2.3.238 Problems 23701 to 23800

Table 2.1019: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
23701	11550	\begin{align*} x \left (y x -2\right ) y^{\prime }+x^{2} y^{3}+x y^{2}-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	19.480
23702	11774	\begin{align*} y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	19.480
23703	5087	\begin{align*} \left (3+2 x -2 y\right ) y^{\prime }&=1+6 x -2 y \\ \end{align*}	✓	✓	✓	✓	19.486
23704	3286	\begin{align*} 1+\left (2 y-x^{2}\right ) {y^{\prime }}^{2}-2 x^{2} y {y^{\prime }}^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	19.492
23705	4803	\begin{align*} y^{\prime } x&=4 y-4 \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	19.517
23706	7247	\begin{align*} \left (x -y\right ) y^{\prime }+x +y+1&=0 \\ \end{align*}	✓	✓	✓	✓	19.519
23707	14916	\begin{align*} x^{\prime }&=k x-x^{2} \\ \end{align*}	✓	✓	✓	✓	19.528
23708	3638	\begin{align*} \sin \left (\frac {y}{x}\right ) \left (-y+y^{\prime } x \right )&=x \cos \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	19.582
23709	20690	\begin{align*} y^{\prime }+x \sin \left (2 y\right )&=x^{3} \cos \left (y\right )^{2} \\ \end{align*}	✓	✓	✓	✗	19.586
23710	11445	\begin{align*} x^{2} y^{\prime }+x y^{3}+a y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	19.594
23711	12491	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -v \left (v -1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	19.614
23712	8684	\begin{align*} \left (x +2 y\right ) y^{\prime }&=1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	19.644
23713	5749	\begin{align*} \left (x^{4}+\operatorname {a1} \,x^{2}+\operatorname {a0} \right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	19.668
23714	13875	\begin{align*} x^{4} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a \,x^{n -1}+a b \,x^{-2+n}+b^{2}\right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	19.677
23715	5358	\begin{align*} {y^{\prime }}^{2}+x^{2}&=4 y \\ \end{align*}	✓	✓	✓	✗	19.694
23716	12115	\begin{align*} y^{\prime }&=-\frac {-y+x^{4} \sqrt {x^{2}+y^{2}}-x^{3} \sqrt {x^{2}+y^{2}}\, y}{x} \\ \end{align*}	✗	✓	✓	✗	19.696
23717	18733	\begin{align*} y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+3 y \ln \left (t \right )&=0 \\ y \left (2\right ) &= 3 \\ y^{\prime }\left (2\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	19.705
23718	6814	\begin{align*} y^{\prime }&=\frac {x y}{x^{2}-y^{2}} \\ \end{align*}	✓	✓	✓	✓	19.707
23719	4829	\begin{align*} y^{\prime } x&=\left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y \\ \end{align*}	✓	✓	✓	✓	19.710
23720	25006	\begin{align*} y^{\prime }&=\frac {y^{2}+2 t y}{t^{2}+t y} \\ \end{align*}	✓	✓	✓	✗	19.714
23721	20834	\begin{align*} x^{2}-y x +y^{2}-y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	19.719
23722	16476	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ y \left (\sqrt {\pi }\right ) &= 3 \\ y^{\prime }\left (\sqrt {\pi }\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	19.734
23723	21840	\begin{align*} \left (1+{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	19.752
23724	13631	\begin{align*} x \left (2 a x y+b \right ) y^{\prime }&=-a \left (m +3\right ) x y^{2}-b \left (m +2\right ) y+c \,x^{m} \\ \end{align*}	✓	✓	✓	✗	19.772
23725	19287	\begin{align*} y^{\prime }&=\frac {x +y+4}{x -y-6} \\ \end{align*}	✓	✓	✓	✓	19.774
23726	21839	\begin{align*} y^{3} \left (x +y y^{\prime }\right )&=\left (x^{2}+y^{2}\right )^{3} y^{\prime } \\ \end{align*}	✓	✗	✗	✗	19.784
23727	14024	\begin{align*} x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	19.794
23728	19144	\begin{align*} a^{3} y^{\prime \prime \prime } y^{\prime \prime }&=\sqrt {1+c^{2} {y^{\prime \prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	19.796
23729	24220	\begin{align*} y^{2} \left (-x^{2}+1\right )+x \left (y^{2} x^{2}+2 x +y\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	19.808
23730	23193	\begin{align*} y^{\prime }&=\frac {y-x +1}{3-x +y} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	19.809
23731	14050	\begin{align*} 2 y^{\prime } x -y+\ln \left (y^{\prime }\right )&=0 \\ \end{align*}	✓	✓	✓	✓	19.819
23732	2985	\begin{align*} y y^{\prime } x&=x^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✓	19.823
23733	11413	\begin{align*} y^{\prime } x +a \sqrt {x^{2}+y^{2}}-y&=0 \\ \end{align*}	✓	✓	✓	✗	19.823
23734	13400	\begin{align*} y^{\prime }&=y^{2}+a \lambda +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2} \\ \end{align*}	✗	✓	✗	✗	19.838
23735	6904	\begin{align*} {\mathrm e}^{\frac {y}{x}} x -y \sin \left (\frac {y}{x}\right )+x \sin \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	19.841
23736	12874	\begin{align*} y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b \sin \left (y\right )&=0 \\ \end{align*}	✗	✗	✗	✗	19.865
23737	20127	\begin{align*} y^{\prime \prime }&=\frac {1}{\sqrt {a y}} \\ \end{align*}	✓	✓	✓	✗	19.872
23738	6906	\begin{align*} {\mathrm e}^{\frac {y}{x}} x +y&=y^{\prime } x \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	19.874
23739	20693	\begin{align*} \left (x y \sin \left (y x \right )+\cos \left (y x \right )\right ) y+\left (x y \sin \left (y x \right )-\cos \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	19.892
23740	16683	\begin{align*} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=\frac {10}{x} \\ \end{align*}	✓	✓	✓	✓	19.905
23741	15646	\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✗	19.925
23742	15360	\begin{align*} \frac {-y^{\prime } x +y}{\sqrt {x^{2}+y^{2}}}&=m \\ \end{align*}	✓	✓	✓	✗	19.930
23743	12035	\begin{align*} y^{\prime }&=\frac {\left (x +1+x^{4} \ln \left (y\right )\right ) y \ln \left (y\right )}{x \left (x +1\right )} \\ \end{align*}	✗	✓	✓	✓	19.987
23744	14536	\begin{align*} 4 y y^{\prime } x&=1+y^{2} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	20.026
23745	4082	\begin{align*} x -2 y-3+\left (2 x +y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.032
23746	4351	\begin{align*} y^{2}+\left (y x +\tan \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.038
23747	12109	\begin{align*} y^{\prime }&=-\frac {-y+x^{3} \sqrt {x^{2}+y^{2}}-x^{2} \sqrt {x^{2}+y^{2}}\, y}{x} \\ \end{align*}	✗	✓	✓	✗	20.040
23748	6808	\begin{align*} y^{\prime \prime } y^{\prime \prime \prime }&=a \sqrt {1+b^{2} {y^{\prime \prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	20.049
23749	11514	\begin{align*} \left (1-2 x +y\right ) y^{\prime }+y+x&=0 \\ \end{align*}	✓	✓	✓	✓	20.050
23750	11498	\begin{align*} y^{\prime } \sin \left (2 x \right )+\sin \left (2 y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	20.057
23751	24349	\begin{align*} 2 x +3 y-5+\left (3 x -y-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.060
23752	21608	\begin{align*} \frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+y x +y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✗	✗	20.091
23753	14027	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\ \end{align*}	✓	✓	✓	✓	20.093
23754	20823	\begin{align*} \sin \left (y x \right )+x y \cos \left (y x \right )+x^{2} \cos \left (y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.109
23755	1701	\begin{align*} 7 x +4 y+\left (4 x +3 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.121
23756	13637	\begin{align*} y^{\prime }&=a y^{3}+\frac {b}{x^{{3}/{2}}} \\ \end{align*}	✓	✓	✓	✗	20.122
23757	4710	\begin{align*} y^{\prime }+x^{3}&=x \sqrt {x^{4}+4 y} \\ \end{align*}	✓	✓	✓	✓	20.123
23758	12596	\begin{align*} y^{\prime \prime }&=-\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (x -1\right )}+\frac {v \left (v +1\right ) y}{4 x^{2}} \\ \end{align*}	✗	✓	✓	✗	20.123
23759	14155	\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} \left (x +1\right ) y^{\prime }+n^{2} y&=0 \\ \end{align*}	✗	✓	✗	✗	20.143
23760	8674	\begin{align*} \frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}}&=0 \\ \end{align*}	✓	✓	✓	✓	20.144
23761	19373	\begin{align*} y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✗	20.151
23762	16686	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 \sqrt {x} \\ \end{align*}	✓	✓	✓	✓	20.155
23763	14235	\begin{align*} x^{\prime }&=\frac {t^{2}}{1-x^{2}} \\ x \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	20.166
23764	15016	\begin{align*} 12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.189
23765	13973	\begin{align*} \left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	20.230
23766	4401	\begin{align*} y^{\prime }&={\mathrm e}^{\frac {x y^{\prime }}{y}} \\ \end{align*}	✓	✓	✓	✗	20.246
23767	11889	\begin{align*} y^{\prime }&=-\left (-{\mathrm e}^{-x^{2}}+x^{2} {\mathrm e}^{-x^{2}}-F \left (y-\frac {x^{2} {\mathrm e}^{-x^{2}}}{2}\right )\right ) x \\ \end{align*}	✗	✓	✓	✗	20.252
23768	19069	\begin{align*} y^{\prime }&=\frac {2 y x}{x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	20.257
23769	19389	\begin{align*} y^{2}-3 y x -2 x^{2}&=\left (x^{2}-y x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	20.269
23770	2554	\begin{align*} t^{2} y^{\prime \prime }+5 y^{\prime } t -2 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	20.292
23771	26256	\begin{align*} x^{2} y^{\prime }+\sin \left (2 y\right )&=1 \\ y \left (\infty \right ) &= \frac {11 \pi }{4} \\ \end{align*}	✗	✓	✗	✓	20.300
23772	7744	\begin{align*} 2 y y^{\prime } x&=x^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✓	20.307
23773	6918	\begin{align*} 3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.332
23774	1658	\begin{align*} y^{\prime }&=\frac {x +2 y}{2 x +y} \\ \end{align*}	✓	✓	✓	✓	20.345
23775	18610	\begin{align*} 5 \left (t^{2}+1\right ) y^{\prime }&=4 t y \left (y^{3}-1\right ) \\ \end{align*}	✓	✓	✓	✓	20.366
23776	14496	\begin{align*} y^{\prime } x +y&=-2 x^{6} y^{4} \\ \end{align*}	✓	✓	✓	✓	20.377
23777	5628	\begin{align*} {y^{\prime }}^{3}+{\mathrm e}^{-2 y} \left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x -2 y}&=0 \\ \end{align*}	✓	✓	✗	✗	20.389
23778	15121	\begin{align*} y^{\prime }&=t \ln \left (y^{2 t}\right )+t^{2} \\ \end{align*}	✗	✗	✓	✗	20.394
23779	20323	\begin{align*} x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	20.403
23780	11823	\begin{align*} x^{3} {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+\left (3 x y^{2}+x^{6}\right ) y^{\prime }-y^{3}-2 y x^{5}&=0 \\ \end{align*}	✓	✗	✓	✗	20.409
23781	25860	\begin{align*} x \left (-y x +1\right ) y^{\prime }+\left (y x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	20.412
23782	12302	\begin{align*} y^{\prime \prime }+\left (a \cos \left (2 x \right )+b \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	20.413
23783	23838	\begin{align*} y^{\prime }&=1-\frac {y^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	20.434
23784	19811	\begin{align*} 5 y y^{\prime } x -x^{2}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	20.461
23785	5161	\begin{align*} 2 y y^{\prime } x&=x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✓	20.491
23786	20950	\begin{align*} y^{\prime }&=\cos \left (y\right ) \\ \end{align*}	✓	✓	✓	✗	20.515
23787	21451	\begin{align*} \frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+y x +y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✗	✗	20.517
23788	15823	\begin{align*} S^{\prime }&=S^{3}-2 S^{2}+S \\ S \left (0\right ) &= -{\frac {1}{2}} \\ \end{align*}	✓	✓	✗	✓	20.520
23789	25212	\begin{align*} \sin \left (t \right ) y^{\prime \prime }+y&=\cos \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= y_{1} \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= y_{1} \\ \end{align*}	✗	✗	✗	✗	20.525
23790	5261	\begin{align*} x \left (x^{2}+a x y+y^{2}\right ) y^{\prime }&=\left (x^{2}+b x y+y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✗	20.540
23791	13980	\begin{align*} x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.552
23792	24381	\begin{align*} x -2 y+3+2 \left (x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.573
23793	24176	\begin{align*} y x +2 \left (x^{2}+2 y^{2}\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	20.582
23794	15289	\begin{align*} x^{\prime }&=7 x-4 y+10 \,{\mathrm e}^{t} \\ y^{\prime }&=3 x+14 y+6 \,{\mathrm e}^{2 t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	20.602
23795	18285	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=8 \,{\mathrm e}^{x}+9 \\ y \left (-\infty \right ) &= 3 \\ \end{align*}	✗	✓	✗	✓	20.605
23796	19282	\begin{align*} y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✗	20.612
23797	24164	\begin{align*} x +\sin \left (\frac {y}{x}\right )^{2} \left (-y^{\prime } x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	20.623
23798	13554	\begin{align*} y y^{\prime }&=\left (a x +b \right ) y+1 \\ \end{align*}	✗	✓	✓	✗	20.634
23799	17048	\begin{align*} y^{\prime }&=\sqrt {y^{2}-1} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	20.653
23800	2979	\begin{align*} y+2 \left (x -2 y^{2}\right ) y^{\prime }&=0 \\ y \left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	20.668