2.3.247 Problems 24601 to 24700

Table 2.1025: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
24601	2923	\begin{align*} x y^{2}+2 y+\left (2 y^{3}-x^{2} y+2 x \right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	57.472
24602	21921	\begin{align*} 4 y+y^{\prime \prime }&=x \sin \left (x \right ) \\ y \left (0\right ) &= {\frac {7}{9}} \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{6}-1 \\ \end{align*}	✓	✓	✓	✓	57.520
24603	12681	\begin{align*} y^{\prime \prime }&=-\frac {x \sin \left (x \right ) y^{\prime }}{\cos \left (x \right ) x -\sin \left (x \right )}+\frac {\sin \left (x \right ) y}{\cos \left (x \right ) x -\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	57.684
24604	1686	\begin{align*} -2 \sin \left (x \right ) y^{2}+3 y^{3}-2 x +\left (4 \cos \left (x \right ) y+9 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	57.690
24605	3546	\begin{align*} y^{\prime } x&=\sqrt {16 x^{2}-y^{2}}+y \\ \end{align*}	✓	✓	✓	✓	57.819
24606	14897	\begin{align*} x^{\prime }&=-x \left (k^{2}+x^{2}\right ) \\ x \left (0\right ) &= x_{0} \\ \end{align*}	✓	✗	✓	✗	57.937
24607	10019	\begin{align*} p^{\prime }&=a p-b p^{2} \\ p \left (\operatorname {t0} \right ) &= \operatorname {p0} \\ \end{align*}	✓	✓	✓	✓	57.968
24608	25496	\begin{align*} y^{\prime }&=\frac {c t -a y}{A t +b y} \\ \end{align*}	✓	✓	✓	✗	58.061
24609	11665	\begin{align*} {y^{\prime }}^{2}-2 y^{\prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	58.110
24610	25007	\begin{align*} y^{\prime }&=\frac {3 y^{2}-t^{2}}{2 t y} \\ \end{align*}	✓	✓	✓	✓	58.116
24611	19275	\begin{align*} x^{2}-2 y^{2}+y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	58.183
24612	13327	\begin{align*} y^{\prime }&=\alpha y^{2}+\beta +\gamma \cosh \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	58.184
24613	2398	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	58.189
24614	12090	\begin{align*} y^{\prime }&=\frac {\left (1+2 y\right ) \left (1+y\right )}{x \left (-2 y-2+x +2 y x \right )} \\ \end{align*}	✓	✓	✓	✓	58.197
24615	13551	\begin{align*} y y^{\prime }-y&=a x +b \,x^{m} \\ \end{align*}	✗	✗	✗	✗	58.210
24616	12097	\begin{align*} y^{\prime }&=\frac {\left (3+y\right )^{3} {\mathrm e}^{\frac {9 x^{2}}{2}} x \,{\mathrm e}^{\frac {3 x^{2}}{2}} {\mathrm e}^{-3 x^{2}}}{243 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+243 y} \\ \end{align*}	✗	✓	✓	✗	58.216
24617	11790	\begin{align*} x y^{2} {y^{\prime }}^{2}-\left (y^{3}+x^{3}-a \right ) y^{\prime }+x^{2} y&=0 \\ \end{align*}	✗	✓	✓	✗	58.264
24618	7503	\begin{align*} y^{\prime }&=\frac {x^{2}-y^{2}}{3 x y} \\ \end{align*}	✓	✓	✓	✓	58.343
24619	9146	\begin{align*} x^{2}-2 y^{2}+y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	58.500
24620	12572	\begin{align*} x^{3} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+y x&=0 \\ \end{align*}	✗	✓	✓	✗	58.686
24621	19137	\begin{align*} {y^{\prime }}^{4}&=4 y \left (y^{\prime } x -2 y\right )^{2} \\ \end{align*}	✓	✓	✓	✗	58.692
24622	6890	\begin{align*} y y^{\prime }+x&=a \sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	58.769
24623	5003	\begin{align*} x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\ \end{align*}	✗	✓	✓	✗	58.840
24624	24305	\begin{align*} y \left (y^{2}-3 x^{2}\right )+x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	58.878
24625	363	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	58.881
24626	11744	\begin{align*} x \left (x^{2}-1\right ) {y^{\prime }}^{2}+2 \left (-x^{2}+1\right ) y y^{\prime }+x y^{2}-x&=0 \\ \end{align*}	✗	✓	✓	✗	58.881
24627	11990	\begin{align*} y^{\prime }&=\frac {\left (-\ln \left (-1+y\right )+\ln \left (1+y\right )+2 \ln \left (x \right )\right )^{2} x \left (1+y\right )^{2}}{16} \\ \end{align*}	✗	✓	✓	✗	58.883
24628	13433	\begin{align*} y^{\prime }&=\lambda \arccos \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\ \end{align*}	✗	✓	✓	✗	58.923
24629	19863	\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	58.930
24630	870	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=3 x +4 \\ \end{align*}	✓	✓	✓	✓	58.976
24631	3188	\begin{align*} y^{\prime \prime }+2 y&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	58.977
24632	19290	\begin{align*} y^{\prime }&=\frac {x +y-1}{x +4 y+2} \\ \end{align*}	✓	✓	✓	✗	59.034
24633	4788	\begin{align*} y^{\prime } x +a_{0} +a_{1} x +\left (a_{2} +a_{3} x y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	59.109
24634	13378	\begin{align*} y^{\prime }&=\alpha y^{2}+\beta +\gamma \cos \left (\lambda x \right ) \\ \end{align*}	✓	✓	✓	✗	59.147
24635	10067	\begin{align*} y^{\prime }&=x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✗	59.366
24636	17244	\begin{align*} 5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	59.383
24637	13612	\begin{align*} y y^{\prime }+a \left (1+2 b \sqrt {x}\right ) {\mathrm e}^{2 b \sqrt {x}} y&=-a^{2} b \,x^{{3}/{2}} {\mathrm e}^{4 b \sqrt {x}} \\ \end{align*}	✗	✓	✗	✗	59.392
24638	1741	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= -5 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	59.409
24639	20527	\begin{align*} \left (-b \,x^{2}+a x \right ) y^{\prime \prime }+2 a y^{\prime }+2 b y&=0 \\ \end{align*}	✓	✓	✓	✗	59.500
24640	11935	\begin{align*} y^{\prime }&=\frac {2 a +x \sqrt {-y^{2}+4 a x}}{y} \\ \end{align*}	✗	✓	✓	✗	59.503
24641	13339	\begin{align*} \left (a \tanh \left (\lambda x \right )+b \right ) y^{\prime }&=y^{2}+c \tanh \left (\mu x \right ) y-d^{2}+c d \tanh \left (\mu x \right ) \\ \end{align*}	✓	✓	✓	✗	59.522
24642	4713	\begin{align*} y^{\prime }&=y \sqrt {a +b y} \\ \end{align*}	✓	✓	✓	✓	59.579
24643	7760	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-2 x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	59.582
24644	15361	\begin{align*} \frac {y y^{\prime }+x}{\sqrt {x^{2}+y^{2}}}&=m \\ \end{align*}	✓	✓	✓	✓	59.599
24645	19870	\begin{align*} y^{\prime \prime }&=\frac {1}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	59.641
24646	6598	\begin{align*} f \left (\frac {y^{\prime \prime }}{y^{\prime }}\right ) y^{\prime }&={y^{\prime }}^{2}-y y^{\prime \prime } \\ \end{align*}	✓	✓	✗	✗	59.673
24647	1838	\begin{align*} \left (x +1\right ) \left (2 x +3\right ) y^{\prime \prime }+2 \left (2+x \right ) y^{\prime }-2 y&=\left (2 x +3\right )^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	59.742
24648	6121	\begin{align*} 2 \left (1-x \right ) y-\left (-x^{2}+2\right ) y^{\prime }+\left (-x +2\right ) x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	59.747
24649	5982	\begin{align*} -\left (p^{2}+x^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	59.750
24650	13655	\begin{align*} y^{\prime }&=\frac {y^{3}}{\sqrt {a \,x^{2}+b x +c}}+y^{2} \\ \end{align*}	✗	✗	✗	✗	59.778
24651	12668	\begin{align*} y^{\prime \prime }&=\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {\left (a \,x^{4}+10 x^{2}+1\right ) y}{4 x^{6}} \\ \end{align*}	✓	✓	✓	✗	59.803
24652	13476	\begin{align*} y^{\prime }&=\lambda \sin \left (\lambda x \right ) y^{2}+f \left (x \right ) \cos \left (\lambda x \right ) y-f \left (x \right ) \\ \end{align*}	✓	✓	✗	✗	59.822
24653	13558	\begin{align*} y y^{\prime }&=\frac {3 y}{\sqrt {a \,x^{{3}/{2}}+8 x}}+1 \\ \end{align*}	✗	✓	✗	✗	59.869
24654	6130	\begin{align*} -3 y+\left (-x +2\right ) y^{\prime }+\left (-x +2\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	59.918
24655	11998	\begin{align*} y^{\prime }&=\frac {3 x^{4}+3 x^{3}+\sqrt {9 x^{4}-4 y^{3}}}{\left (x +1\right ) y^{2}} \\ \end{align*}	✗	✓	✓	✗	59.937
24656	4331	\begin{align*} 3+y+2 y^{2} \sin \left (x \right )^{2}+\left (x +2 y x -y \sin \left (2 x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	59.944
24657	12518	\begin{align*} \left (x^{2}+x -2\right ) y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }-\left (6 x^{2}+7 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	59.945
24658	8029	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=\ln \left (x +1\right )^{2}+x -1 \\ \end{align*}	✓	✓	✓	✗	59.949
24659	20601	\begin{align*} y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}}&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✗	✗	59.983
24660	7814	\begin{align*} y^{\prime \prime }-60 y^{\prime }-900 y&=5 \,{\mathrm e}^{10 x} \\ \end{align*}	✓	✓	✓	✓	60.026
24661	2595	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{t} t^{2} \\ \end{align*}	✓	✓	✓	✓	60.088
24662	13444	\begin{align*} y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+\lambda \operatorname {arccot}\left (x \right )^{n} \left (x^{1+k} y-1\right ) \\ \end{align*}	✓	✓	✗	✗	60.142
24663	4671	\begin{align*} y^{\prime }&=a \,x^{n}+b y^{2} \\ \end{align*}	✓	✓	✓	✗	60.286
24664	17902	\begin{align*} x^{2} y^{\prime } \cos \left (y\right )+1&=0 \\ y \left (\infty \right ) &= \frac {16 \pi }{3} \\ \end{align*}	✗	✓	✗	✗	60.288
24665	201	\begin{align*} {\mathrm e}^{y}+\cos \left (x \right ) y+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	60.323
24666	13215	\begin{align*} y^{\prime }&=a \,x^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{n +2 m} \\ \end{align*}	✓	✓	✓	✗	60.329
24667	16108	\begin{align*} y^{\prime \prime }+4 y&=t +{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	60.344
24668	3161	\begin{align*} 4 y+y^{\prime \prime }&=\sec \left (x \right ) \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	60.418
24669	14836	\begin{align*} t^{3} x^{\prime \prime }-\left (t^{3}+2 t^{2}-t \right ) x^{\prime }+\left (t^{2}+t -1\right ) x&=0 \\ \end{align*}	✓	✓	✓	✗	60.547
24670	10038	\begin{align*} y^{\prime \prime }+\frac {\left (t^{2}-1\right ) y^{\prime }}{t}+\frac {t^{2} y}{\left (1+{\mathrm e}^{\frac {t^{2}}{2}}\right )^{2}}&=0 \\ \end{align*}	✗	✓	✓	✗	60.556
24671	13917	\begin{align*} \left (x^{n}+a \right )^{2} y^{\prime \prime }+b \,x^{m} \left (x^{n}+a \right ) y^{\prime }-x^{-2+n} \left (b \,x^{m +1}+a n -a \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	60.676
24672	5980	\begin{align*} \left (b x +a \right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	60.683
24673	17052	\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (4\right ) &= -5 \\ \end{align*}	✓	✓	✓	✗	60.801
24674	4133	\begin{align*} y^{\prime \prime }+2 y&={\mathrm e}^{x}+2 \\ \end{align*}	✓	✓	✓	✓	60.841
24675	3163	\begin{align*} y^{\prime \prime }+9 y&=\sec \left (x \right ) \csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	60.887
24676	3639	\begin{align*} y^{\prime } x&=\sqrt {16 x^{2}-y^{2}}+y \\ \end{align*}	✓	✓	✓	✓	60.969
24677	5988	\begin{align*} \left (m +1\right ) x^{m} a \left (m \right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✓	60.973
24678	22500	\begin{align*} y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	61.002
24679	4134	\begin{align*} y^{\prime \prime }-y&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	61.051
24680	4130	\begin{align*} y^{\prime \prime }+y&=x^{3}+x \\ \end{align*}	✓	✓	✓	✓	61.120
24681	5979	\begin{align*} -a^{2} y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	61.138
24682	13268	\begin{align*} x^{3} y^{\prime }&=a \,x^{3} y^{2}+\left (b \,x^{2}+c \right ) y+s x \\ \end{align*}	✓	✓	✓	✗	61.177
24683	3486	\begin{align*} f^{\prime \prime }+6 f^{\prime }+9 f&={\mathrm e}^{-t} \\ f \left (0\right ) &= 0 \\ f^{\prime }\left (0\right ) &= \lambda \\ \end{align*}	✓	✓	✓	✓	61.238
24684	13431	\begin{align*} y^{\prime }&=\lambda \arccos \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arccos \left (x \right )^{n} y+b m \,x^{m -1} \\ \end{align*}	✓	✗	✗	✗	61.247
24685	5665	\begin{align*} y^{3} {y^{\prime }}^{3}-\left (1-3 x \right ) y^{2} {y^{\prime }}^{2}+3 x^{2} y y^{\prime }+x^{3}-y^{2}&=0 \\ \end{align*}	✗	✓	✗	✗	61.298
24686	19901	\begin{align*} y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	61.298
24687	6117	\begin{align*} -a y-\left (a -\left (2-a \right ) x \right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	61.300
24688	5981	\begin{align*} -\left (p^{2}-x^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	61.322
24689	18851	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{4}+2 y&=2 \cos \left (w t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	61.326
24690	5205	\begin{align*} x^{7} y y^{\prime }&=2 x^{2}+2+5 x^{3} y \\ \end{align*}	✗	✓	✓	✗	61.361
24691	20457	\begin{align*} \left (8 {y^{\prime }}^{3}-27\right ) x&=\frac {12 {y^{\prime }}^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	61.377
24692	18307	\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y&=x \\ \end{align*}	✓	✓	✓	✗	61.444
24693	14172	\begin{align*} x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	61.487
24694	4136	\begin{align*} y^{\prime \prime }-y&=4 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	61.563
24695	3653	\begin{align*} -y+y^{\prime } x&=\sqrt {4 x^{2}-y^{2}} \\ \end{align*}	✓	✓	✓	✓	61.646
24696	10023	\begin{align*} y^{\prime } x -y+y^{2}&=x^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✗	61.654
24697	7462	\begin{align*} 2 x +y^{2}-\cos \left (x +y\right )+\left (2 y x -\cos \left (x +y\right )-{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	61.655
24698	14152	\begin{align*} \left (2 x^{3}-1\right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 y x&=0 \\ \end{align*}	✓	✓	✓	✓	61.805
24699	6259	\begin{align*} -\left (a^{2}-k \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	61.885
24700	5985	\begin{align*} -\left (c \,x^{2}+b x +a \right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	61.946