2.3.190 Problems 18901 to 19000

Table 2.911: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18901	6984	\begin{align*} 2 \cos \left (x \right ) y^{\prime }&=\sin \left (x \right ) y-y^{3} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.154
18902	19073	\begin{align*} x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.154
18903	5882	\begin{align*} 3 y-10 y^{\prime }+3 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.155
18904	23357	\begin{align*} y^{\prime \prime }+9 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.156
18905	8409	\begin{align*} m^{\prime }&=-\frac {k}{m^{2}} \\ m \left (0\right ) &= m_{0} \\ \end{align*}	✓	✗	✓	✓	6.158
18906	5022	\begin{align*} y^{\prime } \sqrt {x^{4}+x^{2}+1}&=\sqrt {1+y^{2}+y^{4}} \\ \end{align*}	✓	✓	✓	✓	6.160
18907	10216	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-8\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	6.161
18908	4824	\begin{align*} y^{\prime } x&=y-x \tan \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	6.163
18909	6056	\begin{align*} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.163
18910	19943	\begin{align*} y^{\prime }+\frac {y}{\sqrt {-x^{2}+1}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	6.167
18911	19776	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	6.168
18912	4826	\begin{align*} y^{\prime } x&={\mathrm e}^{\frac {y}{x}} x +y \\ \end{align*}	✓	✓	✓	✗	6.169
18913	20261	\begin{align*} x^{2}+3 y^{2}-2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	6.169
18914	25663	\begin{align*} y^{\prime }&=2 x y^{2} \\ \end{align*}	✓	✓	✓	✓	6.169
18915	13793	\begin{align*} x^{2} y^{\prime \prime }+a x y^{\prime }+\left (b \,x^{n}+c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	6.170
18916	5011	\begin{align*} y^{\prime } \sqrt {-x^{2}+1}&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	6.171
18917	25236	\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✗	✗	✗	✗	6.171
18918	25656	\begin{align*} y^{2}-1+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	6.173
18919	22110	\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	6.174
18920	22570	\begin{align*} y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	6.174
18921	21846	\begin{align*} y^{\prime } x +y&=y^{2} x^{3} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	6.175
18922	10226	\begin{align*} y^{\prime }&=y \left (1-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	6.176
18923	2852	\begin{align*} y^{\prime } x +y&=y^{2} \\ \end{align*}	✓	✓	✓	✓	6.178
18924	3485	\begin{align*} f^{\prime \prime }+2 f^{\prime }+5 f&={\mathrm e}^{-t} \cos \left (3 t \right ) \\ f \left (0\right ) &= 0 \\ f^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	6.178
18925	5167	\begin{align*} x \left (x -2 y\right ) y^{\prime }+y \left (2 x -y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	6.178
18926	2370	\begin{align*} y^{\prime \prime }-6 y^{\prime }+y&=0 \\ y \left (2\right ) &= 1 \\ y^{\prime }\left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.181
18927	16254	\begin{align*} y^{\prime }&=\frac {-1+y^{2}}{y x} \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	6.181
18928	16568	\begin{align*} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x +5 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.182
18929	21299	\begin{align*} x^{\prime \prime }+2 x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	6.185
18930	23327	\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.187
18931	20315	\begin{align*} \left (2 x +2 y+3\right ) y^{\prime }&=x +y+1 \\ \end{align*}	✓	✓	✓	✓	6.188
18932	14496	\begin{align*} y^{\prime } x +y&=-2 x^{6} y^{4} \\ \end{align*}	✓	✓	✓	✓	6.189
18933	18797	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ y \left (\frac {\pi }{4}\right ) &= 2 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	6.189
18934	10394	\begin{align*} y^{\prime \prime }+y^{\prime }&=x^{3}+x^{2}+x +1 \\ \end{align*}	✓	✓	✓	✓	6.190
18935	14293	\begin{align*} x^{\prime \prime }+x^{\prime }+x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.191
18936	20277	\begin{align*} 1+y^{2}&=\left (\arctan \left (y\right )-x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	6.192
18937	9316	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.193
18938	19729	\begin{align*} y-\cos \left (x \right ) y^{\prime }&=y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	6.196
18939	20647	\begin{align*} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=-4 x^{3} \\ \end{align*}	✓	✓	✓	✗	6.196
18940	14438	\begin{align*} y^{\prime }&=y^{{1}/{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	6.197
18941	25779	\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.197
18942	1315	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+82 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	6.201
18943	1819	\begin{align*} x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y&=x^{1+a} \\ \end{align*}	✓	✓	✓	✓	6.201
18944	10030	\begin{align*} y&=x {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	6.201
18945	19122	\begin{align*} y&=x {y^{\prime }}^{2}+{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	6.201
18946	19765	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	6.201
18947	18796	\begin{align*} y^{\prime \prime }+8 y^{\prime }-9 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	6.202
18948	21370	\begin{align*} y+y^{\prime } x +\frac {y^{3} \left (-y^{\prime } x +y\right )}{x}&=0 \\ \end{align*}	✓	✓	✓	✗	6.204
18949	23854	\begin{align*} \cos \left (x \right ) \cot \left (y\right )+\sin \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.204
18950	25223	\begin{align*} 2 t^{2} y^{\prime \prime }-5 y^{\prime } t +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.204
18951	18774	\begin{align*} y^{\prime \prime }-9 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.207
18952	7689	\begin{align*} 2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.208
18953	16302	\begin{align*} \left (x +y\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	6.208
18954	21378	\begin{align*} \left (x +y\right ) y^{\prime }+3 x +y&=0 \\ \end{align*}	✓	✓	✓	✓	6.208
18955	24235	\begin{align*} x^{4}+2 y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	6.213
18956	19468	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.214
18957	6573	\begin{align*} y^{\prime } y^{\prime \prime }&=x y^{2}+x^{2} y y^{\prime } \\ \end{align*}	✗	✗	✗	✗	6.215
18958	6895	\begin{align*} 2 y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.218
18959	16474	\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x -y&=0 \\ y \left (1\right ) &= 8 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.219
18960	3673	\begin{align*} y^{\prime }&=\sin \left (3 x -3 y+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	6.220
18961	17949	\begin{align*} x^{2} y^{\prime }+y&=\left (x^{2}+1\right ) {\mathrm e}^{x} \\ y \left (-\infty \right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	6.220
18962	21872	\begin{align*} y&=y^{\prime } x +\ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	6.221
18963	23216	\begin{align*} y^{\prime }&=\frac {3 x -2 y+7}{2 x +3 y+9} \\ \end{align*}	✓	✓	✓	✓	6.221
18964	3061	\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.223
18965	3499	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+6\right ) y&={\mathrm e}^{-x^{2}} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✗	6.223
18966	17528	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=t \\ \end{align*}	✓	✓	✓	✓	6.227
18967	15485	\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	6.230
18968	850	\begin{align*} y^{\prime \prime }+5 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.231
18969	13949	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+2 b -\lambda \right ) y^{\prime }+\left (c \,{\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+b^{2}-b \lambda \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	6.234
18970	14605	\begin{align*} 9 y^{\prime \prime }-6 y^{\prime }+y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	6.235
18971	16598	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=1 \\ \end{align*}	✓	✓	✓	✓	6.235
18972	8997	\begin{align*} 4 x^{2} y^{\prime \prime }-4 \,{\mathrm e}^{x} y^{\prime } x +3 \cos \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	6.237
18973	4350	\begin{align*} 2 y^{2} x^{2}+y+\left (x^{3} y-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.238
18974	2846	\begin{align*} \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.241
18975	20548	\begin{align*} y^{\prime \prime }&={\mathrm e}^{2 y} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	6.241
18976	187	\begin{align*} y^{\prime } x +2 y&=6 \sqrt {y}\, x^{2} \\ \end{align*}	✓	✓	✓	✓	6.243
18977	3051	\begin{align*} 4 x y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.243
18978	17121	\begin{align*} y^{\prime }&={\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.243
18979	19088	\begin{align*} y^{\prime }+y^{2}+\frac {y}{x}-\frac {4}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	6.244
18980	830	\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.245
18981	8792	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.246
18982	23050	\begin{align*} x^{\prime \prime }+3 x^{\prime }&={\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	6.250
18983	23336	\begin{align*} 9 y^{\prime \prime }-6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	6.250
18984	19425	\begin{align*} -2 y+y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	6.251
18985	5367	\begin{align*} {y^{\prime }}^{2}&=\left (-1+y\right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	6.253
18986	21568	\begin{align*} y^{\prime \prime }+k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	6.253
18987	2973	\begin{align*} \sin \left (\theta \right ) r^{\prime }+1+r \tan \left (\theta \right )&=\cos \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	6.256
18988	9010	\begin{align*} y^{\prime }&=y^{2} x^{2}-4 x^{2} \\ \end{align*}	✓	✓	✓	✗	6.257
18989	17937	\begin{align*} x \ln \left (x \right ) y^{\prime }-y&=3 x^{3} \ln \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	6.259
18990	17667	\begin{align*} \left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (4 x^{2}-4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	6.260
18991	36	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✗	✓	✓	✗	6.262
18992	19206	\begin{align*} y^{\prime \prime } x -y^{\prime }-x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	6.269
18993	10214	\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	6.271
18994	6017	\begin{align*} \left (a \left (1+a \right )+b^{2} x^{2}\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.275
18995	18724	\begin{align*} a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y&=d \\ \end{align*}	✓	✓	✓	✓	6.276
18996	7967	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.277
18997	8798	\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	6.277
18998	12029	\begin{align*} y^{\prime }&=-\frac {y \left (\tan \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tan \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	6.277
18999	4838	\begin{align*} \left (x +1\right ) y^{\prime }+y+\left (x +1\right )^{4} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	6.278
19000	5098	\begin{align*} \left (2 x +3 y+2\right ) y^{\prime }&=1-2 x -3 y \\ \end{align*}	✓	✓	✓	✓	6.278