2.3.16 Problems 1501 to 1600

Table 2.605: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1501	19565	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=9 x^{2}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	0.130
1502	20058	\begin{align*} y^{\prime \prime \prime \prime }+y&=x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.130
1503	20094	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.130
1504	26789	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+\alpha y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.130
1505	3622	\begin{align*} y^{\prime }+\alpha y&={\mathrm e}^{\beta x} \\ \end{align*}	✓	✓	✓	✓	0.131
1506	8050	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.131
1507	13056	\begin{align*} 9 {y^{\prime \prime }}^{2} y^{\left (5\right )}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+40 y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.131
1508	14593	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.131
1509	15419	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.131
1510	19037	\begin{align*} x_{1}^{\prime }&=-x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.131
1511	22126	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+16 y^{\prime }+32 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.131
1512	23407	\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.131
1513	23408	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.131
1514	23410	\begin{align*} x^{2} \left (1-\ln \left (x \right )\right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.131
1515	23426	\begin{align*} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.131
1516	24024	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }&={\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.131
1517	26526	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime }&=3 \\ \end{align*}	✓	✓	✓	✓	0.131
1518	26547	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=1 \\ \end{align*}	✓	✓	✓	✓	0.131
1519	27710	\begin{align*} y^{\prime \prime }-\tan \left (x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.131
1520	308	\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*}	✓	✓	✓	✓	0.132
1521	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 \(x=0\).	✗	✗	✓	✗	0.132
1522	1774	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.132
1523	1779	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.132
1524	2139	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-8 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -2 \\ y^{\prime \prime }\left (0\right ) &= 6 \\ y^{\prime \prime \prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.132
1525	3782	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.132
1526	9292	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.132
1527	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*}	✓	✓	✓	✗	0.132
1528	15424	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.132
1529	16173	\begin{align*} y^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.132
1530	16456	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.132
1531	19165	\begin{align*} y^{\prime \prime \prime }-\frac {3 y^{\prime \prime }}{x}+\frac {6 y^{\prime }}{x^{2}}-\frac {6 y}{x^{3}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.132
1532	19447	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.132
1533	20195	\begin{align*} \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.132
1534	22663	\begin{align*} y^{\left (6\right )}-64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.132
1535	23409	\begin{align*} x y^{\prime \prime }+\left (x -1\right ) y^{\prime }+\left (3-12 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.132
1536	25155	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.132
1537	26529	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.132
1538	26545	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+6&=0 \\ \end{align*}	✓	✓	✓	✓	0.132
1539	26571	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=x^{2}+x \\ \end{align*}	✓	✓	✓	✓	0.132
1540	26824	\begin{align*} x^{\prime \prime }-7 x^{\prime }&=-14 t -5 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 8 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.132
1541	3157	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.133
1542	6769	\begin{align*} -a^{2} y+12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.133
1543	10245	\begin{align*} y^{\prime }&=\frac {1}{x} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.133
1544	10578	\begin{align*} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.133
1545	20613	\begin{align*} \left (2 x^{3}-a \right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.133
1546	22633	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.133
1547	23522	\begin{align*} e i u^{\prime \prime \prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.133
1548	26528	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.133
1549	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*}	✓	✓	✓	✓	0.134
1550	1773	\begin{align*} x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.134
1551	3201	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-2 x} \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.134
1552	6685	\begin{align*} 2 x^{3} y+\left (-2 x^{3}+6\right ) y^{\prime }+x \left (-x^{2}+6\right ) y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.134
1553	19570	\begin{align*} y^{\prime \prime \prime \prime }-y&=-x^{3}+1 \\ \end{align*}	✓	✓	✓	✓	0.134
1554	24521	\begin{align*} y^{\prime \prime \prime }+y^{\prime }+2 y&=5 \\ \end{align*}	✓	✓	✓	✓	0.134
1555	25927	\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }-4 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.134
1556	27093	\(\left [\begin {array}{cc} 0 & 1 \\ 0 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.134
1557	27760	\begin{align*} y^{\prime }&=y^{2}-x \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.134
1558	317	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.135
1559	2137	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+7 y^{\prime \prime }+6 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= -8 \\ y^{\prime \prime }\left (0\right ) &= -14 \\ y^{\prime \prime \prime }\left (0\right ) &= -62 \\ \end{align*}	✓	✓	✓	✓	0.135
1560	3125	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-12 y&=x +{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.135
1561	3128	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.135
1562	3196	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.135
1563	7822	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.135
1564	8015	\begin{align*} y^{\prime \prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.135
1565	14589	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.135
1566	16452	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}-4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.135
1567	16541	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+9 y^{\prime \prime }+9 y^{\prime }&=0 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 6 \\ y^{\prime \prime \prime }\left (0\right ) &= -60 \\ \end{align*}	✓	✓	✓	✓	0.135
1568	19599	\begin{align*} x^{4} y^{\prime \prime }+y \sin \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.135
1569	20164	\begin{align*} y^{\prime \prime \prime }&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.135
1570	22631	\begin{align*} 2 y^{\prime \prime \prime }-5 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.135
1571	23413	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-7 x y^{\prime }+7 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.135
1572	23423	\begin{align*} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.135
1573	23459	\begin{align*} y^{\prime \prime \prime }+y^{\prime }-2 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.135
1574	24023	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=x^{2}-x \\ \end{align*}	✓	✓	✓	✓	0.135
1575	26525	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.135
1576	26829	\begin{align*} x^{\prime \prime }-4 x^{\prime }+4 x&=\left (t -1\right ) {\mathrm e}^{2 t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.135
1577	26830	\begin{align*} 4 x^{\prime \prime }-4 x^{\prime }+x&={\mathrm e}^{\frac {t}{2}} \\ x \left (0\right ) &= -2 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.135
1578	2128	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -2 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.136
1579	14594	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.136
1580	23308	\begin{align*} 6 y^{\prime \prime \prime }-4 i y^{\prime \prime }+\left (3+i\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.136
1581	27784	\begin{align*} y^{\prime }&=4 \mu \left (x +1\right )-y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.136
1582	3787	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.137
1583	8144	\begin{align*} x^{3} y^{\prime \prime }+\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.137
1584	23518	\begin{align*} e i u^{\prime \prime \prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.137
1585	23998	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }&=1+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.137
1586	24037	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.137
1587	25926	\begin{align*} y^{\left (6\right )}+18 y^{\prime \prime \prime \prime }+81 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.137
1588	1775	\begin{align*} x^{2} \ln \left (x \right )^{2} y^{\prime \prime }-2 x \ln \left (x \right ) y^{\prime }+\left (2+\ln \left (x \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.138
1589	3126	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y&={\mathrm e}^{4 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.138
1590	10473	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.138
1591	17012	\begin{align*} y^{\prime \prime \prime \prime }+\frac {25 y^{\prime \prime }}{2}-5 y^{\prime }+\frac {629 y}{16}&=0 \\ 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*}	✓	✓	✓	✓	0.138
1592	17567	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= -7 \\ y^{\prime \prime \prime }\left (0\right ) &= 15 \\ \end{align*}	✓	✓	✓	✓	0.138
1593	17571	\begin{align*} y^{\left (5\right )}+8 y^{\prime \prime \prime \prime }&=0 \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 48 \\ y^{\prime \prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.138
1594	20065	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{2 x}+x^{2}+x \\ \end{align*}	✓	✓	✓	✓	0.138
1595	20486	\begin{align*} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.138
1596	23376	\begin{align*} 2 y-2 x y^{\prime }+3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.138
1597	23489	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.138
1598	23997	\begin{align*} y^{\prime \prime \prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.138
1599	24607	\begin{align*} y^{\prime \prime \prime }-y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.138
1600	24609	\begin{align*} y^{\prime \prime \prime }-y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.138