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	16449	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.086
1302	17208	\begin{align*} y^{2}+2 t y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.086
1303	18462	\begin{align*} x^{\prime \prime }&=1 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.086
1304	19754	\begin{align*} y^{\prime \prime \prime \prime }-a^{4} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.086
1305	20193	\begin{align*} y^{\prime \prime } x -\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.086
1306	23952	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.086
1307	25632	\begin{align*} y^{\prime \prime }&={\mathrm e}^{a t} \\ y \left (0\right ) &= A \\ y^{\prime }\left (0\right ) &= B \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.086
1308	7241	\begin{align*} x^{\prime }+x-{\mathrm e}^{y}&=0 \\ \end{align*}	✓	✓	✓	✓	0.087
1309	7273	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.087
1310	9283	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.087
1311	10496	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.087
1312	10499	\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*}	✓	✓	✓	✗	0.087
1313	15099	\begin{align*} x^{3} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.087
1314	18167	\begin{align*} y^{\prime \prime \prime \prime }-y&=1 \\ \end{align*}	✓	✓	✓	✓	0.087
1315	18186	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.087
1316	19273	\begin{align*} 2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.087
1317	21188	\begin{align*} x^{\prime \prime \prime \prime }-x^{\prime \prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.087
1318	22243	\begin{align*} y^{\prime }+5 y&=0 \\ y \left (1\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.087
1319	22509	\begin{align*} \left (y^{2}+2 y x \right ) \left (x^{2}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.087
1320	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*}	✓	✓	✓	✓	0.088
1321	332	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=3 x -1 \\ \end{align*}	✓	✓	✓	✓	0.088
1322	1468	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.088
1323	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*}	✓	✓	✓	✓	0.088
1324	3928	\begin{align*} y+y^{\prime }&=8 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.088
1325	7614	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.088
1326	9107	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.088
1327	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*}	✗	✓	✓	✗	0.088
1328	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*}	✓	✓	✓	✓	0.088
1329	16447	\begin{align*} x^{2} y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.088
1330	18751	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.088
1331	18972	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.088
1332	19784	\begin{align*} y^{2} y^{\prime \prime \prime }-\left (3 y^{\prime } y+2 x y^{2}\right ) y^{\prime \prime }+\left (2 {y^{\prime }}^{2}+2 x y^{\prime } y+3 y^{2} x^{2}\right ) y^{\prime }+x^{3} y^{3}&=0 \\ \end{align*}	✗	✓	✗	✗	0.088
1333	21573	\begin{align*} y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+54 y^{\prime \prime }+108 y^{\prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.088
1334	21959	\begin{align*} {y^{\prime \prime }}^{{3}/{2}}+y&=x \\ \end{align*}	✗	✓	✓	✗	0.088
1335	23992	\begin{align*} y^{\prime \prime \prime }-y&=1 \\ \end{align*}	✓	✓	✓	✓	0.088
1336	24036	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.088
1337	24429	\begin{align*} 4 y^{\prime \prime \prime \prime }-45 y^{\prime \prime }-70 y^{\prime }-24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.088
1338	24634	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=2 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.088
1339	460	\begin{align*} 3 x^{3} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.089
1340	746	\begin{align*} \left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.089
1341	928	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.089
1342	931	\begin{align*} \left (x +1\right ) y^{\prime \prime }-\left (2+x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.089
1343	1730	\begin{align*} y^{4} x^{4}+x^{5} y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.089
1344	3615	\begin{align*} 2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right )&=4 \cos \left (x \right )^{4} \\ \end{align*}	✓	✓	✓	✓	0.089
1345	3622	\begin{align*} y^{\prime }+\alpha y&={\mathrm e}^{\beta x} \\ \end{align*}	✓	✓	✓	✓	0.089
1346	4253	\begin{align*} y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.089
1347	6627	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.089
1348	6652	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=x \\ \end{align*}	✓	✓	✓	✓	0.089
1349	7182	\begin{align*} x^{3} y^{\prime \prime }-\left (2 x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.089
1350	7231	\begin{align*} y^{\prime }+2 y x -x \,{\mathrm e}^{-x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.089
1351	10491	\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*}	✓	✓	✓	✗	0.089
1352	10498	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.089
1353	15196	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.089
1354	15262	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=5 \\ \end{align*}	✓	✓	✓	✓	0.089
1355	16173	\begin{align*} y^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.089
1356	17560	\begin{align*} y^{\left (6\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.089
1357	19528	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.089
1358	21183	\begin{align*} x^{\prime \prime \prime }+x^{\prime \prime }-2 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.089
1359	21195	\begin{align*} x^{\left (6\right )}-x^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.089
1360	22651	\begin{align*} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.089
1361	24467	\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+3 y^{\prime }-9 y&=0 \\ y \left (0\right ) &= -1 \\ y \left (1\right ) &= 0 \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.089
1362	24612	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.089
1363	24778	\begin{align*} x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.089
1364	2133	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.090
1365	3101	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.090
1366	3785	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.090
1367	3786	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}+4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.090
1368	7073	\begin{align*} 3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.090
1369	9287	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.090
1370	11219	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.090
1371	11232	\begin{align*} x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.090
1372	14612	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.090
1373	17199	\begin{align*} y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.090
1374	18467	\begin{align*} x^{\prime \prime }+x&=t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.090
1375	18588	\begin{align*} \frac {y^{\prime }}{-\sin \left (y\right )+\frac {x}{y}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.090
1376	18900	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.090
1377	19532	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.090
1378	23762	\begin{align*} y^{\prime \prime }&=0 \\ y \left (0\right ) &= \operatorname {c1} \\ y \left (L \right ) &= \operatorname {c2} \\ \end{align*}	✓	✓	✓	✓	0.090
1379	25153	\begin{align*} y^{\left (6\right )}+27 y^{\prime \prime \prime \prime }+243 y^{\prime \prime }+729 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.090
1380	1475	\begin{align*} y^{\left (6\right )}+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.091
1381	1680	\begin{align*} 6 y^{2} x^{2}+4 x^{3} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.091
1382	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*}	✓	✓	✓	✓	0.091
1383	6693	\begin{align*} -y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.091
1384	7327	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.091
1385	9102	\begin{align*} y^{\prime }+y&=\frac {1}{{\mathrm e}^{2 x}+1} \\ \end{align*}	✓	✓	✓	✓	0.091
1386	9392	\begin{align*} x^{4} y^{\prime \prime }+y \sin \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.091
1387	10802	\begin{align*} y^{\prime \prime } x +\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.091
1388	10912	\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*}	✓	✓	✓	✗	0.091
1389	11248	\begin{align*} u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u&=0 \\ \end{align*}	✓	✓	✓	✗	0.091
1390	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*}	✓	✓	✓	✗	0.091
1391	18749	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.091
1392	19540	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.091
1393	20090	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.091
1394	21954	\begin{align*} {y^{\prime \prime }}^{2}-3 y^{\prime } y+y x&=0 \\ \end{align*}	✗	✗	✗	✗	0.091
1395	22242	\begin{align*} y^{\prime }+2 y&=0 \\ y \left (1\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.091
1396	24622	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=9 \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.091
1397	24664	\begin{align*} y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y&=36 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.091
1398	25088	\begin{align*} y^{\prime \prime \prime }+y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.091
1399	25251	\begin{align*} 4 t^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.091
1400	2129	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 14 \\ y^{\prime \prime }\left (0\right ) &= -40 \\ \end{align*}	✓	✓	✓	✓	0.092