2.3.199 Problems 19801 to 19900

Table 2.929: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19801	18818	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=3+4 \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	7.657
19802	15301	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y&=x \\ \end{align*}	✓	✓	✓	✗	7.658
19803	9237	\begin{align*} 2 x^{2} y^{\prime \prime }+10 y^{\prime } x +8 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.662
19804	13806	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x +b \left (a \,x^{n}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	7.664
19805	16351	\begin{align*} \sin \left (y\right )+\left (x +1\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.665
19806	1304	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	7.666
19807	3039	\begin{align*} x \sqrt {1-y}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	7.668
19808	4932	\begin{align*} \left (-a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.670
19809	16525	\begin{align*} y^{\prime \prime }-y^{\prime }+\left (\frac {1}{4}+4 \pi ^{2}\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -{\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	7.670
19810	18792	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (-1\right ) &= 2 \\ y^{\prime }\left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.670
19811	19931	\begin{align*} 1+y^{2}&=\left (\arctan \left (y\right )-x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	7.670
19812	13748	\begin{align*} y^{\prime \prime } x +\left (a \,x^{2}+b \right ) x y^{\prime }+\left (3 a \,x^{2}+b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	7.672
19813	16286	\begin{align*} y^{\prime }&=\frac {\left (3 x -2 y\right )^{2}+1}{3 x -2 y}+\frac {3}{2} \\ \end{align*}	✓	✓	✓	✓	7.672
19814	16685	\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=64 x^{2} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	7.672
19815	16285	\begin{align*} y^{\prime }&=\frac {1}{\left (3 x +3 y+2\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	7.674
19816	18183	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=-2 \\ \end{align*}	✓	✓	✓	✓	7.674
19817	14188	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	7.675
19818	5598	\begin{align*} a^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) {y^{\prime }}^{2}+2 a \,b^{2} c y^{\prime }+c^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	7.681
19819	14227	\begin{align*} x^{\prime }&=2 t x^{2} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.681
19820	19317	\begin{align*} y^{\prime } x +y+3 x^{3} y^{4} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.683
19821	23354	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}	✓	✗	✗	✗	7.684
19822	11654	\begin{align*} \left (x \sin \left (y x \right )+\cos \left (x +y\right )-\sin \left (y\right )\right ) y^{\prime }+y \sin \left (y x \right )+\cos \left (x +y\right )+\cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	7.686
19823	8977	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	7.692
19824	2941	\begin{align*} \left (x^{3} y^{3}-1\right ) y^{\prime }+x^{2} y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	7.693
19825	22760	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=\sqrt {x}+\frac {1}{\sqrt {x}} \\ \end{align*}	✓	✓	✓	✓	7.694
19826	15784	\begin{align*} y^{\prime }&=t y^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✓	7.697
19827	14549	\begin{align*} 3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.701
19828	12450	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y-x^{4}+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.704
19829	5657	\begin{align*} y {y^{\prime }}^{3}-3 y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.706
19830	21386	\begin{align*} y^{\prime }&=\frac {y^{3}-2 x^{3}}{x y^{2}} \\ \end{align*}	✓	✓	✓	✓	7.707
19831	4886	\begin{align*} x^{2} y^{\prime }&=2 y \left (x -y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	7.708
19832	12521	\begin{align*} x \left (x -1\right ) y^{\prime \prime }+\left (\left (1+a \right ) x +b \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.708
19833	7546	\begin{align*} y-x +\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.709
19834	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*}	✓	✓	✓	✗	7.709
19835	22406	\begin{align*} y^{\prime }&=\frac {\left (x -3 y-5\right )^{2}}{\left (x +y-1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	7.709
19836	11417	\begin{align*} y^{\prime } x -y \ln \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	7.710
19837	6044	\begin{align*} \left (4 x^{4}+2 x^{2}+1\right ) y+4 x^{3} y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.714
19838	13271	\begin{align*} x^{2} \left (a +x \right ) \left (y^{\prime }+\lambda y^{2}\right )+x \left (b x +c \right ) y+x \alpha +\beta &=0 \\ \end{align*}	✓	✓	✓	✗	7.714
19839	200	\begin{align*} y^{\prime } x&=6 y+12 x^{4} y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	7.717
19840	25508	\begin{align*} y^{\prime }&=-\frac {3 t^{2}+2 y^{2}}{4 t y+6 y^{2}} \\ \end{align*}	✓	✓	✓	✗	7.718
19841	2942	\begin{align*} y \left (-x^{2}+y\right )+x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.724
19842	11444	\begin{align*} x^{2} y^{\prime }+a y^{3}-a \,x^{2} y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	7.724
19843	7981	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.730
19844	21396	\begin{align*} y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\ \end{align*}	✓	✓	✓	✓	7.730
19845	4078	\begin{align*} y^{2} \left (x^{2}+1\right )+y+\left (2 y x +1\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	7.731
19846	12089	\begin{align*} y^{\prime }&=-\frac {1}{-x -\textit {\_F1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}} \\ \end{align*}	✗	✓	✓	✗	7.731
19847	17777	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.732
19848	23980	\begin{align*} y^{\prime \prime }+\frac {327 y^{\prime }}{100}-\frac {21 y}{50}&=0 \\ \end{align*}	✓	✓	✓	✓	7.732
19849	14337	\begin{align*} t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x&=4 t^{7} \\ \end{align*}	✓	✓	✓	✓	7.734
19850	14446	\begin{align*} \frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	7.734
19851	20589	\begin{align*} y^{\prime \prime }&={\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	7.734
19852	12935	\begin{align*} y y^{\prime \prime }-3 {y^{\prime }}^{2}+3 y y^{\prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	7.739
19853	17733	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.740
19854	21801	\begin{align*} y y^{\prime }+x&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.740
19855	7456	\begin{align*} \cos \left (x \right ) \cos \left (y\right )+2 x -\left (\sin \left (x \right ) \sin \left (y\right )+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.742
19856	3066	\begin{align*} 2 y^{\prime \prime }+2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	7.744
19857	19313	\begin{align*} \frac {-y^{\prime } x +y}{\left (x +y\right )^{2}}+y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✗	7.744
19858	21965	\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.745
19859	24469	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.747
19860	9585	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	7.757
19861	12225	\begin{align*} y^{\prime }&=\frac {-32 y x -8 x^{3}-16 a \,x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}+96 a x y^{2}+12 x^{4} y+48 y a \,x^{3}+48 y a^{2} x^{2}+x^{6}+6 x^{5} a +12 a^{2} x^{4}+8 a^{3} x^{3}}{64 y+16 x^{2}+32 a x +64} \\ \end{align*}	✓	✓	✓	✗	7.757
19862	1199	\begin{align*} {\mathrm e}^{x} \sin \left (y\right )-2 \sin \left (x \right ) y+\left (2 \cos \left (x \right )+{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.758
19863	24867	\begin{align*} {y^{\prime }}^{2}+y y^{\prime }-x -1&=0 \\ \end{align*}	✓	✓	✓	✗	7.764
19864	8720	\begin{align*} y^{\prime }&=\frac {y}{x +y} \\ \end{align*}	✓	✓	✓	✓	7.767
19865	9328	\begin{align*} y^{\prime \prime }&=\tan \left (x \right ) \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	7.767
19866	7555	\begin{align*} y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\ y \left (1\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	7.768
19867	2971	\begin{align*} 2 y&=\left (y^{4}+x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	7.769
19868	11351	\begin{align*} y^{\prime }-f_{3} \left (x \right ) y^{3}-f_{2} \left (x \right ) y^{2}-f_{1} \left (x \right ) y-f_{0} \left (x \right )&=0 \\ \end{align*}	✗	✗	✗	✗	7.769
19869	20963	\begin{align*} y^{\prime }&=\frac {1+y}{2+x}+{\mathrm e}^{\frac {1+y}{2+x}} \\ \end{align*}	✓	✓	✓	✗	7.771
19870	21362	\begin{align*} x +2 y-1+3 \left (x +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.771
19871	25745	\begin{align*} y^{\prime } x +y&=2 x \\ y \left (x_{0} \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.773
19872	8290	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ y \left (3\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	7.774
19873	25718	\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	7.774
19874	11539	\begin{align*} 2 y y^{\prime } x +2 y^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	7.780
19875	1279	\begin{align*} y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	7.781
19876	19966	\begin{align*} 2 y^{2} x^{2}+y-\left (x^{3} y-3 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.781
19877	10254	\begin{align*} y^{\prime }&=\frac {y}{2 y \ln \left (y\right )+y-x} \\ \end{align*}	✓	✓	✓	✓	7.783
19878	24829	\begin{align*} 8 y&={y^{\prime }}^{2}+3 x^{2} \\ \end{align*}	✓	✓	✓	✗	7.783
19879	12023	\begin{align*} y^{\prime }&=\frac {\left (a y^{2}+b \,x^{2}\right )^{3} x}{a^{{5}/{2}} \left (a y^{2}+b \,x^{2}+a \right ) y} \\ \end{align*}	✗	✓	✓	✗	7.785
19880	23289	\begin{align*} \left (1-x \right ) y^{\prime \prime }-y^{\prime } x +{\mathrm e}^{x} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✗	✗	✗	✗	7.786
19881	20132	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.789
19882	21054	\begin{align*} x^{\prime }&=4 t^{3} x^{4} \\ \end{align*}	✓	✓	✓	✓	7.793
19883	23883	\begin{align*} 2 x +2 y-3+\left (1-2 y+2 x \right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.793
19884	9783	\begin{align*} -x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=-x^{2}+3 \\ \end{align*}	✓	✓	✓	✓	7.794
19885	4816	\begin{align*} y^{\prime } x&=y-x \cot \left (\frac {y}{x}\right )^{2} \\ \end{align*}	✓	✓	✓	✗	7.796
19886	3648	\begin{align*} y^{\prime } x&=x \tan \left (\frac {y}{x}\right )+y \\ \end{align*}	✓	✓	✓	✓	7.798
19887	19772	\begin{align*} y^{\prime \prime } x +2 y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	7.798
19888	3000	\begin{align*} 2 y&=\left (x^{2} y^{4}+x \right ) y^{\prime } \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.811
19889	24412	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.812
19890	13798	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }-b y&=0 \\ \end{align*}	✓	✓	✓	✓	7.815
19891	20962	\begin{align*} y^{\prime }&=\frac {1+y}{2+x}-{\mathrm e}^{\frac {1+y}{2+x}} \\ \end{align*}	✓	✓	✓	✗	7.815
19892	21346	\begin{align*} y^{\prime }&=-\frac {x}{y} \\ y \left (0\right ) &= a_{0} \\ \end{align*}	✓	✗	✓	✓	7.816
19893	17624	\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.817
19894	16718	\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.830
19895	24150	\begin{align*} \left (2 x +y\right ) y^{\prime }+x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.830
19896	24125	\begin{align*} y^{\prime }&=x y^{2} \\ \end{align*}	✓	✓	✓	✓	7.833
19897	14835	\begin{align*} t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x&=0 \\ \end{align*}	✓	✓	✓	✗	7.835
19898	21129	\begin{align*} x^{\prime \prime }+2 x^{\prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (\infty \right ) &= a \\ \end{align*}	✗	✓	✗	✓	7.836
19899	2589	\begin{align*} y^{\prime \prime }-y&=f \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.839
19900	21604	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }-k^{2} \cos \left (x \right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	7.839