^{\prime \prime \prime }&=a^{2} y \\ \end{align*}	✓	✓	✓	✓	0.119
1351	6683	\begin{align*} a \,x^{2} y+6 y^{\prime }+6 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.119
1352	6794	\begin{align*} \left (1-y\right ) y^{\prime }+{y^{\prime }}^{2} x -x \left (1-y\right ) y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.119
1353	10802	\begin{align*} x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.119
1354	11248	\begin{align*} u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u&=0 \\ \end{align*}	✓	✓	✓	✗	0.119
1355	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 (a -1\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 \left (a -1\right ) a -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*}	✗	✓	✓	✗	0.119
1356	18135	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+10 y^{\prime \prime }+12 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.119
1357	20081	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime }-6 y&={\mathrm e}^{2 x} \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✓	0.119
1358	22671	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.119
1359	23404	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.119
1360	23430	\begin{align*} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.119
1361	24463	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+2 y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= -5 \\ y^{\prime \prime \prime }\left (0\right ) &= 9 \\ \end{align*}	✓	✓	✓	✓	0.119
1362	6751	\begin{align*} y^{2}-2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x^{3} \\ \end{align*}	✗	✗	✗	✗	0.120
1363	10787	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.120
1364	10921	\begin{align*} x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.120
1365	15398	\begin{align*} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.120
1366	16480	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 8 \\ y^{\prime \prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.120
1367	19444	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.120
1368	20079	\begin{align*} y^{\prime \prime \prime \prime }-y&={\mathrm e}^{x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.120
1369	20083	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.120
1370	20139	\begin{align*} y^{\left (5\right )}-m^{2} y^{\prime \prime \prime }&={\mathrm e}^{a x} \\ \end{align*}	✓	✓	✓	✓	0.120
1371	26544	\begin{align*} 5 y^{\prime \prime \prime }-7 y^{\prime \prime }-3&=0 \\ \end{align*}	✓	✓	✓	✓	0.120
1372	1325	\begin{align*} x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.121
1373	3123	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&=x^{2}+8 \\ \end{align*}	✓	✓	✓	✓	0.121
1374	3170	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.121
1375	3191	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime }&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.121
1376	6660	\begin{align*} -8 a x y-2 \left (-4 x^{2}-2 a +1\right ) y^{\prime }-6 x y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.121
1377	6666	\begin{align*} f \left (x \right ) y+y^{\prime }+f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.121
1378	7191	\begin{align*} 2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x}&=\sqrt {x} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.121
1379	8923	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.121
1380	9361	\begin{align*} x^{2} y^{\prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.121
1381	10733	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.121
1382	10810	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.121
1383	11078	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.121
1384	14095	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.121
1385	15420	\begin{align*} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.121
1386	19449	\begin{align*} y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1}&=0 \\ \end{align*}	✓	✓	✓	✗	0.121
1387	22128	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.121
1388	23429	\begin{align*} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.121
1389	25918	\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.121
1390	25921	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-9 y^{\prime \prime }+8 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.121
1391	26441	\begin{align*} y^{\prime \prime \prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.121
1392	265	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.122
1393	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*}	✓	✓	✓	✓	0.122
1394	4142	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.122
1395	6750	\begin{align*} y^{2}-2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.122
1396	7169	\begin{align*} x^{4} y^{\prime \prime }+x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.122
1397	7989	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&=5 \\ \end{align*}	✓	✓	✓	✓	0.122
1398	10012	\begin{align*} \frac {y^{\prime }}{x +y}&=0 \\ \end{align*}	✓	✓	✓	✓	0.122
1399	10492	\begin{align*} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.122
1400	10710	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.122