2.3.168 Problems 16701 to 16800

Table 2.867: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16701	18778	\begin{align*} 4 y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.199
16702	6563	\begin{align*} 2 \left (1-x \right )^{2} x^{2} \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime }&=\operatorname {a0} x \left (1-y\right )^{2} \left (x -y\right )^{2}+\left (-1+\operatorname {a2} \right ) \left (1-x \right ) x \left (1-y\right )^{2} y^{2}+\operatorname {a1} \left (1-x \right ) \left (x -y\right )^{2} y^{2}+\operatorname {a3} \left (1-y\right )^{2} \left (x -y\right )^{2} y^{2}+2 \left (1-x \right ) x \left (1-y\right )^{2} y \left (x^{2}+y-2 y x \right ) y^{\prime }+\left (1-x \right )^{2} x^{2} \left (x -2 y-2 y x +3 y^{2}\right ) {y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	4.200
16703	17096	\begin{align*} y^{\prime }&=\frac {5^{-t}}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.200
16704	18484	\begin{align*} y^{\prime }&=x \left (y-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	4.200
16705	6361	\begin{align*} y^{\prime \prime }&=a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	4.201
16706	18578	\begin{align*} \ln \left (y\right ) x +y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.205
16707	25675	\begin{align*} y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.205
16708	7471	\begin{align*} y^{2}+2 y x -x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.207
16709	25618	\begin{align*} y^{\prime \prime }+4 y^{\prime }&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	4.207
16710	22518	\begin{align*} y^{\prime }&=\frac {y}{x}+\arctan \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	4.209
16711	10157	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.210
16712	14534	\begin{align*} y^{2} {\mathrm e}^{2 x}-2 x +y \,{\mathrm e}^{2 x} y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.210
16713	8346	\begin{align*} y \ln \left (x \right ) y^{\prime }&=\frac {\left (1+y\right )^{2}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.211
16714	21995	\begin{align*} {\mathrm e}^{x}-y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.211
16715	1607	\begin{align*} y^{\prime }-2 y&=\frac {x \,{\mathrm e}^{2 x}}{1-y \,{\mathrm e}^{-2 x}} \\ \end{align*}	✓	✓	✓	✗	4.212
16716	2860	\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.212
16717	15807	\begin{align*} y^{\prime }&=2 t y^{2}+3 t^{2} y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.212
16718	17113	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{t}}{1+y} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	4.212
16719	17414	\begin{align*} t^{2} y^{\prime \prime }-y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	4.213
16720	21559	\begin{align*} -y^{\prime }+y^{\prime \prime } x&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	4.213
16721	12424	\begin{align*} x^{2} y^{\prime \prime }+a y^{\prime }-\left (b^{2} x^{2}+a b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	4.214
16722	24589	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{x}-x +\sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	4.214
16723	7003	\begin{align*} y^{\prime } x +y&=x^{2} \left ({\mathrm e}^{x}+1\right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	4.215
16724	21618	\begin{align*} y^{\prime \prime }+2 b y^{\prime }+y&=k \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.219
16725	2361	\begin{align*} 2 t^{2} y^{\prime \prime }+3 y^{\prime } t -y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.220
16726	20858	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.221
16727	5081	\begin{align*} \left (x +2 y\right ) y^{\prime }+2 x -y&=0 \\ \end{align*}	✓	✓	✓	✓	4.222
16728	11603	\begin{align*} \left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x&=0 \\ \end{align*}	✓	✓	✓	✓	4.222
16729	4751	\begin{align*} y^{\prime } x +x +y&=0 \\ \end{align*}	✓	✓	✓	✓	4.223
16730	14719	\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	4.223
16731	4439	\begin{align*} \left (\cos \left (x \right )+1\right ) y^{\prime }+\sin \left (x \right ) \left (\sin \left (x \right )+\cos \left (x \right ) \sin \left (x \right )-y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.224
16732	8404	\begin{align*} y^{\prime }&=\sqrt {1+y^{2}}\, \sin \left (y\right )^{2} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✗	✓	4.224
16733	19167	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.227
16734	21977	\begin{align*} y^{\prime }&=\frac {y^{2}}{x} \\ \end{align*}	✓	✓	✓	✓	4.227
16735	18756	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.228
16736	1713	\begin{align*} 3 x^{2} y+2 x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.229
16737	23356	\begin{align*} y^{\prime \prime }+20 y^{\prime }+64 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.229
16738	4340	\begin{align*} 2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.231
16739	12031	\begin{align*} y^{\prime }&=\frac {\left (x -y\right )^{2} \left (x +y\right )^{2} x}{y} \\ \end{align*}	✗	✓	✓	✗	4.231
16740	17073	\begin{align*} 4 \sinh \left (4 y\right ) y^{\prime }&=6 \cosh \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✗	4.231
16741	2365	\begin{align*} y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.232
16742	5127	\begin{align*} y y^{\prime } x&=a \,x^{3} \cos \left (x \right )+y^{2} \\ \end{align*}	✓	✓	✓	✓	4.232
16743	7937	\begin{align*} x^{2} y^{\prime } \cos \left (y\right )&=2 x \sin \left (y\right )-1 \\ \end{align*}	✓	✓	✓	✗	4.233
16744	17944	\begin{align*} y^{\prime }-y \ln \left (2\right )&=2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right ) \\ \end{align*}	✓	✓	✓	✓	4.233
16745	19436	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.235
16746	12373	\begin{align*} y^{\prime \prime } x +\left (x +b \right ) y^{\prime }+a y&=0 \\ \end{align*}	✗	✓	✓	✗	4.236
16747	24876	\begin{align*} y^{\prime \prime } x +y^{\prime }+x&=0 \\ y \left (2\right ) &= -1 \\ y^{\prime }\left (2\right ) &= -{\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	4.237
16748	17242	\begin{align*} y+2 t^{2}+\left (t^{2} y-t \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.238
16749	17024	\begin{align*} y \cos \left (y x \right )+\sin \left (x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.239
16750	18847	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=\sin \left (\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	4.240
16751	521	\begin{align*} 4 x^{2} y^{\prime \prime }-12 y^{\prime } x +\left (15+16 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.241
16752	1606	\begin{align*} y^{\prime }-y&=\frac {\left (x +1\right ) {\mathrm e}^{4 x}}{\left ({\mathrm e}^{x}+y\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	4.241
16753	6492	\begin{align*} 12 y y^{\prime \prime }&=-8 y^{3}+15 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.241
16754	17341	\begin{align*} {\mathrm e}^{t y} y-2 t +t \,{\mathrm e}^{t y} y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.242
16755	24958	\begin{align*} 1-y^{2}-t y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.242
16756	25594	\begin{align*} y^{\prime \prime }+y^{\prime }&=t^{2}+1 \\ \end{align*}	✓	✓	✓	✓	4.242
16757	93	\begin{align*} y^{\prime } x&=3 y+x^{4} \cos \left (x \right ) \\ y \left (2 \pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.243
16758	7394	\begin{align*} x +x y^{2}+{\mathrm e}^{x^{2}} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.243
16759	4313	\begin{align*} y^{\prime }+\frac {x}{y}+2&=0 \\ \end{align*}	✓	✓	✓	✗	4.244
16760	12280	\begin{align*} y^{\prime }&=\frac {2 x^{2} y+x^{3}+x y \ln \left (x \right )-y^{2}-y x}{x^{2} \left (\ln \left (x \right )+x \right )} \\ \end{align*}	✓	✓	✓	✗	4.244
16761	1679	\begin{align*} y^{\prime }&=1+x -\left (2 x +1\right ) y+x y^{2} \\ \end{align*}	✓	✓	✓	✓	4.245
16762	7988	\begin{align*} y^{\prime \prime }-4 y^{\prime }&=5 \\ \end{align*}	✓	✓	✓	✓	4.245
16763	1638	\begin{align*} y^{\prime }-2 y&=2 \sqrt {y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.246
16764	25766	\begin{align*} y^{\prime \prime } x +y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.246
16765	20679	\begin{align*} x^{3}+x y^{2}+a^{2} y+\left (y^{3}+x^{2} y-a^{2} x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.247
16766	25056	\begin{align*} y^{\prime } t&=2 y-t \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✗	✓	✓	4.247
16767	7607	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	4.248
16768	3557	\begin{align*} y^{\prime \prime }-25 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.250
16769	18014	\begin{align*} y&=x {y^{\prime }}^{2}-\frac {1}{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	4.250
16770	1351	\begin{align*} t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=4 t^{2} \\ \end{align*}	✓	✓	✓	✓	4.251
16771	1355	\begin{align*} u^{\prime \prime }+2 u&=0 \\ \end{align*}	✓	✓	✓	✓	4.251
16772	17858	\begin{align*} y^{\prime }&=\cos \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	4.251
16773	94	\begin{align*} y^{\prime }&=2 y x +3 x^{2} {\mathrm e}^{x^{2}} \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	4.252
16774	13752	\begin{align*} y^{\prime \prime } x +a \,x^{n} y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}-b^{2} x +2 b \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	4.253
16775	136	\begin{align*} 4 x -y+\left (6 y-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.254
16776	11304	\begin{align*} y^{\prime }+a y-c \,{\mathrm e}^{b x}&=0 \\ \end{align*}	✓	✓	✓	✓	4.254
16777	13951	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime }+\left (\alpha \,{\mathrm e}^{2 \lambda x}+\beta \,{\mathrm e}^{\lambda x}+\gamma \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.256
16778	25095	\begin{align*} 2 y^{\prime \prime }-12 y^{\prime }+18 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.256
16779	2375	\begin{align*} y^{\prime \prime }+2 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.257
16780	115	\begin{align*} \left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	4.258
16781	4772	\begin{align*} y^{\prime } x +x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	4.258
16782	7858	\begin{align*} 1+y-\left (x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.258
16783	10255	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	4.258
16784	19362	\begin{align*} 2 y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.259
16785	23899	\begin{align*} 3 x^{2} y \ln \left (y\right )+\left (2 x^{3}+2 y^{3}+3 y^{3} \ln \left (y\right )^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.259
16786	6826	\begin{align*} x y \left (x^{2}+1\right ) y^{\prime }-1-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.260
16787	21633	\begin{align*} \left (x -1\right ) y^{\prime \prime }+y^{\prime } x +\frac {y}{x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.260
16788	23214	\begin{align*} y^{\prime }&=\frac {x -y}{x +y+2} \\ \end{align*}	✓	✓	✓	✓	4.260
16789	17118	\begin{align*} y^{\prime }&=\frac {\sin \left (x \right )}{\cos \left (y\right )+1} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	4.261
16790	4657	\begin{align*} y^{\prime }&=3 y-3 x +3+\left (x -y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.262
16791	8397	\begin{align*} y^{\prime }&=\frac {\sin \left (\sqrt {x}\right )}{\sqrt {y}} \\ \end{align*}	✓	✓	✓	✓	4.263
16792	19357	\begin{align*} y^{\prime } \sin \left (2 x \right )&=2 y+2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	4.263
16793	16709	\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.264
16794	1284	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.265
16795	5274	\begin{align*} x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	4.265
16796	12016	\begin{align*} y^{\prime }&=\frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{3}\right ) y}{x +1} \\ \end{align*}	✗	✓	✓	✓	4.265
16797	16888	\begin{align*} x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{x -2}+\frac {2 y}{2+x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	4.265
16798	4277	\begin{align*} y^{2}&=\left (x^{3}-y x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	4.266
16799	5002	\begin{align*} x \left (-x^{4}+1\right ) y^{\prime }&=2 x \left (x^{2}-y^{2}\right )+\left (-x^{4}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	4.266
16800	4857	\begin{align*} \left (1-2 x \right ) y^{\prime }&=16+32 x -6 y \\ \end{align*}	✓	✓	✓	✓	4.268