2.3.18 Problems 1701 to 1800

Table 2.609: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1701	10492	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.251
1702	12298	\begin{align*} a \,{\mathrm e}^{b x} y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.251
1703	18181	\begin{align*} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.251
1704	21899	\begin{align*} y^{\prime }+y-x^{\prime \prime }+x&={\mathrm e}^{t} \\ y^{\prime }-x^{\prime }+x&={\mathrm e}^{-t} \\ \end{align*}	✗	✓	✓	✓	0.251
1705	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*}	✓	✓	✓	✓	0.251
1706	2775	\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2}+t \\ x_{2}^{\prime }&=2 x_{1}-2 x_{2}+3 \,{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.252
1707	11188	\begin{align*} x \left (-1+x \right )^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.252
1708	331	\begin{align*} 2 y^{\prime \prime }+9 y&=2 \cos \left (3 x \right )+3 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.253
1709	377	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.253
1710	389	\begin{align*} x^{\prime \prime }+3 x^{\prime }+5 x&=-4 \cos \left (5 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.253
1711	4370	\begin{align*} y^{\prime }&=\left (\sin \left (x \right )^{2}-y\right ) \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.253
1712	10299	\begin{align*} y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
1713	10620	\begin{align*} x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (-3 x +4\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.253
1714	10751	\begin{align*} y^{\prime \prime }-y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.253
1715	11298	\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}	✓	✓	✓	✗	0.253
1716	17649	\begin{align*} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+5 y^{\prime } x -5 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= -1 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.253
1717	18966	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+3 y&=t \\ \end{align*}	✓	✓	✓	✗	0.253
1718	22115	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-4 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
1719	25143	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
1720	934	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
1721	8165	\begin{align*} \left (-x +y\right ) y^{\prime }&=-x +y \\ \end{align*}	✓	✓	✓	✓	0.254
1722	10495	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
1723	10969	\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
1724	11111	\begin{align*} 4 y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.254
1725	11287	\begin{align*} y^{\prime \prime }+\frac {y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
1726	17648	\begin{align*} x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+54 y^{\prime } x +42 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.254
1727	18745	\begin{align*} a y^{\prime \prime }+b y^{\prime }+\frac {b^{2} y}{4 a}&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
1728	22633	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
1729	2774	\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2} \\ x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.255
1730	10501	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
1731	22118	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+32 y^{\prime \prime }-64 y^{\prime }+64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
1732	22128	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
1733	25148	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
1734	25650	\begin{align*} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\ \end{align*}	✗	✗	✓	✗	0.255
1735	2314	\begin{align*} y^{\prime }+\frac {y}{\sqrt {t}}&={\mathrm e}^{\frac {\sqrt {t}}{2}} \\ \end{align*}	✓	✓	✓	✓	0.256
1736	10489	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.256
1737	10745	\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.256
1738	11037	\begin{align*} 9 \left (x +3\right ) x^{2} y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (4 x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.256
1739	18182	\begin{align*} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.256
1740	19444	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.256
1741	22631	\begin{align*} 2 y^{\prime \prime \prime }-5 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.256
1742	26107	\begin{align*} y^{\left (5\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.256
1743	3609	\begin{align*} y^{\prime }+y&=4 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.257
1744	4514	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=9 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.257
1745	10010	\begin{align*} \left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.257
1746	10687	\begin{align*} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.257
1747	10847	\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}	✓	✓	✓	✗	0.257
1748	10866	\begin{align*} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.257
1749	11126	\begin{align*} x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.257
1750	11156	\begin{align*} 4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.257
1751	11223	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.257
1752	11275	\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}	✓	✓	✓	✗	0.257
1753	27619	\begin{align*} y^{\prime \prime \prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.257
1754	3158	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }&={\mathrm e}^{2 x}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.258
1755	10498	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.258
1756	10886	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.258
1757	15138	\begin{align*} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.258
1758	27605	\begin{align*} x^{2} \left (y^{2} y^{\prime \prime \prime }-{y^{\prime }}^{3}\right )&=2 y^{2} y^{\prime }-3 x y {y^{\prime }}^{2} \\ \end{align*}	✗	✓	✗	✗	0.258
1759	1486	\begin{align*} y^{\prime \prime }-2 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.259
1760	10621	\begin{align*} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.259
1761	10815	\begin{align*} 2 y^{\prime \prime } x +\left (x -2\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.259
1762	11315	\begin{align*} y^{\prime }+y^{2}-a x -b&=0 \\ \end{align*}	✓	✓	✓	✗	0.259
1763	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*}	✓	✓	✓	✓	0.259
1764	17585	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=2 \,{\mathrm e}^{-3 t}-t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.259
1765	3612	\begin{align*} y^{\prime }+2 y x&=2 x^{3} \\ \end{align*}	✓	✓	✓	✓	0.260
1766	6729	\begin{align*} y^{\prime \prime \prime \prime }&={\mathrm e}^{x} \cos \left (x \right )+y \\ \end{align*}	✓	✓	✓	✓	0.260
1767	9105	\begin{align*} y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.260
1768	9106	\begin{align*} y^{\prime } x -3 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.260
1769	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*}	✓	✓	✓	✗	0.260
1770	10698	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.260
1771	10731	\begin{align*} 4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.260
1772	10849	\begin{align*} x^{3} y^{\prime \prime }+y^{\prime }-\frac {y}{x}&=0 \\ \end{align*}	✓	✓	✓	✗	0.260
1773	11145	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.260
1774	11146	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.260
1775	11229	\begin{align*} 2 x \left (-1+x \right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.260
1776	12287	\begin{align*} y^{\prime \prime }-2 y-4 x^{2} {\mathrm e}^{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.260
1777	17650	\begin{align*} x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+17 y^{\prime } x -17 y&=0 \\ y \left (1\right ) &= -2 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.260
1778	18977	\begin{align*} \left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y&=0 \\ \end{align*}	✗	✗	✗	✗	0.260
1779	20146	\begin{align*} x^{4} y^{\prime \prime }+y^{\prime } x +y&=\frac {1}{x} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.260
1780	22671	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.260
1781	22894	\begin{align*} x y^{\prime }+y x^{\prime }&=t^{2} \\ 2 x^{\prime \prime }-y^{\prime }&=5 t \\ \end{align*}	✗	✗	✗	✗	0.260
1782	10841	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.261
1783	10975	\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.261
1784	17208	\begin{align*} y^{2}+2 t y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.261
1785	19573	\begin{align*} y^{\prime }-y^{\prime \prime }+y^{\prime \prime \prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.261
1786	26106	\begin{align*} y^{\prime \prime \prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.261
1787	3284	\begin{align*} 4 y^{2}&=x^{2} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.262
1788	7229	\begin{align*} y^{\prime }+y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.262
1789	10768	\begin{align*} x \left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.262
1790	10878	\begin{align*} t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.262
1791	11106	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.262
1792	11252	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.262
1793	378	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.263
1794	2549	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-10 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.263
1795	3333	\begin{align*} y^{2}-2 y y^{\prime } x +{y^{\prime }}^{2} \left (x^{2}-1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
1796	3611	\begin{align*} x^{2} y^{\prime }-4 y x&=x^{7} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.263
1797	4253	\begin{align*} y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
1798	8829	\begin{align*} a^{2} y^{\prime \prime \prime \prime }&=y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.263
1799	10496	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
1800	10582	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.263