2.3.18 Problems 1701 to 1800

Table 2.567: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
1701	6911	\begin{align*} x +y+1+\left (2 x +2 y+2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
1702	7454	\begin{align*} 2 y x +3+\left (x^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
1703	8532	\begin{align*} x^{3} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.105
1704	8958	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
1705	9285	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
1706	9310	\begin{align*} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
1707	15691	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ y^{\prime \prime \prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.105
1708	16481	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.105
1709	16579	\begin{align*} -8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
1710	16660	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=12 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.105
1711	16790	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.105
1712	18088	\begin{align*} y^{\prime \prime \prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.105
1713	18190	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=1 \\ \end{align*}	✓	✓	✓	✓	0.105
1714	18367	\begin{align*} y^{\prime \prime \prime \prime }-\lambda ^{4} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime \prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.105
1715	18887	\begin{align*} 6 y^{\prime \prime }+5 y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.105
1716	19535	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
1717	21878	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+7 y^{\prime \prime }+6 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
1718	22579	\begin{align*} x^{4} y^{\prime \prime \prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
1719	23406	\begin{align*} x^{3} y^{\prime \prime }+\left (5 x^{3}-x^{2}\right ) y^{\prime }+2 \left (3 x^{3}-x^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.105
1720	24620	\begin{align*} y^{\prime \prime \prime }-12 y^{\prime \prime }+48 y^{\prime }-64 y&=15 \,{\mathrm e}^{4 x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.105
1721	24782	\begin{align*} y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.105
1722	25630	\begin{align*} y^{\prime \prime }+10 y^{\prime }+16 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.105
1723	1777	\begin{align*} y^{\prime \prime } x -\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.106
1724	2295	\begin{align*} y^{\prime }-2 t y&=t \\ \end{align*}	✓	✓	✓	✓	0.106
1725	2572	\begin{align*} y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1}&=0 \\ \end{align*}	✓	✓	✓	✗	0.106
1726	4358	\begin{align*} 1+y \cos \left (x \right )-\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.106
1727	5743	\begin{align*} \left (b x +a \right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.106
1728	8198	\begin{align*} x^{\prime \prime }&=4 y+{\mathrm e}^{t} \\ y^{\prime \prime }&=4 x-{\mathrm e}^{t} \\ \end{align*}	✗	✓	✓	✓	0.106
1729	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*}	✗	✓	✓	✗	0.106
1730	14121	\begin{align*} y^{\prime \prime \prime \prime }-y&={\mathrm e}^{x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.106
1731	14129	\begin{align*} -2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.106
1732	15080	\begin{align*} x^{\prime \prime \prime \prime }-2 x^{\prime \prime }+x&=t^{2}-3 \\ \end{align*}	✓	✓	✓	✓	0.106
1733	16445	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.106
1734	16455	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.106
1735	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*}	✓	✓	✓	✓	0.106
1736	17579	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.106
1737	18168	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.106
1738	18311	\begin{align*} x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.106
1739	20079	\begin{align*} y^{\prime \prime \prime \prime }-y&={\mathrm e}^{x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.106
1740	20770	\begin{align*} y^{\prime \prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.106
1741	23636	\begin{align*} y^{\prime \prime }-y&=6 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.106
1742	23638	\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=2 \,{\mathrm e}^{-5 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.106
1743	23683	\begin{align*} x^{2} y^{\prime \prime }+\left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.106
1744	25262	\begin{align*} t^{2} y^{\prime \prime }-2 t y^{\prime }+\left (t^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.106
1745	25344	\begin{align*} t^{2} y^{\prime \prime }+5 t y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.106
1746	1479	\begin{align*} y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.107
1747	6601	\begin{align*} y^{\prime \prime \prime }&=\cos \left (x \right )+1 \\ \end{align*}	✓	✓	✓	✓	0.107
1748	14568	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.107
1749	16664	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.107
1750	17370	\begin{align*} t^{2} y^{\prime \prime }+6 t y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.107
1751	20083	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.107
1752	20357	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime }&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	0.107
1753	23423	\begin{align*} y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.107
1754	25142	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.107
1755	25156	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.107
1756	25635	\begin{align*} y^{\prime \prime }+y&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.107
1757	955	\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*}	✓	✓	✓	✓	0.108
1758	1780	\begin{align*} y^{\prime \prime } x -\left (4 x +1\right ) y^{\prime }+\left (2+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.108
1759	1784	\begin{align*} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.108
1760	2107	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-7 y^{\prime \prime }-y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -6 \\ y^{\prime \prime }\left (0\right ) &= 10 \\ y^{\prime \prime \prime }\left (0\right ) &= -36 \\ \end{align*}	✓	✓	✓	✓	0.108
1761	3334	\begin{align*} y^{\prime }&=\sqrt {1-y} \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.108
1762	3587	\begin{align*} y^{\prime \prime \prime }&=6 x \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.108
1763	3685	\begin{align*} y+3 x^{2}+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.108
1764	3934	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.108
1765	6697	\begin{align*} -8 y+3 y^{\prime } x +x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.108
1766	6726	\begin{align*} y^{\prime \prime \prime \prime }&=\cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.108
1767	6738	\begin{align*} y-2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=4+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.108
1768	9384	\begin{align*} x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.108
1769	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*}	✓	✓	✓	✗	0.108
1770	11216	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.108
1771	11230	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+4 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.108
1772	11301	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.108
1773	14340	\begin{align*} x^{\prime \prime }-t x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✗	0.108
1774	14567	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.108
1775	14613	\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 ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.108
1776	14813	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.108
1777	15190	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.108
1778	15678	\begin{align*} y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.108
1779	17369	\begin{align*} t^{2} y^{\prime \prime }+4 t y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.108
1780	17564	\begin{align*} y^{\prime \prime \prime \prime }+16 y^{\prime \prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.108
1781	18171	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.108
1782	20486	\begin{align*} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.108
1783	21506	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.108
1784	22181	\begin{align*} \left (x +1\right )^{3} y^{\prime \prime }+\left (x^{2}-1\right ) \left (x +1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=-1\).	✗	✗	✓	✗	0.108
1785	22746	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=x^{5}+1 \\ \end{align*}	✓	✓	✓	✓	0.108
1786	23411	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {9 y}{x^{4}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.108
1787	23428	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.108
1788	24774	\begin{align*} x^{2} {y^{\prime }}^{2}+y^{\prime } x -y^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.108
1789	24779	\begin{align*} {y^{\prime }}^{2}-y^{2} x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.108
1790	1326	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.109
1791	2315	\begin{align*} \frac {y}{t}+y^{\prime }&=\cos \left (t \right )+\frac {\sin \left (t \right )}{t} \\ \end{align*}	✓	✓	✓	✓	0.109
1792	2573	\begin{align*} y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.109
1793	3623	\begin{align*} y^{\prime }+\frac {m y}{x}&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.109
1794	3937	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=36 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.109
1795	6777	\begin{align*} 12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.109
1796	7810	\begin{align*} y^{\prime \prime \prime \prime }&=5 x \\ \end{align*}	✓	✓	✓	✓	0.109
1797	7836	\begin{align*} x^{3} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.109
1798	8207	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 y^{\prime } x -78 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.109
1799	9108	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=2 x \csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.109
1800	10998	\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*}	✓	✓	✓	✗	0.109