2.3.159 Problems 15801 to 15900

Table 2.849: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15801	19895	\begin{align*} y^{\prime \prime }-k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	3.628
15802	6018	\begin{align*} \operatorname {a2} y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.632
15803	12406	\begin{align*} a x y^{\prime \prime }+b y^{\prime }+c y&=0 \\ \end{align*}	✓	✓	✓	✗	3.632
15804	19525	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	3.632
15805	11838	\begin{align*} {y^{\prime }}^{n}-f \left (x \right ) g \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.634
15806	15802	\begin{align*} y^{\prime }&=t y^{2}+2 y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.634
15807	13712	\begin{align*} y^{\prime \prime }+\left (a \,x^{n}+2 b \right ) y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}+b^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	3.635
15808	14459	\begin{align*} 2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.635
15809	24375	\begin{align*} 3 x^{2}+3 y^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.635
15810	18488	\begin{align*} r^{\prime }&=\frac {r^{2}}{\theta } \\ r \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.636
15811	24477	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.636
15812	4395	\begin{align*} x y^{2} \left (y^{\prime } x +y\right )&=1 \\ \end{align*}	✓	✓	✓	✓	3.637
15813	12265	\begin{align*} y^{\prime }&=\frac {\left (y x +1\right ) \left (y^{2} x^{2}+x^{2} y+2 y x +1+x +x^{2}\right )}{x^{5}} \\ \end{align*}	✓	✓	✓	✓	3.637
15814	16371	\begin{align*} y^{2}-y^{2} \cos \left (x \right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.637
15815	2968	\begin{align*} x^{2} y^{\prime }+y-2 y x -2 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.638
15816	5610	\begin{align*} {y^{\prime }}^{3}&=\left (a +b y+c y^{2}\right ) f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.638
15817	19252	\begin{align*} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	3.638
15818	21680	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.638
15819	23849	\begin{align*} 2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	3.639
15820	4846	\begin{align*} \left (a +x \right ) y^{\prime }&=-b -c y \\ \end{align*}	✓	✓	✓	✓	3.640
15821	6448	\begin{align*} y y^{\prime \prime }&=y^{2}-3 y y^{\prime }+3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.640
15822	10112	\begin{align*} y^{\prime \prime }-y x -x^{6}-x^{3}+42&=0 \\ \end{align*}	✓	✓	✓	✓	3.641
15823	20217	\begin{align*} \left (y x +1\right ) y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.641
15824	20782	\begin{align*} y^{\prime \prime } x -\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.641
15825	23861	\begin{align*} y^{\prime }&=3 x^{2} y-3 x^{4}+2 x^{2}-2 y+2 x \\ \end{align*}	✓	✓	✓	✓	3.641
15826	4686	\begin{align*} y^{\prime }&=y \sec \left (x \right )+\left (\sin \left (x \right )-1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.642
15827	19328	\begin{align*} y^{\prime } x&=x^{5}+x^{3} y^{2}+y \\ \end{align*}	✓	✓	✓	✓	3.644
15828	1534	\begin{align*} y^{\prime }&=a y^{\frac {-1+a}{a}} \\ \end{align*}	✓	✓	✓	✓	3.645
15829	8168	\begin{align*} 2 y^{\prime }&=y^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.645
15830	16257	\begin{align*} y^{2} y^{\prime }+3 x^{2} y&=\sin \left (x \right ) \\ \end{align*}	✗	✗	✗	✗	3.645
15831	19420	\begin{align*} -y^{\prime }+y^{\prime \prime } x&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	3.645
15832	18533	\begin{align*} \left (1+t \right ) y+y^{\prime } t&=2 t \,{\mathrm e}^{-t} \\ y \left (1\right ) &= a \\ \end{align*}	✓	✓	✓	✓	3.646
15833	19740	\begin{align*} y^{\prime }&=x \left (a y^{2}+b \right ) \\ \end{align*}	✓	✓	✓	✓	3.646
15834	2960	\begin{align*} y^{\prime }&=y+3 \,{\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	3.649
15835	17387	\begin{align*} y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.649
15836	3577	\begin{align*} y^{\prime }&=\frac {1-y^{2}}{2 y x +2} \\ \end{align*}	✓	✓	✓	✓	3.650
15837	2540	\begin{align*} y^{\prime }&={\mathrm e}^{t} y^{2}-2 y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.651
15838	23728	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.652
15839	1733	\begin{align*} 3 y x +2 y^{2}+y+\left (x^{2}+2 y x +x +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.653
15840	4737	\begin{align*} y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.653
15841	6358	\begin{align*} y^{\prime \prime }&=a \sqrt {b y^{2}+{y^{\prime }}^{2}} \\ \end{align*}	✗	✓	✓	✗	3.653
15842	6886	\begin{align*} y&=y^{\prime } x +\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	3.653
15843	4117	\begin{align*} y^{\prime \prime }+8 y^{\prime }+15 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.654
15844	14278	\begin{align*} t \cot \left (x\right ) x^{\prime }&=-2 \\ \end{align*}	✓	✓	✓	✓	3.654
15845	4271	\begin{align*} y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	3.655
15846	6575	\begin{align*} \operatorname {f5} y^{2}+\operatorname {f4} y y^{\prime }+\operatorname {f3} {y^{\prime }}^{2}+\operatorname {f2} y y^{\prime \prime }+\operatorname {f1} y^{\prime } y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✗	✗	3.655
15847	18788	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.655
15848	22527	\begin{align*} y^{\prime } \left (2 x +y^{2}\right )&=y \\ \end{align*}	✓	✓	✓	✓	3.655
15849	22076	\begin{align*} y^{\prime }+\frac {2 y}{x}&=-x^{9} y^{5} \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.656
15850	23075	\begin{align*} y^{\prime \prime }+2 y&=7 \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	3.656
15851	2975	\begin{align*} y^{2}+1+\left (2 y x -y^{2}\right ) y^{\prime }&=0 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.657
15852	1616	\begin{align*} y^{\prime }&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✗	✗	✗	✗	3.658
15853	3680	\begin{align*} \frac {y^{\prime }}{y}+p \left (x \right ) \ln \left (y\right )&=q \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	3.658
15854	8365	\begin{align*} \left (x^{4}+1\right ) y^{\prime }+x \left (1+4 y^{2}\right )&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	3.658
15855	19017	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-5 x_{2}+8 x_{3}+14 x_{4} \\ x_{2}^{\prime }&=-6 x_{1}-8 x_{2}+11 x_{3}+27 x_{4} \\ x_{3}^{\prime }&=-6 x_{1}-4 x_{2}+7 x_{3}+17 x_{4} \\ x_{4}^{\prime }&=-2 x_{2}+2 x_{3}+4 x_{4} \\ \end{align*}	✓	✓	✓	✓	3.659
15856	22313	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.659
15857	2504	\begin{align*} y^{\prime }&=\frac {y+t}{t -y} \\ \end{align*}	✓	✓	✓	✓	3.661
15858	5797	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.661
15859	7268	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.661
15860	8460	\begin{align*} y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le x \le 1 \\ -\frac {2}{x} & 1<x \end {array}\right .\right ) y&=4 x \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	3.661
15861	689	\begin{align*} y^{\prime }&=\frac {1+\sqrt {x}}{1+\sqrt {y}} \\ \end{align*}	✓	✓	✓	✗	3.662
15862	4997	\begin{align*} x \left (-x^{3}+1\right ) y^{\prime }&=x^{2}+\left (1-2 y x \right ) y \\ \end{align*}	✓	✓	✓	✓	3.662
15863	9360	\begin{align*} y^{\prime } x&=y \\ \end{align*}	✓	✓	✓	✓	3.662
15864	22448	\begin{align*} y^{\prime }+\frac {y}{x}&=1 \\ \end{align*}	✓	✓	✓	✓	3.662
15865	24306	\begin{align*} y^{\prime }&=\cos \left (x \right )-y \sec \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.662
15866	9085	\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.663
15867	19688	\begin{align*} x^{\prime \prime }-5 x^{\prime }+6 x&=0 \\ \end{align*}	✓	✓	✓	✓	3.665
15868	20977	\begin{align*} \cos \left (x +y^{2}\right )+3 y+\left (2 y \cos \left (x +y^{2}\right )+3 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.665
15869	23857	\begin{align*} \left (x^{3}+1\right ) y^{\prime }+x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.666
15870	8687	\begin{align*} y^{\prime }+\sin \left (x +y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.667
15871	14236	\begin{align*} x^{\prime }&=6 t \left (x-1\right )^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	3.667
15872	14545	\begin{align*} 2 x y^{2}+y+\left (2 y^{3}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.667
15873	6035	\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=x^{3} \\ \end{align*}	✓	✓	✓	✗	3.668
15874	5751	\begin{align*} \left (a +b \cos \left (2 x \right )\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	3.669
15875	25802	\begin{align*} y^{\prime }&=y-y^{3} \\ \end{align*}	✓	✓	✓	✓	3.669
15876	1540	\begin{align*} y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.670
15877	2509	\begin{align*} 2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (\cos \left (y\right ) t^{2}+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.670
15878	20241	\begin{align*} -y^{\prime } x +y&=a \left (y^{\prime }+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.670
15879	23063	\begin{align*} r^{\prime }&=c \\ r \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	3.670
15880	21936	\begin{align*} y^{\prime \prime } x +y^{\prime }&=16 x^{3} \\ \end{align*}	✓	✓	✓	✓	3.671
15881	22710	\begin{align*} y^{\prime \prime }+y&=x \,{\mathrm e}^{-x}+3 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.672
15882	2329	\begin{align*} y^{\prime } t&=y+\sqrt {t^{2}+y^{2}} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.673
15883	3023	\begin{align*} y^{\prime }&=\cos \left (y\right ) \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	3.673
15884	7011	\begin{align*} \left (y^{2}+a \sin \left (x \right )\right ) y^{\prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.673
15885	22460	\begin{align*} y^{\prime } x&=2 x^{2} y+y \ln \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	3.673
15886	1273	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.674
15887	22404	\begin{align*} y^{\prime }&=\frac {3 x^{5}+3 y^{2} x^{2}}{2 x^{3} y-2 y^{3}} \\ \end{align*}	✓	✓	✓	✓	3.674
15888	4441	\begin{align*} 2 x y^{4} {\mathrm e}^{y}+2 x y^{3}+y+\left (x^{2} y^{4} {\mathrm e}^{y}-y^{2} x^{2}-3 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.675
15889	13791	\begin{align*} x^{2} y^{\prime \prime }-2 a x y^{\prime }+\left (-b^{2} x^{2}+a \left (1+a \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.675
15890	18304	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{m} \\ \end{align*}	✓	✓	✓	✓	3.675
15891	13739	\begin{align*} y^{\prime \prime } x -\left (2 a x +1\right ) y^{\prime }+b \,x^{3} y&=0 \\ \end{align*}	✗	✓	✗	✗	3.676
15892	12069	\begin{align*} y^{\prime }&=\frac {x \left (-x -1+x^{2}-2 x^{2} y+2 x^{4}\right )}{\left (x^{2}-y\right ) \left (x +1\right )} \\ \end{align*}	✓	✓	✓	✗	3.680
15893	18290	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	3.680
15894	20318	\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \left ({\mathrm e}^{x}-{\mathrm e}^{y}\right ) \\ \end{align*}	✗	✓	✓	✓	3.681
15895	21873	\begin{align*} x {y^{\prime }}^{2}&=y \\ \end{align*}	✓	✓	✓	✓	3.681
15896	21986	\begin{align*} y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	3.681
15897	22757	\begin{align*} x^{2} y^{\prime \prime }+y&=16 \sin \left (\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	3.681
15898	25811	\begin{align*} y^{\prime }&=\left ({\mathrm e}^{y} y-9 y\right ) {\mathrm e}^{-y} \\ \end{align*}	✓	✓	✓	✓	3.681
15899	3596	\begin{align*} y-\left (x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.683
15900	15057	\begin{align*} y^{\prime }&=\frac {-3+x +y}{y-x +1} \\ \end{align*}	✓	✓	✓	✓	3.684