2.3.247 Problems 24601 to 24700

Table 2.1067: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
24601	25872	\begin{align*} x y^{\prime }+y&=3 x^{3} y^{2} \\ \end{align*}	✓	✓	✓	✓	14.421
24602	14001	\begin{align*} \frac {x y^{\prime }-y}{\sqrt {x^{2}-y^{2}}}&=x y^{\prime } \\ \end{align*}	✓	✓	✓	✗	14.428
24603	200	\begin{align*} x y^{\prime }&=6 y+12 x^{4} y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	14.431
24604	2938	\begin{align*} \left (-2 y x +x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	14.432
24605	1685	\begin{align*} 4 x +7 y+\left (3 x +4 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.451
24606	21166	\begin{align*} x x^{\prime \prime }-2 {x^{\prime }}^{2}-x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	14.452
24607	15529	\begin{align*} y^{\prime }&=4-y^{2} \\ \end{align*}	✓	✓	✓	✓	14.454
24608	19670	\begin{align*} x^{\prime }&=\tan \left (x\right ) \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	14.457
24609	11524	\begin{align*} \left (4 y-3 x -5\right ) y^{\prime }-3 y+7 x +2&=0 \\ \end{align*}	✓	✓	✓	✓	14.461
24610	17091	\begin{align*} x \sin \left (x^{2}\right )&=\frac {\cos \left (\sqrt {y}\right ) y^{\prime }}{\sqrt {y}} \\ \end{align*}	✓	✓	✓	✓	14.462
24611	19770	\begin{align*} 1+{y^{\prime }}^{2}+\frac {m y^{\prime \prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=0 \\ \end{align*}	✓	✓	✓	✗	14.468
24612	18508	\begin{align*} y^{\prime }&=\frac {t y \left (4-y\right )}{t +1} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	14.471
24613	3554	\begin{align*} 2 x \left (2 x +y\right ) y^{\prime }&=y \left (4 x -y\right ) \\ \end{align*}	✓	✓	✓	✓	14.490
24614	5102	\begin{align*} \left (3+2 x +4 y\right ) y^{\prime }&=x +2 y+1 \\ \end{align*}	✓	✓	✓	✓	14.498
24615	19721	\begin{align*} \frac {2 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	14.498
24616	27518	\begin{align*} x y y^{\prime }-x^{2} \sqrt {1+y^{2}}&=\left (x +1\right ) \left (1+y^{2}\right ) \\ \end{align*}	✗	✓	✓	✓	14.511
24617	4931	\begin{align*} \left (a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	14.516
24618	6580	\begin{align*} 4 y {y^{\prime }}^{2} y^{\prime \prime }&=3+{y^{\prime }}^{4} \\ \end{align*}	✓	✓	✓	✗	14.526
24619	5124	\begin{align*} x y y^{\prime }&=x +y^{2} \\ \end{align*}	✓	✓	✓	✓	14.530
24620	7923	\begin{align*} \left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime }&=2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✗	14.530
24621	14454	\begin{align*} 4 x +3 y^{2}+2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.530
24622	7348	\begin{align*} \left (2 x +y\right ) y^{\prime }-x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	14.533
24623	4906	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=x \left (3 x^{2}-y\right ) \\ \end{align*}	✓	✓	✓	✓	14.553
24624	15637	\begin{align*} y^{\prime }&=\frac {y}{-x +y} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	14.573
24625	8403	\begin{align*} y^{\prime }&=x \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	14.575
24626	2877	\begin{align*} x^{2}+y^{2}&=x y y^{\prime } \\ \end{align*}	✓	✓	✓	✓	14.587
24627	21390	\begin{align*} x +y-\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.587
24628	9165	\begin{align*} {\mathrm e}^{\frac {x}{y}}-\frac {y y^{\prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	14.589
24629	24154	\begin{align*} x^{2}+2 y^{2}-x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.590
24630	2971	\begin{align*} 2 y&=\left (y^{4}+x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	14.592
24631	14714	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+4 y&=2 x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	14.594
24632	8380	\begin{align*} x y^{\prime }&=y^{2}-y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	14.598
24633	24314	\begin{align*} y^{3}-x^{3}&=x y \left (y y^{\prime }+x \right ) \\ \end{align*}	✓	✓	✓	✗	14.602
24634	15058	\begin{align*} x y^{\prime }-y^{2} \ln \left (x \right )+y&=0 \\ \end{align*}	✓	✓	✓	✓	14.608
24635	27162	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=x_{3} \\ x_{3}^{\prime }&=x_{4} \\ x_{4}^{\prime }&=-x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✗	14.612
24636	26275	\begin{align*} x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.622
24637	4945	\begin{align*} \left (x -a \right ) \left (x -b \right ) y^{\prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	14.625
24638	12235	\begin{align*} y^{\prime }&=\frac {-150 x^{3} y+60 x^{6}+350 x^{{7}/{2}}-150 x^{3}-125 y \sqrt {x}+250 x -125 \sqrt {x}-125 y^{3}+150 x^{3} y^{2}+750 y^{2} \sqrt {x}-60 x^{6} y-600 y x^{{7}/{2}}-1500 y x +8 x^{9}+120 x^{{13}/{2}}+600 x^{4}+1000 x^{{3}/{2}}}{25 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \\ \end{align*}	✓	✓	✓	✗	14.628
24639	6457	\begin{align*} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	14.629
24640	4905	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=x \left (x^{2}+1\right )-y x \\ \end{align*}	✓	✓	✓	✓	14.639
24641	22333	\begin{align*} y^{\prime }&=y^{p} \\ \end{align*}	✓	✓	✓	✓	14.644
24642	4334	\begin{align*} y \left (2 x -y+2\right )+2 \left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.654
24643	12858	\begin{align*} y^{\prime \prime }+3 a y^{\prime }-2 y^{3}+2 a^{2} y&=0 \\ \end{align*}	✗	✓	✓	✗	14.662
24644	15553	\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ \end{align*}	✓	✓	✓	✓	14.672
24645	21990	\begin{align*} y^{\prime }&=\frac {x y^{2}}{x^{2} y+y^{3}} \\ \end{align*}	✓	✓	✓	✓	14.697
24646	20685	\begin{align*} 2 x +y+1+\left (4 x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.701
24647	5204	\begin{align*} 3 x^{4} y y^{\prime }&=1-2 x^{3} y^{2} \\ \end{align*}	✓	✓	✓	✓	14.707
24648	5851	\begin{align*} \left (a \cot \left (x \right )^{2}+b \cot \left (x \right ) \csc \left (x \right )+c \csc \left (x \right )^{2}\right ) y+k \cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	14.707
24649	27458	\begin{align*} \left (\cos \left (x \right )-x \sin \left (x \right )\right ) y+\left (x \cos \left (x \right )-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	14.710
24650	4394	\begin{align*} 2 x y^{\prime }-y&=\ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	14.717
24651	24299	\begin{align*} \sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\ y \left (0\right ) &= -\frac {\sqrt {3}}{2} \\ \end{align*}	✓	✓	✓	✗	14.724
24652	7568	\begin{align*} y^{\prime }&=\frac {\sqrt {x^{2}+y^{2}}-x}{y} \\ \end{align*}	✓	✓	✓	✓	14.728
24653	4237	\begin{align*} x y y^{\prime }&=\sqrt {y^{2}-9} \\ y \left ({\mathrm e}^{4}\right ) &= 5 \\ \end{align*}	✓	✓	✓	✗	14.737
24654	26671	\begin{align*} 2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y&=\frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}} \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✗	✓	✗	✗	14.738
24655	5131	\begin{align*} x y y^{\prime }&=a \,x^{n}+b y^{2} \\ \end{align*}	✓	✓	✓	✗	14.744
24656	4829	\begin{align*} x y^{\prime }&=\left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y \\ \end{align*}	✓	✓	✓	✓	14.752
24657	804	\begin{align*} y^{\prime }&=\frac {x +3 y}{y-3 x} \\ \end{align*}	✓	✓	✓	✓	14.753
24658	18844	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	14.755
24659	22377	\begin{align*} y^{\prime }&=\frac {4 y^{2}-x^{4}}{4 y x} \\ \end{align*}	✓	✓	✓	✓	14.757
24660	12461	\begin{align*} -y+x \left (x +3\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✓	14.762
24661	6269	\begin{align*} \left (c \,x^{2}+b x +a \right ) y+x^{2} \left (1-x \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	14.769
24662	5272	\begin{align*} x \left (x +6 y^{2}\right ) y^{\prime }+y x -3 y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	14.771
24663	18560	\begin{align*} y^{\prime }&=2 t y^{2} \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	14.780
24664	13482	\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}-f \left (x \right ) g \left (x \right ) y+g^{\prime }\left (x \right ) \\ \end{align*}	✓	✗	✗	✗	14.788
24665	5133	\begin{align*} x y y^{\prime }+x^{2} \operatorname {arccot}\left (\frac {y}{x}\right )-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	14.790
24666	1160	\begin{align*} y^{\prime }&=\frac {4 y-3 x}{2 x -y} \\ \end{align*}	✓	✓	✓	✓	14.795
24667	12237	\begin{align*} y^{\prime }&=\frac {y \left (-1-x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}}-x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} \ln \left (x \right )+x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y+2 x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y \ln \left (x \right )+x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y \ln \left (x \right )^{2}\right )}{\left (1+\ln \left (x \right )\right ) x} \\ \end{align*}	✗	✓	✓	✓	14.797
24668	22448	\begin{align*} y^{\prime }+\frac {y}{x}&=1 \\ \end{align*}	✓	✓	✓	✓	14.799
24669	12155	\begin{align*} y^{\prime }&=-\frac {-y x -y+x^{5} \sqrt {x^{2}+y^{2}}-x^{4} \sqrt {x^{2}+y^{2}}\, y}{x \left (x +1\right )} \\ \end{align*}	✗	✓	✓	✗	14.825
24670	13698	\begin{align*} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	14.829
24671	15031	\begin{align*} y^{\prime }&=\frac {y}{y^{3}+x} \\ \end{align*}	✓	✓	✓	✗	14.829
24672	2850	\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	14.834
24673	21423	\begin{align*} 3 x^{2} y+\left (y^{4}-x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.838
24674	19336	\begin{align*} x y^{\prime }+y+x^{2} y^{5} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.852
24675	17262	\begin{align*} y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{t +y}&=0 \\ \end{align*}	✓	✓	✓	✗	14.856
24676	4664	\begin{align*} y^{\prime }&=\left (3+x -4 y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	14.872
24677	13445	\begin{align*} y^{\prime }&=\lambda \operatorname {arccot}\left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \operatorname {arccot}\left (x \right )^{n} \\ \end{align*}	✓	✓	✓	✗	14.887
24678	16299	\begin{align*} 3 y^{\prime }+\frac {2 y}{x}&=4 \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	14.889
24679	5583	\begin{align*} \left (a^{2} x^{2}-y^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+x^{2} \left (a^{2}-1\right )&=0 \\ \end{align*}	✓	✓	✓	✗	14.899
24680	4242	\begin{align*} x^{2} y^{\prime }&=3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+y x \\ \end{align*}	✓	✓	✓	✓	14.914
24681	21796	\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	14.915
24682	12212	\begin{align*} y^{\prime }&=\frac {\left (27 y^{3}+27 \,{\mathrm e}^{3 x^{2}} y+18 \,{\mathrm e}^{3 x^{2}} y^{2}+3 y^{3} {\mathrm e}^{3 x^{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y+9 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y^{2}+{\mathrm e}^{\frac {9 x^{2}}{2}} y^{3}\right ) {\mathrm e}^{3 x^{2}} x \,{\mathrm e}^{-\frac {9 x^{2}}{2}}}{243 y} \\ \end{align*}	✓	✓	✓	✗	14.927
24683	21806	\begin{align*} x^{3}-y^{3}+x y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.930
24684	5237	\begin{align*} \left (1-3 x -y\right )^{2} y^{\prime }&=\left (-2 y+1\right ) \left (3-6 x -4 y\right ) \\ \end{align*}	✓	✓	✓	✗	14.933
24685	6915	\begin{align*} 7 y-3+\left (2 x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.941
24686	7715	\begin{align*} y-3 x +\left (3 x +4 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.953
24687	21397	\begin{align*} y+\sqrt {x^{2}+y^{2}}-x y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	14.957
24688	13026	\begin{align*} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	14.962
24689	5596	\begin{align*} \left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-3 a^{2} x y y^{\prime }-a^{2} x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	14.963
24690	12390	\begin{align*} x y^{\prime \prime }-2 \left (x^{2}-a \right ) y^{\prime }+2 n x y&=0 \\ \end{align*}	✗	✓	✓	✗	14.963
24691	18059	\begin{align*} x -y+2+\left (x -y+3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.971
24692	5325	\begin{align*} 2 x \left (x^{3}+y^{4}\right ) y^{\prime }&=\left (x^{3}+2 y^{4}\right ) y \\ \end{align*}	✓	✓	✓	✗	14.973
24693	4404	\begin{align*} x y^{\prime }-y&=x \tan \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	14.982
24694	12463	\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}-2 x \right ) y^{\prime }-\left (x +a \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	14.985
24695	5111	\begin{align*} 3 \left (x +2 y\right ) y^{\prime }&=-2 y-x +1 \\ \end{align*}	✓	✓	✓	✓	14.990
24696	14193	\begin{align*} x^{\prime }&=-\frac {t}{x} \\ \end{align*}	✓	✓	✓	✓	14.992
24697	11967	\begin{align*} y^{\prime }&=\frac {y+\sqrt {x^{2}+y^{2}}\, x^{2}}{x} \\ \end{align*}	✗	✓	✓	✗	15.028
24698	11635	\begin{align*} x \left (3 \,{\mathrm e}^{y x}+2 \,{\mathrm e}^{-y x}\right ) \left (x y^{\prime }+y\right )+1&=0 \\ \end{align*}	✓	✓	✓	✓	15.047
24699	1707	\begin{align*} y^{\prime }+\frac {2 y}{x}&=-\frac {2 x y}{x^{2}+2 x^{2} y+1} \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✗	15.056
24700	18306	\begin{align*} \left (x +1\right )^{3} y^{\prime \prime }+3 \left (x +1\right )^{2} y^{\prime }+\left (x +1\right ) y&=6 \ln \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✗	15.056