2.3.209 Problems 20801 to 20900

Table 2.949: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20801	11470	\begin{align*} x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	3.766
20802	11320	\begin{align*} y^{\prime }-y^{2}-y x -x +1&=0 \\ \end{align*}	✓	✓	✓	✗	3.767
20803	6842	\begin{align*} \left (-x^{2}+1\right ) z^{\prime }-x z&=a x z^{2} \\ \end{align*}	✓	✓	✓	✓	3.769
20804	15062	\begin{align*} \left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	3.770
20805	22963	\begin{align*} x \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=5 \\ \end{align*}	✓	✓	✓	✓	3.770
20806	21257	\begin{align*} x^{\prime \prime }&=x^{3}-x \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	3.771
20807	21406	\begin{align*} y^{\prime }&=2 y x -x \\ \end{align*}	✓	✓	✓	✓	3.771
20808	17982	\begin{align*} x +y^{2}-2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	3.772
20809	5339	\begin{align*} \left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.773
20810	6827	\begin{align*} 1+y^{2}-\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.776
20811	2988	\begin{align*} x^{2} y^{\prime }+y^{2}&=y x \\ \end{align*}	✓	✓	✓	✓	3.777
20812	16204	\begin{align*} \left (y-2\right ) y^{\prime }&=x -3 \\ \end{align*}	✓	✓	✓	✓	3.777
20813	7000	\begin{align*} x^{2} y+y^{2}+x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.779
20814	4418	\begin{align*} y^{3}+\left (3 x^{2}-2 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.780
20815	7499	\begin{align*} x^{2} y^{\prime }+y^{2}-y x&=0 \\ \end{align*}	✓	✓	✓	✓	3.780
20816	15951	\begin{align*} y^{\prime }&=3+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.781
20817	11456	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+a \left (y^{2}-2 y x +1\right )&=0 \\ \end{align*}	✗	✓	✓	✗	3.782
20818	2819	\begin{align*} z^{\prime \prime }+z^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	3.783
20819	11664	\begin{align*} {y^{\prime }}^{2}+a^{2} y^{2} \left (\ln \left (y\right )^{2}-1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.783
20820	18058	\begin{align*} x^{2}+y^{2}-x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	3.783
20821	15962	\begin{align*} y^{\prime }&=1-y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.784
20822	5188	\begin{align*} \left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.785
20823	22587	\begin{align*} 3 y^{2}+4 y x +\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.785
20824	20266	\begin{align*} \cos \left (x \right )^{2} y^{\prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.786
20825	4347	\begin{align*} y \sqrt {1+y^{2}}+\left (x \sqrt {1+y^{2}}-y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.789
20826	19676	\begin{align*} 2 t +3 x+\left (3 t -x\right ) x^{\prime }&=t^{2} \\ \end{align*}	✓	✓	✓	✗	3.789
20827	60	\begin{align*} y^{\prime }&=3 x^{2} \left (1+y^{2}\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.790
20828	15749	\begin{align*} y_{1}^{\prime }&=y_{2}-2 y_{1}+\sin \left (2 x \right ) \\ y_{2}^{\prime }&=-3 y_{1}+y_{2}-2 \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	3.790
20829	20242	\begin{align*} \left (x +y-1\right ) y^{\prime }&=x +y+1 \\ \end{align*}	✓	✓	✓	✓	3.792
20830	7513	\begin{align*} x^{\prime }+t x^{3}+\frac {x}{t}&=0 \\ \end{align*}	✓	✓	✓	✓	3.793
20831	15384	\begin{align*} \frac {x}{\left (x +y\right )^{2}}+\frac {\left (2 x +y\right ) y^{\prime }}{\left (x +y\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	3.794
20832	23946	\begin{align*} y^{5} x^{2}+{\mathrm e}^{x^{3}} y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.794
20833	212	\begin{align*} y^{\prime }&=\frac {x +3 y}{-3 x +y} \\ \end{align*}	✓	✓	✓	✓	3.795
20834	22438	\begin{align*} y^{\prime }&=\frac {y}{y^{3}-3 x} \\ \end{align*}	✓	✓	✓	✓	3.795
20835	7736	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=\cos \left (x \right )-2 x \sin \left (x \right ) \\ y \left (\frac {\pi }{6}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.796
20836	8383	\begin{align*} 2 x \sin \left (y\right )^{2}-\left (x^{2}+10\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.796
20837	8719	\begin{align*} y^{\prime }+\frac {x +2 y}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	3.796
20838	10161	\begin{align*} y^{\prime }&=2 x^{2} \sin \left (\frac {y}{x}\right )^{2}+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✗	3.796
20839	25469	\begin{align*} y^{\prime }&=a y-b y^{2} \\ \end{align*}	✓	✓	✓	✓	3.797
20840	4313	\begin{align*} y^{\prime }+\frac {x}{y}+2&=0 \\ \end{align*}	✓	✓	✓	✗	3.799
20841	4857	\begin{align*} \left (1-2 x \right ) y^{\prime }&=16+32 x -6 y \\ \end{align*}	✓	✓	✓	✓	3.803
20842	3549	\begin{align*} y^{\prime } x +y \ln \left (x \right )&=y \ln \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	3.805
20843	22428	\begin{align*} \left (x +y\right ) y^{\prime }+x -y&=0 \\ \end{align*}	✓	✓	✓	✓	3.805
20844	4340	\begin{align*} 2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.806
20845	11910	\begin{align*} y^{\prime }&=\frac {\left (-1+y \ln \left (x \right )\right )^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	3.806
20846	17045	\begin{align*} y^{\prime }&=\sqrt {y^{2}-1} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	3.807
20847	4687	\begin{align*} y^{\prime }+\tan \left (x \right ) \left (1-y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.808
20848	14526	\begin{align*} y^{\prime }&=\frac {4 x^{3} y^{2}-3 x^{2} y}{x^{3}-2 x^{4} y} \\ \end{align*}	✓	✓	✓	✓	3.808
20849	19973	\begin{align*} {y^{\prime }}^{3}&=a \,x^{4} \\ \end{align*}	✓	✓	✓	✓	3.810
20850	21021	\begin{align*} x^{\prime }+x&=4 t \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.810
20851	6830	\begin{align*} \left (y-x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.814
20852	8666	\begin{align*} 2 x^{2} y y^{\prime }+y^{2}&=2 \\ \end{align*}	✓	✓	✓	✓	3.814
20853	1214	\begin{align*} {\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.815
20854	12425	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y-a \,x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.816
20855	15623	\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.816
20856	741	\begin{align*} y^{\prime } x&=y+\sqrt {y^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.818
20857	4675	\begin{align*} y^{\prime }&=f \left (x \right )+g \left (x \right ) y+a y^{2} \\ \end{align*}	✗	✗	✗	✗	3.822
20858	17654	\begin{align*} 9 x^{2} y^{\prime \prime }+27 y^{\prime } x +10 y&=\frac {1}{x} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.823
20859	17956	\begin{align*} y^{\prime }+3 y x&=y \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.823
20860	19092	\begin{align*} y^{\prime } \left (x^{2}+y^{2}+3\right )&=2 x \left (2 y-\frac {x^{2}}{y}\right ) \\ \end{align*}	✗	✓	✓	✗	3.823
20861	778	\begin{align*} x^{2} y^{\prime }+2 y x&=y^{2} \\ \end{align*}	✓	✓	✓	✓	3.824
20862	2846	\begin{align*} \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.828
20863	5684	\begin{align*} 2 \left (1+y\right )^{{3}/{2}}+3 y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.832
20864	19297	\begin{align*} y-x^{3}+\left (y^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.832
20865	9014	\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ \end{align*}	✓	✓	✓	✓	3.833
20866	8320	\begin{align*} y^{\prime }&=1-\frac {y}{x} \\ y \left (\frac {3}{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.836
20867	12338	\begin{align*} y^{\prime \prime }-\left (1+2 \,{\mathrm e}^{x}\right ) y^{\prime }+y \,{\mathrm e}^{2 x}-{\mathrm e}^{3 x}&=0 \\ \end{align*}	✓	✓	✓	✗	3.836
20868	25008	\begin{align*} y^{\prime }&=\frac {t^{2}+y^{2}}{t y} \\ y \left ({\mathrm e}\right ) &= 2 \,{\mathrm e} \\ \end{align*}	✓	✓	✓	✓	3.836
20869	23882	\begin{align*} 3 y^{2}+y \sin \left (2 y x \right )+\left (6 y x +x \sin \left (2 y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.837
20870	3647	\begin{align*} 2 x \left (2 x +y\right ) y^{\prime }&=y \left (4 x -y\right ) \\ \end{align*}	✓	✓	✓	✓	3.840
20871	19683	\begin{align*} t x^{\prime }+x g \left (t \right )&=h \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.840
20872	16275	\begin{align*} 2 \sqrt {x}\, y^{\prime }+y&=2 x \,{\mathrm e}^{-\sqrt {x}} \\ \end{align*}	✓	✓	✓	✓	3.843
20873	11455	\begin{align*} \left (x^{2}-1\right ) y^{\prime }-y \left (y-x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.845
20874	25827	\begin{align*} \left (1+{\mathrm e}^{y}\right )^{2} {\mathrm e}^{-y}+\left ({\mathrm e}^{x}+1\right )^{3} {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.845
20875	13890	\begin{align*} \left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+\left (a \,x^{2}+b \right ) \left (c \,x^{2}+d \right ) y^{\prime }+2 \left (-a d +b c \right ) x y&=0 \\ \end{align*}	✓	✓	✓	✗	3.846
20876	15851	\begin{align*} y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✗	✗	3.846
20877	4867	\begin{align*} x^{2} y^{\prime }+\left (1-2 x \right ) y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	3.849
20878	9987	\begin{align*} y^{\prime }&=\frac {\cos \left (y\right ) \sec \left (x \right )}{x} \\ \end{align*}	✓	✓	✓	✓	3.849
20879	22389	\begin{align*} y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right )^{2} \\ \end{align*}	✓	✓	✓	✗	3.851
20880	3016	\begin{align*} y^{\prime }+y \ln \left (y\right ) \tan \left (x \right )&=2 y \\ \end{align*}	✓	✓	✓	✓	3.852
20881	24252	\begin{align*} 1+y x -\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.852
20882	1593	\begin{align*} \left (x^{2}+2\right ) y^{\prime }&=4 x \left (y^{2}+2 y+1\right ) \\ \end{align*}	✓	✓	✓	✓	3.853
20883	17301	\begin{align*} 1+y-t y^{\prime }&=\ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	3.855
20884	2931	\begin{align*} \frac {x \cos \left (\frac {x}{y}\right )}{y}+\sin \left (\frac {x}{y}\right )+\cos \left (x \right )-\frac {x^{2} \cos \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	3.856
20885	16302	\begin{align*} \left (x +y\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	3.857
20886	17237	\begin{align*} -4 x^{3}+6 y \sin \left (6 y x \right )+\left (4 y^{3}+6 x \sin \left (6 y x \right )\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.858
20887	22537	\begin{align*} y^{\prime }&={\mathrm e}^{\frac {y}{x}}+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✗	3.858
20888	174	\begin{align*} x^{\prime }&=9-4 x^{2} \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.859
20889	3009	\begin{align*} 2 \,{\mathrm e}^{x}-t^{2}+t \,{\mathrm e}^{x} x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.859
20890	12704	\begin{align*} y^{\prime \prime }&=-\frac {\left (2 f \left (x \right ) {g^{\prime }\left (x \right )}^{2} g \left (x \right )-\left (g \left (x \right )^{2}-1\right ) \left (f \left (x \right ) g^{\prime \prime }\left (x \right )+2 f^{\prime }\left (x \right ) g^{\prime }\left (x \right )\right )\right ) y^{\prime }}{f \left (x \right ) g^{\prime }\left (x \right ) \left (g \left (x \right )^{2}-1\right )}-\frac {\left (\left (g \left (x \right )^{2}-1\right ) \left (f^{\prime }\left (x \right ) \left (f \left (x \right ) g^{\prime \prime }\left (x \right )+2 f^{\prime }\left (x \right ) g^{\prime }\left (x \right )\right )-f \left (x \right ) f^{\prime \prime }\left (x \right ) g^{\prime }\left (x \right )\right )-\left (2 f^{\prime }\left (x \right ) g \left (x \right )+v \left (v +1\right ) f \left (x \right ) g^{\prime }\left (x \right )\right ) f \left (x \right ) {g^{\prime }\left (x \right )}^{2}\right ) y}{f \left (x \right )^{2} g^{\prime }\left (x \right ) \left (g \left (x \right )^{2}-1\right )} \\ \end{align*}	✗	✓	✓	✗	3.860
20891	8689	\begin{align*} y^{\prime }&=\left (x +y+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.864
20892	17971	\begin{align*} 2 x +\frac {y^{2}+x^{2}}{x^{2} y}&=\frac {\left (y^{2}+x^{2}\right ) y^{\prime }}{x y^{2}} \\ \end{align*}	✓	✓	✓	✗	3.868
20893	14026	\begin{align*} y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	3.869
20894	742	\begin{align*} y^{\prime } y+x&=\sqrt {y^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.870
20895	3547	\begin{align*} -y+y^{\prime } x&=\sqrt {9 x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.870
20896	8356	\begin{align*} y^{\prime }&=\frac {y x +3 x -y-3}{y x -2 x +4 y-8} \\ \end{align*}	✓	✓	✓	✓	3.873
20897	4243	\begin{align*} x \sin \left (\frac {y}{x}\right ) y^{\prime }&=\sin \left (\frac {y}{x}\right ) y+x \\ \end{align*}	✓	✓	✓	✓	3.874
20898	11480	\begin{align*} x^{4} \left (y^{\prime }+y^{2}\right )+a&=0 \\ \end{align*}	✓	✓	✓	✓	3.875
20899	11596	\begin{align*} \left (y^{2} x^{2}+x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.878
20900	7256	\begin{align*} y^{\prime }&=x y^{2}-\frac {2 y}{x}-\frac {1}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	3.880