2.3.248 Problems 24701 to 24800

Table 2.1045: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
24701	6998	\begin{align*} \left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	27.621
24702	2923	\begin{align*} x y^{2}+2 y+\left (2 y^{3}-x^{2} y+2 x \right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	27.622
24703	11536	\begin{align*} y^{2}-3 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	27.631
24704	20964	\begin{align*} y^{\prime }&=\frac {x +y+1}{2+x}-{\mathrm e}^{\frac {x +y+1}{2+x}} \\ \end{align*}	✓	✓	✓	✗	27.671
24705	4304	\begin{align*} y^{\prime }&=\frac {x \left (1+y^{2}\right )}{y \left (x^{2}+1\right )} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	27.682
24706	21066	\begin{align*} x +3 y+\left (3 x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	27.701
24707	11605	\begin{align*} \left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	27.715
24708	13281	\begin{align*} y^{\prime }&=a y^{2}+b \,{\mathrm e}^{\lambda x} \\ \end{align*}	✓	✓	✓	✗	27.743
24709	15170	\begin{align*} -\csc \left (x \right )^{2} y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	27.749
24710	6917	\begin{align*} x +2 y+\left (-1+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	27.772
24711	20435	\begin{align*} a^{2} y {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	27.797
24712	10071	\begin{align*} y^{\prime }&=x^{2}+y^{2}-1 \\ \end{align*}	✓	✓	✓	✗	27.811
24713	22415	\begin{align*} r^{\prime }&=\frac {r \sin \left (t \right )}{2 r \cos \left (t \right )-1} \\ \end{align*}	✓	✓	✓	✓	27.813
24714	18362	\begin{align*} y^{\prime \prime }+\alpha ^{2} y&=1 \\ y^{\prime }\left (0\right ) &= \alpha \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	27.816
24715	23223	\begin{align*} x^{2}+y^{2}-2 y y^{\prime } x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	27.832
24716	13836	\begin{align*} \left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (d x +k \right ) y^{\prime }+\left (d -2 a \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	27.875
24717	18535	\begin{align*} y \cos \left (t \right )+\sin \left (t \right ) y^{\prime }&={\mathrm e}^{t} \\ y \left (1\right ) &= a \\ \end{align*}	✓	✓	✓	✓	27.888
24718	13253	\begin{align*} x^{2} y^{\prime }&=c \,x^{2} y^{2}+\left (a \,x^{2}+b x \right ) y+\alpha \,x^{2}+\beta x +\gamma \\ \end{align*}	✗	✓	✓	✗	27.891
24719	18609	\begin{align*} t^{2} y^{\prime }+2 t y-y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	27.907
24720	6983	\begin{align*} y^{\prime }+\frac {y}{x}&=\frac {y^{2}}{x} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	27.909
24721	26199	\begin{align*} y^{\prime }&=-\sin \left (2 x -y\right ) \\ \end{align*}	✓	✓	✓	✓	27.914
24722	13792	\begin{align*} x^{2} y^{\prime \prime }+\lambda x y^{\prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	27.955
24723	22423	\begin{align*} y^{\prime }&=\frac {2 \sin \left (2 x \right )-\tan \left (y\right )}{x \sec \left (y\right )^{2}} \\ y \left (\pi \right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✗	✓	✗	27.957
24724	18604	\begin{align*} y y^{\prime } x&=x^{2}+y^{2} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	27.968
24725	2913	\begin{align*} x +y+\left (x -2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	27.969
24726	2927	\begin{align*} y^{2} \csc \left (x \right )^{2}+6 y x -2&=\left (2 \cot \left (x \right ) y-3 x^{2}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	27.985
24727	17277	\begin{align*} y^{2}&=\left (t y-4 t^{2}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	27.986
24728	11657	\begin{align*} \left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }-\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	28.025
24729	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*}	✓	✓	✓	✗	28.066
24730	24331	\begin{align*} \cos \left (y\right ) \sin \left (2 x \right )+\left (\cos \left (y\right )^{2}-\cos \left (x \right )^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	28.069
24731	18620	\begin{align*} y^{\prime }&=\frac {x y^{2}-\frac {\sin \left (2 x \right )}{2}}{\left (-x^{2}+1\right ) y} \\ \end{align*}	✓	✓	✓	✓	28.072
24732	11868	\begin{align*} y^{\prime }&=F \left (\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )\right ) y \\ \end{align*}	✗	✓	✓	✗	28.080
24733	11540	\begin{align*} x \left (x +2 y-1\right ) y^{\prime }-\left (2 x +y+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	28.085
24734	21328	\begin{align*} -x^{\prime \prime }&=2 x-x^{2} \\ x \left (0\right ) &= 0 \\ x \left (\pi \right ) &= 0 \\ \end{align*}	✗	✓	✗	✗	28.095
24735	25044	\begin{align*} y^{\prime }&=t +y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	28.122
24736	11541	\begin{align*} y \left (2 x -y-1\right )+x \left (2 y-x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	28.151
24737	26165	\begin{align*} y^{\prime }&=\frac {y}{\left (\ln \left (x \right )-\ln \left (y\right )\right ) x} \\ \end{align*}	✓	✓	✓	✓	28.154
24738	5415	\begin{align*} {y^{\prime }}^{2}-2 y y^{\prime }-2 x&=0 \\ \end{align*}	✓	✓	✓	✗	28.175
24739	9151	\begin{align*} x -y-\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	28.175
24740	4239	\begin{align*} y y^{\prime } x&=2 x^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✓	28.187
24741	2524	\begin{align*} y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	28.221
24742	15850	\begin{align*} \theta ^{\prime }&=\frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \\ \theta \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	28.224
24743	5702	\begin{align*} \ln \left (y^{\prime }\right )+y^{\prime } x +a +b y&=0 \\ \end{align*}	✓	✓	✓	✓	28.239
24744	5467	\begin{align*} x {y^{\prime }}^{2}-\left (3 x -y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	28.296
24745	26410	\begin{align*} \sqrt {x^{2}+1}+n y+\left (\sqrt {1+y^{2}}+x n \right ) y^{\prime }&=0 \\ y \left (0\right ) &= n \\ \end{align*}	✓	✓	✓	✗	28.324
24746	7252	\begin{align*} y^{2}-y x +\left (y x +x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	28.339
24747	7558	\begin{align*} 2 y^{2}+4 x^{2}-y y^{\prime } x&=0 \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	28.346
24748	17987	\begin{align*} 3 y^{2}-x +\left (2 y^{3}-6 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	28.355
24749	17320	\begin{align*} y-t +\left (y+t \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	28.358
24750	3029	\begin{align*} 2 y^{\prime } x -y+\frac {x^{2}}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	28.415
24751	6805	\begin{align*} \left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }&=\left (a +3 y^{\prime }\right ) {y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	28.435
24752	13808	\begin{align*} x^{2} y^{\prime \prime }+x \left (2 x^{n} a +b \right ) y^{\prime }+\left (a^{2} x^{2 n}+a \left (b +n -1\right ) x^{n}+\alpha \,x^{2 m}+\beta \,x^{m}+\gamma \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	28.470
24753	2525	\begin{align*} y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\ y \left (1\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	28.485
24754	6808	\begin{align*} y^{\prime \prime } y^{\prime \prime \prime }&=a \sqrt {1+b^{2} {y^{\prime \prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	28.488
24755	17340	\begin{align*} \cos \left (t -y\right )+\left (1-\cos \left (t -y\right )\right ) y^{\prime }&=0 \\ y \left (\pi \right ) &= \pi \\ \end{align*}	✓	✓	✓	✓	28.492
24756	21279	\begin{align*} t^{2} x^{\prime \prime }+t x^{\prime }+t^{2} x&=\lambda x \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✗	✗	✓	✓	28.497
24757	9149	\begin{align*} x \sin \left (\frac {y}{x}\right ) y^{\prime }&=y \sin \left (\frac {y}{x}\right )+x \\ \end{align*}	✓	✓	✓	✓	28.507
24758	2526	\begin{align*} y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	28.523
24759	19938	\begin{align*} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	28.553
24760	5135	\begin{align*} \left (y x +1\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	28.561
24761	2350	\begin{align*} y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\ y \left (1\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	28.571
24762	5422	\begin{align*} {y^{\prime }}^{2}-a y y^{\prime }-a x&=0 \\ \end{align*}	✓	✓	✓	✗	28.578
24763	12132	\begin{align*} y^{\prime }&=\frac {b^{3}+y^{2} b^{3}+2 a \,b^{2} x y+b \,x^{2} a^{2}+b^{3} y^{3}+3 a \,b^{2} x y^{2}+3 a^{2} b \,x^{2} y+a^{3} x^{3}}{b^{3}} \\ \end{align*}	✓	✓	✓	✗	28.582
24764	11484	\begin{align*} x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\ \end{align*}	✗	✓	✓	✗	28.588
24765	7488	\begin{align*} 2 x +2 y+2 x^{3} y+4 y^{2} x^{2}+\left (2 x +x^{4}+2 x^{3} y\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✓	✗	28.603
24766	21826	\begin{align*} x^{2} y^{\prime }-y x&=x^{2}-y^{2} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	28.634
24767	17348	\begin{align*} y^{\prime }&=\frac {t}{y^{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	28.640
24768	13645	\begin{align*} y^{\prime }&=a \,x^{2 n +1} y^{3}+b \,x^{-n -2} \\ \end{align*}	✓	✓	✓	✗	28.652
24769	26327	\begin{align*} \frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}}&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	28.658
24770	20239	\begin{align*} \left (\sin \left (y\right )+y \cos \left (y\right )\right ) y^{\prime }-\left (2 \ln \left (x \right )+1\right ) x&=0 \\ \end{align*}	✓	✓	✓	✓	28.664
24771	17319	\begin{align*} 3 t +\left (t -4 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	28.674
24772	7031	\begin{align*} 2 y y^{\prime } x +3 x^{2}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	28.688
24773	21838	\begin{align*} x y \left (y^{\prime } x +y\right )&=4 x^{3} \\ \end{align*}	✓	✓	✓	✓	28.701
24774	24277	\begin{align*} y \left (x +3 y\right )+x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	28.701
24775	12168	\begin{align*} y^{\prime }&=\frac {6 x^{2} y-2 x +1-5 x^{3} y^{2}-2 y x +y^{3} x^{4}}{x^{2} \left (x^{2} y-x +1\right )} \\ \end{align*}	✓	✓	✓	✗	28.709
24776	20973	\begin{align*} y^{\prime }&=\frac {2 y \left (-1+y\right )}{x \left (2-y\right )} \\ \end{align*}	✓	✓	✓	✓	28.710
24777	19709	\begin{align*} \sqrt {y^{\prime }+y}&=\left (y^{\prime \prime }+2 x \right )^{{1}/{4}} \\ \end{align*}	✗	✗	✗	✗	28.725
24778	12133	\begin{align*} y^{\prime }&=\frac {\alpha ^{3}+y^{2} \alpha ^{3}+2 y \alpha ^{2} \beta x +\alpha \,\beta ^{2} x^{2}+y^{3} \alpha ^{3}+3 y^{2} \alpha ^{2} \beta x +3 y \alpha \,\beta ^{2} x^{2}+\beta ^{3} x^{3}}{\alpha ^{3}} \\ \end{align*}	✓	✓	✓	✗	28.728
24779	14531	\begin{align*} y^{\prime }&=\frac {2 x^{2}+y^{2}}{2 y x -x^{2}} \\ \end{align*}	✓	✓	✓	✓	28.773
24780	8674	\begin{align*} \frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}}&=0 \\ \end{align*}	✓	✓	✓	✓	28.813
24781	24202	\begin{align*} 2 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	28.841
24782	4324	\begin{align*} y^{\prime }&=\left (x +1\right )^{2}+\left (4 y+1\right )^{2}+8 y x +1 \\ \end{align*}	✓	✓	✓	✓	28.850
24783	12139	\begin{align*} y^{\prime }&=\frac {a^{3}+y^{2} a^{3}+2 a^{2} b x y+b^{2} x^{2} a +y^{3} a^{3}+3 a^{2} b x y^{2}+3 a \,b^{2} x^{2} y+b^{3} x^{3}}{a^{3}} \\ \end{align*}	✓	✓	✓	✗	28.858
24784	13553	\begin{align*} y y^{\prime }-y&=a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}} \\ \end{align*}	✗	✗	✗	✗	28.864
24785	6065	\begin{align*} \left (b \,x^{2}+a \right ) y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	28.874
24786	12409	\begin{align*} 2 a x y^{\prime \prime }+\left (b x +a \right ) y^{\prime }+c y&=0 \\ \end{align*}	✗	✓	✓	✗	28.880
24787	20439	\begin{align*} x +y y^{\prime }&=a {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	28.891
24788	6835	\begin{align*} 2 x -y+1+\left (2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	28.902
24789	17282	\begin{align*} t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	28.904
24790	4318	\begin{align*} \left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	28.943
24791	5109	\begin{align*} \left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y&=0 \\ \end{align*}	✗	✓	✓	✗	28.955
24792	7441	\begin{align*} \left ({\mathrm e}^{4 y}+2 x \right ) y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	29.021
24793	20246	\begin{align*} \left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y-\left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	29.024
24794	15016	\begin{align*} 12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	29.036
24795	21827	\begin{align*} y&=\left (2 x^{2} y^{3}-x \right ) y^{\prime } \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✗	✗	✗	29.046
24796	23958	\begin{align*} x^{2} y+2 y^{3}-\left (2 x^{3}+3 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	29.053
24797	18287	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right ) \\ y \left (-\infty \right ) &= 0 \\ \end{align*}	✗	✓	✗	✓	29.085
24798	23294	\begin{align*} \cos \left (x \right ) y^{\prime \prime }+3 y&=1 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✗	✓	✗	29.102
24799	5116	\begin{align*} \left (3+9 x +21 y\right ) y^{\prime }&=45+7 x -5 y \\ \end{align*}	✓	✓	✓	✓	29.120
24800	19725	\begin{align*} y^{\prime }+\frac {y}{x}&=\frac {\sin \left (x \right )}{y^{3}} \\ \end{align*}	✓	✓	✓	✓	29.137